1
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Madathil PT, Wang C, Singh SK, Gupta A, Rosales KAV, Chung YJ, West KW, Baldwin KW, Pfeiffer LN, Engel LW, Shayegan M. Signatures of Correlated Defects in an Ultraclean Wigner Crystal in the Extreme Quantum Limit. Phys Rev Lett 2024; 132:096502. [PMID: 38489610 DOI: 10.1103/physrevlett.132.096502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Revised: 01/04/2024] [Accepted: 02/05/2024] [Indexed: 03/17/2024]
Abstract
Low-disorder two-dimensional electron systems in the presence of a strong, perpendicular magnetic field terminate at very small Landau level filling factors in a Wigner crystal (WC), where the electrons form an ordered array to minimize the Coulomb repulsion. The nature of this exotic, many-body, quantum phase is yet to be fully understood and experimentally revealed. Here we probe one of WC's most fundamental parameters, namely, the energy gap that determines its low-temperature conductivity, in record mobility, ultrahigh-purity, two-dimensional electrons confined to GaAs quantum wells. The WC domains in these samples contain ≃1000 electrons. The measured gaps are a factor of three larger than previously reported for lower quality samples, and agree remarkably well with values predicted for the lowest-energy, intrinsic, hypercorrelated bubble defects in a WC made of flux-electron composite fermions, rather than bare electrons. The agreement is particularly noteworthy, given that the calculations are done for disorder-free composite fermion WCs, and there are no adjustable parameters. The results reflect the exceptionally high quality of the samples, and suggest that composite fermion WCs are indeed more stable compared to their electron counterparts.
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Affiliation(s)
- P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - C Wang
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S K Singh
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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2
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Huang H, Hussain W, Myers SA, Pfeiffer LN, West KW, Baldwin KW, Csáthy GA. Evidence for Topological Protection Derived from Six-Flux Composite Fermions. Nat Commun 2024; 15:1461. [PMID: 38368413 PMCID: PMC10874392 DOI: 10.1038/s41467-024-45860-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 02/05/2024] [Indexed: 02/19/2024] Open
Abstract
The composite fermion theory opened a new chapter in understanding many-body correlations through the formation of emergent particles. The formation of two-flux and four-flux composite fermions is well established. While there are limited data linked to the formation of six-flux composite fermions, topological protection associated with them is conspicuously lacking. Here we report evidence for the formation of a quantized and gapped fractional quantum Hall state at the filling factor ν = 9/11, which we associate with the formation of six-flux composite fermions. Our result provides evidence for the most intricate composite fermion with six fluxes and expands the already diverse family of highly correlated topological phases with a new member that cannot be characterized by correlations present in other known members. Our observations pave the way towards the study of higher order correlations in the fractional quantum Hall regime.
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Affiliation(s)
- Haoyun Huang
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - Waseem Hussain
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - S A Myers
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - G A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA.
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3
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Petrescu M, Berkson-Korenberg Z, Vijayakrishnan S, West KW, Pfeiffer LN, Gervais G. Author Correction: Large composite fermion effective mass at filling factor 5/2. Nat Commun 2023; 14:8408. [PMID: 38110395 PMCID: PMC10728058 DOI: 10.1038/s41467-023-44392-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2023] Open
Affiliation(s)
- M Petrescu
- Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada
| | | | | | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - G Gervais
- Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada.
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4
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Madathil PT, Rosales KAV, Chung YJ, West KW, Baldwin KW, Pfeiffer LN, Engel LW, Shayegan M. Moving Crystal Phases of a Quantum Wigner Solid in an Ultra-High-Quality 2D Electron System. Phys Rev Lett 2023; 131:236501. [PMID: 38134784 DOI: 10.1103/physrevlett.131.236501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 10/24/2023] [Indexed: 12/24/2023]
Abstract
In low-disorder, two-dimensional electron systems (2DESs), the fractional quantum Hall states at very small Landau level fillings (ν) terminate in a Wigner solid (WS) phase, where electrons arrange themselves in a periodic array. The WS is typically pinned by the residual disorder sites and manifests an insulating behavior, with nonlinear current-voltage (I-V) and noise characteristics. We report here measurements on an ultralow-disorder, dilute 2DES, confined to a GaAs quantum well. In the ν<1/5 range, superimposed on a highly insulating longitudinal resistance, the 2DES exhibits a developing fractional quantum Hall state at ν=1/7, attesting to its exceptional high quality and dominance of electron-electron interaction in the low filling regime. In the nearby insulating phases, we observe remarkable nonlinear I-V and noise characteristics as a function of increasing current, with current thresholds delineating three distinct phases of the WS: a pinned phase (P1) with very small noise, a second phase (P2) in which dV/dI fluctuates between positive and negative values and is accompanied by very high noise, and a third phase (P3) where dV/dI is nearly constant and small, and noise is about an order of magnitude lower than in P2. In the depinned (P2 and P3) phases, the noise spectrum also reveals well-defined peaks at frequencies that vary linearly with the applied current, suggestive of washboard frequencies. We discuss the data in light of a recent theory that proposes different dynamic phases for a driven WS.
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Affiliation(s)
- P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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5
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Petrescu M, Berkson-Korenberg Z, Vijayakrishnan S, West KW, Pfeiffer LN, Gervais G. Large composite fermion effective mass at filling factor 5/2. Nat Commun 2023; 14:7250. [PMID: 37945585 PMCID: PMC10636205 DOI: 10.1038/s41467-023-42986-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Accepted: 10/25/2023] [Indexed: 11/12/2023] Open
Abstract
The 5/2 fractional quantum Hall effect in the second Landau level of extremely clean two-dimensional electron gases has attracted much attention due to its topological order predicted to host quasiparticles that obey non-Abelian quantum statistics and could serve as a basis for fault-tolerant quantum computations. While previous works have establish the Fermi liquid (FL) nature of its putative composite fermion (CF) normal phase, little is known regarding its thermodynamics properties and as a result its effective mass is entirely unknown. Here, we report on time-resolved specific heat measurements at filling factor 5/2, and we examine the ratio of specific heat to temperature as a function of temperature. Combining these specific heat data with existing longitudinal thermopower data measuring the entropy in the clean limit we find that, unless a phase transition/crossover gives rise to large specific heat anomaly, both datasets point towards a large effective mass in the FL phase of CFs at 5/2. We estimate the effective-to-bare mass ratio m*/me to be ranging from ~ 2 to 4, which is two to three times larger than previously measured values in the first Landau level.
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Affiliation(s)
- M Petrescu
- Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada
| | | | | | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - G Gervais
- Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada.
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6
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Wang C, Gupta A, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Winkler R, Shayegan M. Highly Anisotropic Even-Denominator Fractional Quantum Hall State in an Orbitally Coupled Half-Filled Landau Level. Phys Rev Lett 2023; 131:056302. [PMID: 37595236 DOI: 10.1103/physrevlett.131.056302] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 07/06/2023] [Indexed: 08/20/2023]
Abstract
The even-denominator fractional quantum Hall states (FQHSs) in half-filled Landau levels are generally believed to host non-Abelian quasiparticles and be of potential use in topological quantum computing. Of particular interest is the competition and interplay between the even-denominator FQHSs and other ground states, such as anisotropic phases and composite fermion Fermi seas. Here, we report the observation of an even-denominator fractional quantum Hall state with highly anisotropic in-plane transport coefficients at Landau level filling factor ν=3/2. We observe this state in an ultra-high-quality GaAs two-dimensional hole system when a large in-plane magnetic field is applied. By increasing the in-plane field, we observe a sharp transition from an isotropic composite fermion Fermi sea to an anisotropic even-denominator FQHS. Our data and calculations suggest that a unique feature of two-dimensional holes, namely the coupling between heavy-hole and light-hole states, combines different orbital components in the wave function of one Landau level, and leads to the emergence of a highly anisotropic even-denominator fractional quantum Hall state. Our results demonstrate that the GaAs two-dimensional hole system is a unique platform for the exploration of exotic, many-body ground states.
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Affiliation(s)
- Chengyu Wang
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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7
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Vijayakrishnan S, Poitevin F, Yu O, Berkson-Korenberg Z, Petrescu M, Lilly MP, Szkopek T, Agarwal K, West KW, Pfeiffer LN, Gervais G. Anomalous electronic transport in high-mobility Corbino rings. Nat Commun 2023; 14:3906. [PMID: 37400458 DOI: 10.1038/s41467-023-39526-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 06/19/2023] [Indexed: 07/05/2023] Open
Abstract
We report low-temperature electronic transport measurements performed in two multi-terminal Corbino samples formed in GaAs/Al-GaAs two-dimensional electron gases (2DEG) with both ultra-high electron mobility ( ≳ 20 × 106 cm2/ Vs) and with distinct electron density of 1.7 and 3.6 × 1011 cm-2. In both Corbino samples, a non-monotonic behavior is observed in the temperature dependence of the resistance below 1 K. Surprisingly, a sharp decrease in resistance is observed with increasing temperature in the sample with lower electron density, whereas an opposite behavior is observed in the sample with higher density. To investigate further, transport measurements were performed in large van der Pauw samples having identical heterostructures, and as expected they exhibit resistivity that is monotonic with temperature. Finally, we discuss the results in terms of various lengthscales leading to ballistic and hydrodynamic electronic transport, as well as a possible Gurzhi effect.
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Affiliation(s)
| | - F Poitevin
- Department of Physics, McGill University, Montréal, Québec, Canada
| | - Oulin Yu
- Department of Physics, McGill University, Montréal, Québec, Canada
| | | | - M Petrescu
- Department of Physics, McGill University, Montréal, Québec, Canada
| | - M P Lilly
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM, USA
| | - T Szkopek
- Department of Electrical and Computer Engineering, McGill University, Montréal, Québec, Canada
| | - Kartiek Agarwal
- Department of Physics, McGill University, Montréal, Québec, Canada
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - G Gervais
- Department of Physics, McGill University, Montréal, Québec, Canada.
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8
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Madathil PT, Villegas Rosales KA, Tai CT, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions. Phys Rev Lett 2023; 130:226503. [PMID: 37327438 DOI: 10.1103/physrevlett.130.226503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 05/12/2023] [Indexed: 06/18/2023]
Abstract
Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence of a scaling picture with a single extended state, characterized by a power-law divergence of the localization length in the zero-temperature limit. Experimentally, scaling has been investigated via measuring the temperature dependence of plateau-to-plateau transitions between the integer quantum Hall states (IQHSs), yielding a critical exponent κ≃0.42. Here we report scaling measurements in the fractional quantum Hall state (FQHS) regime where interaction plays a dominant role. Our Letter is partly motivated by recent calculations, based on the composite fermion theory, that suggest identical critical exponents in both IQHS and FQHS cases to the extent that the interaction between composite fermions is negligible. The samples used in our experiments are two-dimensional electron systems confined to GaAs quantum wells of exceptionally high quality. We find that κ varies for transitions between different FQHSs observed on the flanks of Landau level filling factor ν=1/2 and has a value close to that reported for the IQHS transitions only for a limited number of transitions between high-order FQHSs with intermediate strength. We discuss possible origins of the nonuniversal κ observed in our experiments.
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Affiliation(s)
- P T Madathil
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - C T Tai
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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9
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Yan J, Wu Y, Yuan S, Liu X, Pfeiffer LN, West KW, Liu Y, Fu H, Xie XC, Lin X. Anomalous quantized plateaus in two-dimensional electron gas with gate confinement. Nat Commun 2023; 14:1758. [PMID: 36997525 PMCID: PMC10064851 DOI: 10.1038/s41467-023-37495-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2022] [Accepted: 03/16/2023] [Indexed: 04/01/2023] Open
Abstract
AbstractQuantum information can be coded by the topologically protected edges of fractional quantum Hall (FQH) states. Investigation on FQH edges in the hope of searching and utilizing non-Abelian statistics has been a focused challenge for years. Manipulating the edges, e.g. to bring edges close to each other or to separate edges spatially, is a common and essential step for such studies. The FQH edge structures in a confined region are typically presupposed to be the same as that in the open region in analysis of experimental results, but whether they remain unchanged with extra confinement is obscure. In this work, we present a series of unexpected plateaus in a confined single-layer two-dimensional electron gas (2DEG), which are quantized at anomalous fractions such as 9/4, 17/11, 16/13 and the reported 3/2. We explain all the plateaus by assuming surprisingly larger filling factors in the confined region. Our findings enrich the understanding of edge states in the confined region and in the applications of gate manipulation, which is crucial for the experiments with quantum point contact and interferometer.
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10
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Hossain MS, Ma MK, Chung YJ, Singh SK, Gupta A, West KW, Baldwin KW, Pfeiffer LN, Winkler R, Shayegan M. Valley-Tunable Even-Denominator Fractional Quantum Hall State in the Lowest Landau Level of an Anisotropic System. Phys Rev Lett 2023; 130:126301. [PMID: 37027870 DOI: 10.1103/physrevlett.130.126301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 02/22/2023] [Indexed: 06/19/2023]
Abstract
Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors (ν) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at ν=1/2 in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multivalley degree of freedom offer an unprecedented tunability of the ν=1/2 FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the ν=1/2 FQHS depend strongly on valley occupancy.
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Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Meng K Ma
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S K Singh
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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11
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Ma MK, Wang C, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Winkler R, Shayegan M. Robust Quantum Hall Ferromagnetism near a Gate-Tuned ν=1 Landau Level Crossing. Phys Rev Lett 2022; 129:196801. [PMID: 36399735 DOI: 10.1103/physrevlett.129.196801] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Revised: 08/12/2022] [Accepted: 09/29/2022] [Indexed: 06/16/2023]
Abstract
In a low-disorder two-dimensional electron system, when two Landau levels of opposite spin or pseudospin cross at the Fermi level, the dominance of the exchange energy can lead to a ferromagnetic, quantum Hall ground state whose gap is determined by the exchange energy and has skyrmions as its excitations. This is normally achieved via applying either hydrostatic pressure or uniaxial strain. We study here a very high-quality, low-density, two-dimensional hole system, confined to a 30-nm-wide (001) GaAs quantum well, in which the two lowest-energy Landau levels can be gate tuned to cross at and near filling factor ν=1. As we tune the field position of the crossing from one side of ν=1 to the other by changing the hole density, the energy gap for the quantum Hall state at ν=1 remains exceptionally large, and only shows a small dip near the crossing. The gap overall follows a sqrt[B] dependence, expected for the exchange energy. Our data are consistent with a robust quantum Hall ferromagnet as the ground state.
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Affiliation(s)
- Meng K Ma
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Chengyu Wang
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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12
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Wang C, Gupta A, Singh SK, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Winkler R, Shayegan M. Even-Denominator Fractional Quantum Hall State at Filling Factor ν=3/4. Phys Rev Lett 2022; 129:156801. [PMID: 36269975 DOI: 10.1103/physrevlett.129.156801] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 08/17/2022] [Indexed: 06/16/2023]
Abstract
Fractional quantum Hall states (FQHSs) exemplify exotic phases of low-disorder two-dimensional (2D) electron systems when electron-electron interaction dominates over the thermal and kinetic energies. Particularly intriguing among the FQHSs are those observed at even-denominator Landau level filling factors, as their quasiparticles are generally believed to obey non-Abelian statistics and be of potential use in topological quantum computing. Such states, however, are very rare and fragile, and are typically observed in the excited Landau level of 2D electron systems with the lowest amount of disorder. Here we report the observation of a new and unexpected even-denominator FQHS at filling factor ν=3/4 in a GaAs 2D hole system with an exceptionally high quality (mobility). Our magnetotransport measurements reveal a strong minimum in the longitudinal resistance at ν=3/4, accompanied by a developing Hall plateau centered at (h/e^{2})/(3/4). This even-denominator FQHS is very unusual as it is observed in the lowest Landau level and in a 2D hole system. While its origin is unclear, it is likely a non-Abelian state, emerging from the residual interaction between composite fermions.
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Affiliation(s)
- Chengyu Wang
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S K Singh
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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13
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Hossain MS, Ma MK, Villegas-Rosales KA, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Anisotropic Two-Dimensional Disordered Wigner Solid. Phys Rev Lett 2022; 129:036601. [PMID: 35905352 DOI: 10.1103/physrevlett.129.036601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2021] [Accepted: 06/07/2022] [Indexed: 06/15/2023]
Abstract
The interplay between the Fermi sea anisotropy, electron-electron interaction, and localization phenomena can give rise to exotic many-body phases. An exciting example is an anisotropic two-dimensional (2D) Wigner solid (WS), where electrons form an ordered array with an anisotropic lattice structure. Such a state has eluded experiments up to now as its realization is extremely demanding: First, a WS entails very low densities where the Coulomb interaction dominates over the kinetic (Fermi) energy. Attaining such low densities while keeping the disorder low is very challenging. Second, the low-density requirement has to be fulfilled in a material that hosts an anisotropic Fermi sea. Here, we report transport measurements in a clean (low-disorder) 2D electron system with anisotropic effective mass and Fermi sea. The data reveal that at extremely low electron densities, when the r_{s} parameter, the ratio of the Coulomb to the Fermi energy, exceeds ≃38, the current-voltage characteristics become strongly nonlinear at small dc biases. Several key features of the nonlinear characteristics, including their anisotropic voltage thresholds, are consistent with the formation of a disordered, anisotropic WS pinned by the ubiquitous disorder potential.
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Affiliation(s)
- Md S Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas-Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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14
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Chung YJ, Graf D, Engel LW, Rosales KAV, Madathil PT, Baldwin KW, West KW, Pfeiffer LN, Shayegan M. Correlated States of 2D Electrons near the Landau Level Filling ν=1/7. Phys Rev Lett 2022; 128:026802. [PMID: 35089735 DOI: 10.1103/physrevlett.128.026802] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2021] [Revised: 10/27/2021] [Accepted: 12/08/2021] [Indexed: 06/14/2023]
Abstract
The ground state of two-dimensional electron systems (2DESs) at low Landau level filling factors (ν≲1/6) has long been a topic of interest and controversy in condensed matter. Following the recent breakthrough in the quality of ultrahigh-mobility GaAs 2DESs, we revisit this problem experimentally and investigate the impact of reduced disorder. In a GaAs 2DES sample with density n=6.1×10^{10}/cm^{2} and mobility μ=25×10^{6} cm^{2}/V s, we find a deep minimum in the longitudinal magnetoresistance (R_{xx}) at ν=1/7 when T≃104 mK. There is also a clear sign of a developing minimum in R_{xx} at ν=2/13. While insulating phases are still predominant when ν≲1/6, these minima strongly suggest the existence of fractional quantum Hall states at filling factors that comply with the Jain sequence ν=p/(2mp±1) even in the very low Landau level filling limit. The magnetic-field-dependent activation energies deduced from the relation R_{xx}∝e^{E_{A}/2kT} corroborate this view and imply the presence of pinned Wigner solid states when ν≠p/(2mp±1). Similar results are seen in another sample with a lower density, further generalizing our observations.
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Affiliation(s)
- Yoon Jang Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D Graf
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - K A Villegas Rosales
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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15
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Hossain MS, Ma MK, Villegas-Rosales KA, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Spontaneous Valley Polarization of Itinerant Electrons. Phys Rev Lett 2021; 127:116601. [PMID: 34558923 DOI: 10.1103/physrevlett.127.116601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Accepted: 07/28/2021] [Indexed: 06/13/2023]
Abstract
Memory or transistor devices based on an electron's spin rather than its charge degree of freedom offer certain distinct advantages and comprise a cornerstone of spintronics. Recent years have witnessed the emergence of a new field, valleytronics, which seeks to exploit an electron's valley index rather than its spin. An important component in this quest would be the ability to control the valley index in a convenient fashion. Here we show that the valley polarization can be switched from zero to 1 by a small reduction in density, simply tuned by a gate bias, in a two-dimensional electron system. This phenomenon, which is akin to Bloch spin ferromagnetism, arises fundamentally as a result of electron-electron interaction in an itinerant, dilute electron system. Essentially, the kinetic energy favors an equal distribution of electrons over the available valleys, whereas the interaction between electrons prefers single-valley occupancy below a critical density. The gate-bias-tuned transition we observe is accompanied by a sudden, twofold change in sample resistance, making the phenomenon of interest for potential valleytronic transistor device applications. Our observation constitutes a quintessential demonstration of valleytronics in a very simple experiment.
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Affiliation(s)
- Md S Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas-Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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16
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Villegas Rosales KA, Madathil PT, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Fractional Quantum Hall Effect Energy Gaps: Role of Electron Layer Thickness. Phys Rev Lett 2021; 127:056801. [PMID: 34397247 DOI: 10.1103/physrevlett.127.056801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
The fractional quantum Hall effect stands as a quintessential manifestation of an interacting two-dimensional electron system. One of the fractional quantum Hall effect's most fundamental characteristics is the energy gap separating the incompressible ground state from its excitations. Yet, despite nearly four decades of investigations, a quantitative agreement between the theoretically calculated and experimentally measured energy gaps is lacking. Here we report a systematic experimental study that incorporates very high-quality two-dimensional electron systems confined to GaAs quantum wells with fixed density and varying well widths. The results demonstrate a clear decrease of the energy gap as the electron layer is made thicker and the short-range component of the Coulomb interaction is weakened. We also provide a quantitative comparison between the measured energy gaps and the available theoretical calculations that takes into account the role of finite layer thickness and Landau level mixing. All the measured energy gaps fall below the calculations, but as the electron layer thickness increases, the results of experiments and calculations come closer. Accounting for the role of disorder in a phenomenological manner, we find better overall agreement between the measured and calculated energy gaps, although some puzzling discrepancies remain.
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Affiliation(s)
- K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - P T Madathil
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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17
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Chung YJ, Villegas Rosales KA, Baldwin KW, Madathil PT, West KW, Shayegan M, Pfeiffer LN. Ultra-high-quality two-dimensional electron systems. Nat Mater 2021; 20:632-637. [PMID: 33633355 DOI: 10.1038/s41563-021-00942-3] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2020] [Accepted: 01/22/2021] [Indexed: 06/12/2023]
Abstract
Two-dimensional electrons confined to GaAs quantum wells are hallmark platforms for probing electron-electron interactions. Many key observations have been made in these systems as sample quality has improved over the years. Here, we present a breakthrough in sample quality via source-material purification and innovation in GaAs molecular beam epitaxy vacuum chamber design. Our samples display an ultra-high mobility of 44 × 106 cm2 V-1 s-1 at an electron density of 2.0 × 1011 cm-2. These results imply only 1 residual impurity for every 1010 Ga/As atoms. The impact of such low impurity concentration is manifold. Robust stripe and bubble phases are observed, and several new fractional quantum Hall states emerge. Furthermore, the activation gap (Δ) of the fractional quantum Hall state at the Landau-level filling (ν) = 5/2, which is widely believed to be non-Abelian and of potential use for topological quantum computing, reaches Δ ≈ 820 mK. We expect that our results will stimulate further research on interaction-driven physics in a two-dimensional setting and substantially advance the field.
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Affiliation(s)
- Yoon Jang Chung
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA.
| | | | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - P T Madathil
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
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18
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Hossain MS, Ma MK, Rosales KAV, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Observation of spontaneous ferromagnetism in a two-dimensional electron system. Proc Natl Acad Sci U S A 2020; 117:32244-32250. [PMID: 33273119 PMCID: PMC7768770 DOI: 10.1073/pnas.2018248117] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
What are the ground states of an interacting, low-density electron system? In the absence of disorder, it has long been expected that as the electron density is lowered, the exchange energy gained by aligning the electron spins should exceed the enhancement in the kinetic (Fermi) energy, leading to a (Bloch) ferromagnetic transition. At even lower densities, another transition to a (Wigner) solid, an ordered array of electrons, should occur. Experimental access to these regimes, however, has been limited because of the absence of a material platform that supports an electron system with very high quality (low disorder) and low density simultaneously. Here we explore the ground states of interacting electrons in an exceptionally clean, two-dimensional electron system confined to a modulation-doped AlAs quantum well. The large electron effective mass in this system allows us to reach very large values of the interaction parameter [Formula: see text], defined as the ratio of the Coulomb to Fermi energies. As we lower the electron density via gate bias, we find a sequence of phases, qualitatively consistent with the above scenario: a paramagnetic phase at large densities, a spontaneous transition to a ferromagnetic state when [Formula: see text] surpasses 35, and then a phase with strongly nonlinear current-voltage characteristics, suggestive of a pinned Wigner solid, when [Formula: see text] exceeds [Formula: see text] However, our sample makes a transition to an insulating state at [Formula: see text], preceding the onset of the spontaneous ferromagnetism, implying that besides interaction, the role of disorder must also be taken into account in understanding the different phases of a realistic dilute electron system.
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Affiliation(s)
- M S Hossain
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - M K Ma
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | | | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
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19
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Patlatiuk T, Scheller CP, Hill D, Tserkovnyak Y, Egues JC, Barak G, Yacoby A, Pfeiffer LN, West KW, Zumbühl DM. Edge-State Wave Functions from Momentum-Conserving Tunneling Spectroscopy. Phys Rev Lett 2020; 125:087701. [PMID: 32909808 DOI: 10.1103/physrevlett.125.087701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2020] [Accepted: 07/21/2020] [Indexed: 06/11/2023]
Abstract
We perform momentum-conserving tunneling spectroscopy using a GaAs cleaved-edge overgrowth quantum wire to investigate adjacent quantum Hall edge states. We use the lowest five wire modes with their distinct wave functions to probe each edge state and apply magnetic fields to modify the wave functions and their overlap. This reveals an intricate and rich tunneling conductance fan structure which is succinctly different for each of the wire modes. We self-consistently solve the Poisson-Schrödinger equations to simulate the spectroscopy, reproducing the striking fans in great detail, thus, confirming the calculations. Further, the model predicts hybridization between wire states and Landau levels, which is also confirmed experimentally. This establishes momentum-conserving tunneling spectroscopy as a powerful technique to probe edge state wave functions.
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Affiliation(s)
- T Patlatiuk
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - C P Scheller
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - D Hill
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
| | - Y Tserkovnyak
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
| | - J C Egues
- Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil
| | - G Barak
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - A Yacoby
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D M Zumbühl
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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20
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Hossain MS, Mueed MA, Ma MK, Villegas Rosales KA, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System. Phys Rev Lett 2020; 125:046601. [PMID: 32794794 DOI: 10.1103/physrevlett.125.046601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 06/24/2020] [Indexed: 06/11/2023]
Abstract
A fundamental concept in physics is the Fermi surface, the constant-energy surface in momentum space encompassing all the occupied quantum states at absolute zero temperature. In 1960, Luttinger postulated that the area enclosed by the Fermi surface should remain unaffected even when electron-electron interaction is turned on, so long as the interaction does not cause a phase transition. Understanding what determines the Fermi surface size is a crucial and yet unsolved problem in strongly interacting systems such as high-T_{c} superconductors. Here we present a precise test of the Luttinger theorem for a two-dimensional Fermi liquid system where the exotic quasiparticles themselves emerge from the strong interaction, namely, for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs' Fermi wave vector down to very low electron densities, we show that the Luttinger theorem is obeyed over a significant range of interaction strengths, in the sense that the Fermi sea area is determined by the density of the minority carriers in the lowest Landau level. Our data also address the ongoing debates on whether or not CFs obey particle-hole symmetry, and if they are Dirac particles. We find that particle-hole symmetry is obeyed, but the measured Fermi sea area differs quantitatively from that predicted by the Dirac model for CFs.
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Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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21
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Ma MK, Villegas Rosales KA, Deng H, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Winkler R, Shayegan M. Thermal and Quantum Melting Phase Diagrams for a Magnetic-Field-Induced Wigner Solid. Phys Rev Lett 2020; 125:036601. [PMID: 32745416 DOI: 10.1103/physrevlett.125.036601] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 06/12/2020] [Indexed: 06/11/2023]
Abstract
A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors (ν≃1/5). In dilute GaAs 2D hole systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings (ν≃1/3). Here we report our measurements of the fundamental temperature vs filling phase diagram for the 2D holes' WS-liquid thermal melting. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs filling WS-liquid quantum melting phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.
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Affiliation(s)
- Meng K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - H Deng
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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22
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Pan W, Kang W, Lilly MP, Reno JL, Baldwin KW, West KW, Pfeiffer LN, Tsui DC. Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level. Phys Rev Lett 2020; 124:156801. [PMID: 32357056 DOI: 10.1103/physrevlett.124.156801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2019] [Revised: 12/14/2019] [Accepted: 03/19/2020] [Indexed: 06/11/2023]
Abstract
We report on detailed experimental studies of a high-quality heterojunction insulated-gate field-effect transistor (HIGFET) to probe the particle-hole symmetry of the fractional quantum Hall effect (FQHE) states about half-filling in the lowest Landau level. The HIGFET is specially designed to vary the density of a two-dimensional electronic system under constant magnetic fields. We find in our constant magnetic field, variable density measurements that the sequence of FQHE states at filling factors ν=1/3,2/5,3/7… and its particle-hole conjugate states at filling factors 1-ν=2/3,3/5,4/7… have a very similar energy gap. Moreover, a reflection symmetry can be established in the magnetoconductivities between the ν and 1-ν states about half-filling. Our results demonstrate that the FQHE states in the lowest Landau level are manifestly particle-hole symmetric.
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Affiliation(s)
- W Pan
- Materials Physics Department, Sandia National Laboratories, Livermore, California 94551, USA
- Quantum Phenomena Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - W Kang
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - M P Lilly
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - J L Reno
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D C Tsui
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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23
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Fu X, Shi Q, Zudov MA, Gardner GC, Watson JD, Manfra MJ, Baldwin KW, Pfeiffer LN, West KW. Anomalous Nematic States in High Half-Filled Landau Levels. Phys Rev Lett 2020; 124:067601. [PMID: 32109097 DOI: 10.1103/physrevlett.124.067601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2019] [Accepted: 01/22/2020] [Indexed: 06/10/2023]
Abstract
It is well established that the ground states of a two-dimensional electron gas with half-filled high (N≥2) Landau levels are compressible charge-ordered states, known as quantum Hall stripe (QHS) phases. The generic features of QHSs are a maximum (minimum) in a longitudinal resistance R_{xx} (R_{yy}) and a nonquantized Hall resistance R_{H}. Here, we report on emergent minima (maxima) in R_{xx} (R_{yy}) and plateaulike features in R_{H} in half-filled N≥3 Landau levels. Remarkably, these unexpected features develop at temperatures considerably lower than the onset temperature of QHSs, suggestive of a new ground state.
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Affiliation(s)
- X Fu
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Q Shi
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - M A Zudov
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - G C Gardner
- Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - J D Watson
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - M J Manfra
- Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering and School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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24
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Drichko IL, Yu Smirnov I, Suslov AV, Nestoklon MO, Kamburov D, Baldwin KW, Pfeiffer LN, West KW, Golub LE. Electronic band structure in n-type GaAs/AlGaAs wide quantum wells in tilted magnetic field. J Phys Condens Matter 2020; 32:035303. [PMID: 31578004 DOI: 10.1088/1361-648x/ab4a51] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Oscillations of the real component of AC conductivity [Formula: see text] in a magnetic field were measured in the n-AlGaAs/GaAs structure with a wide (75 nm) quantum well by contactless acoustic methods at [Formula: see text] mK. In a wide quantum well, the electronic band structure is associated with the two-subband electron spectrum, namely the symmetric (S) and antisymmetric (AS) subbands formed due to electrostatic repulsion of electrons. A change of the oscillations amplitude in tilted magnetic field observed in the experiments occurs due to crossings of Landau levels of different subbands (S and AS) at the Fermi level. The theory developed in this work shows that these crossings are caused by the difference in the cyclotron energies in the S and AS subbands induced by the in-plane magnetic field.
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Affiliation(s)
- I L Drichko
- Ioffe Institute, 194021 St. Petersburg, Russia
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25
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Huang K, Wang P, Pfeiffer LN, West KW, Baldwin KW, Liu Y, Lin X. Resymmetrizing Broken Symmetry with Hydraulic Pressure. Phys Rev Lett 2019; 123:206602. [PMID: 31809100 DOI: 10.1103/physrevlett.123.206602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2019] [Indexed: 06/10/2023]
Abstract
Recent progress in condensed matter physics, such as for graphene, topological insulators, and Weyl semimetals, often originate from the specific topological symmetries of their lattice structures. Quantum states with different degrees of freedom, e.g., spin, valley, layer, etc., arise from these symmetries, and the coherent superposition of these states form multiple energy subbands. The pseudospin, a concept analogous to the Dirac spinor matrices, is a successful description of such multisubband systems. When the electron-electron interaction dominates, many-body quantum phases arise. They usually have discrete pseudospin polarizations and exhibit sharp phase transitions at certain universal critical pseudospin energy splittings. In this Letter, we present our discovery of hydrostatic-pressure-induced degeneracy between the two lowest Landau levels. This degeneracy is evidenced by the pseudospin polarization transitions of the fragile correlated quantum liquid phases near the Landau level filling factor ν=3/2. Benefitting from the constant hole concentration and the sensitive nature of these transitions, we study the fine-tuning effect of the hydrostatic pressure at the order of 10 μeV, well beyond the meV-level state-of-the-art resolution of other techniques.
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Affiliation(s)
- Ke Huang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Pengjie Wang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Yang Liu
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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26
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Fu H, Wu Y, Zhang R, Sun J, Shan P, Wang P, Zhu Z, Pfeiffer LN, West KW, Liu H, Xie XC, Lin X. 3/2 fractional quantum Hall plateau in confined two-dimensional electron gas. Nat Commun 2019; 10:4351. [PMID: 31554799 PMCID: PMC6761136 DOI: 10.1038/s41467-019-12245-y] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2017] [Accepted: 08/27/2019] [Indexed: 11/09/2022] Open
Abstract
Even-denominator fractional quantum Hall (FQH) states, such as 5/2 and 7/2, have been well known in a two-dimensional electron gas (2DEG) for decades and are still investigated as candidates of non-Abelian statistics. In this paper, we present the observation of a 3/2 FQH plateau in a single-layer 2DEG with lateral confinement at a bulk filling factor of 5/3. The 3/2 FQH plateau is quantized at \documentclass[12pt]{minimal}
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\begin{document}$$\left( {\frac{h}{{e^2}}} \right)/\left( {\frac{3}{2}} \right)$$\end{document}he2∕32 within 0.02%, and can survive up to 300 mK. This even-denominator FQH plateau may imply intriguing edge structure and excitation in FQH system with lateral confinement. The observations in this work demonstrate that understanding the effect of the lateral confinement on the many-body system is critical in the pursuit of important theoretical proposals involving edge physics, such as the demonstration of non-Abelian statistics and the realization of braiding for fault-tolerant quantum computation. Fractional quantum Hall states in 2D electron gases arise due to strong electron-electron interactions, which makes a general theoretical understanding difficult. Fu et al. present data showing the ν = 5/3 quantum Hall state has a 3/2 plateau in the diagonal resistance that has not been captured by existing models.
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Affiliation(s)
- Hailong Fu
- International Center for Quantum Materials, Peking University, 100871, Beijing, China.,Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Yijia Wu
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Ruoxi Zhang
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Jian Sun
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Pujia Shan
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Pengjie Wang
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Zheyi Zhu
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - Haiwen Liu
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, 100875, Beijing, China
| | - X C Xie
- International Center for Quantum Materials, Peking University, 100871, Beijing, China.,Beijing Academy of Quantum Information Sciences, 100193, Beijing, China.,CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, 100190, Beijing, China
| | - Xi Lin
- International Center for Quantum Materials, Peking University, 100871, Beijing, China. .,Beijing Academy of Quantum Information Sciences, 100193, Beijing, China. .,CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, 100190, Beijing, China.
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27
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Abstract
Tunneling spectroscopy reveals evidence for interlayer electron-hole correlations in quantum Hall bilayer two-dimensional electron systems at layer separations near, but above, the transition to the incompressible exciton condensate at total Landau level filling ν_{T}=1. These correlations are manifested by a nonlinear suppression of the Coulomb pseudogap which inhibits low energy interlayer tunneling in weakly coupled bilayers. The pseudogap suppression is strongest at ν_{T}=1 and grows rapidly as the critical layer separation for exciton condensation is approached from above.
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Affiliation(s)
- J P Eisenstein
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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28
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Deng H, Pfeiffer LN, West KW, Baldwin KW, Engel LW, Shayegan M. Probing the Melting of a Two-Dimensional Quantum Wigner Crystal via its Screening Efficiency. Phys Rev Lett 2019; 122:116601. [PMID: 30951347 DOI: 10.1103/physrevlett.122.116601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Indexed: 06/09/2023]
Abstract
One of the most fundamental and yet elusive collective phases of an interacting electron system is the quantum Wigner crystal (WC), an ordered array of electrons expected to form when the electrons' Coulomb repulsion energy eclipses their kinetic (Fermi) energy. In low-disorder, two-dimensional (2D) electron systems, the quantum WC is known to be favored at very low temperatures (T) and small Landau level filling factors (ν), near the termination of the fractional quantum Hall states. This WC phase exhibits an insulating behavior, reflecting its pinning by the small but finite disorder potential. An experimental determination of a T vs ν phase diagram for the melting of the WC, however, has proved to be challenging. Here we use capacitance measurements to probe the 2D WC through its effective screening as a function of T and ν. We find that, as expected, the screening efficiency of the pinned WC is very poor at very low T and improves at higher T once the WC melts. Surprisingly, however, rather than monotonically changing with increasing T, the screening efficiency shows a well-defined maximum at a T that is close to the previously reported melting temperature of the WC. Our experimental results suggest a new method to map out a T vs ν phase diagram of the magnetic-field-induced WC precisely.
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Affiliation(s)
- H Deng
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
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29
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Hatke AT, Deng H, Liu Y, Engel LW, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Wigner solid pinning modes tuned by fractional quantum Hall states of a nearby layer. Sci Adv 2019; 5:eaao2848. [PMID: 30899780 PMCID: PMC6420311 DOI: 10.1126/sciadv.aao2848] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/11/2018] [Accepted: 01/29/2019] [Indexed: 06/09/2023]
Abstract
We studied a bilayer system hosting two-dimensional electron systems (2DESs) in close proximity but isolated from one another by a thin barrier. One 2DES has low electron density and forms a Wigner solid (WS) at high magnetic fields. The other has much higher density and, in the same field, exhibits fractional quantum Hall states (FQHSs). The WS spectrum has resonances which are understood as pinning modes, oscillations of the WS within the residual disorder. We found the pinning mode frequencies of the WS are strongly affected by the FQHSs in the nearby layer. Analysis of the spectra indicates that the majority layer screens like a dielectric medium even when its Landau filling is ~1/2, at which the layer is essentially a composite fermion (CF) metal. Although the majority layer is only ~ one WS lattice constant away, a WS site only induces an image charge of ~0.1e in the CF metal.
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Affiliation(s)
- A. T. Hatke
- National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA
| | - H. Deng
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - L. W. Engel
- National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA
| | - L. N. Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - K. W. West
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - K. W. Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - M. Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
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30
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Hossain MS, Ma MK, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Unconventional Anisotropic Even-Denominator Fractional Quantum Hall State in a System with Mass Anisotropy. Phys Rev Lett 2018; 121:256601. [PMID: 30608773 DOI: 10.1103/physrevlett.121.256601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2018] [Indexed: 06/09/2023]
Abstract
The fractional quantum Hall state (FQHS) observed at a half-filled Landau level in an interacting two-dimensional electron system (2DES) is among the most exotic states of matter as its quasiparticles are expected to be Majorana excitations with non-Abelian statistics. We demonstrate here the unexpected presence of such a state in a novel 2DES with a strong band-mass anisotropy. The FQHS we observe has unusual characteristics. While its Hall resistance is well quantized at low temperatures, it exhibits highly anisotropic in-plane transport resembling compressible stripe or nematic charge-density-wave phases. More striking, the anisotropy sets in suddenly below a critical temperature, suggesting a finite-temperature phase transition. Our observations highlight how anisotropy modifies the many-body phases of a 2DES, and should further fuel the discussion surrounding the enigmatic even-denominator FQHS.
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Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Meng K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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31
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Hossain MS, Ma MK, Mueed MA, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Erratum: Direct observation of composite fermions and their fully-spin-polarized Fermi sea near ν=5/2 [Phys. Rev. Lett. 120, 256601 (2018)]. Phys Rev Lett 2018; 121:209901. [PMID: 30500222 DOI: 10.1103/physrevlett.121.209901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2018] [Indexed: 06/09/2023]
Abstract
This corrects the article DOI: 10.1103/PhysRevLett.120.256601.
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32
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Patlatiuk T, Scheller CP, Hill D, Tserkovnyak Y, Barak G, Yacoby A, Pfeiffer LN, West KW, Zumbühl DM. Evolution of the quantum Hall bulk spectrum into chiral edge states. Nat Commun 2018; 9:3692. [PMID: 30209251 PMCID: PMC6135798 DOI: 10.1038/s41467-018-06025-3] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2018] [Accepted: 08/13/2018] [Indexed: 11/30/2022] Open
Abstract
One of the most intriguing and fundamental properties of topological systems is the correspondence between the conducting edge states and the gapped bulk spectrum. Here, we use a GaAs cleaved edge quantum wire to perform momentum-resolved spectroscopy of the quantum Hall edge states in a tunnel-coupled 2D electron gas. This reveals the momentum and position of the edge states with unprecedented precision and shows the evolution from very low magnetic fields all the way to high fields where depopulation occurs. We present consistent analytical and numerical models, inferring the edge states from the well-known bulk spectrum, finding excellent agreement with the experiment-thus providing direct evidence for the bulk to edge correspondence. In addition, we observe various features beyond the single-particle picture, such as Fermi level pinning, exchange-enhanced spin splitting and signatures of edge-state reconstruction.
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Affiliation(s)
- T Patlatiuk
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| | - C P Scheller
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| | - D Hill
- Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095, USA
| | - Y Tserkovnyak
- Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095, USA
| | - G Barak
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - A Yacoby
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - D M Zumbühl
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland.
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33
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Mueed MA, Hossain MS, Jo I, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Realization of a Valley Superlattice. Phys Rev Lett 2018; 121:036802. [PMID: 30085799 DOI: 10.1103/physrevlett.121.036802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2017] [Indexed: 06/08/2023]
Abstract
In a number of widely studied materials, such as Si, AlAs, Bi, graphene, MoS_{2}, and many transition metal dichalcogenide monolayers, electrons acquire an additional, spinlike degree of freedom at the degenerate conduction band minima, also known as "valleys." External symmetry-breaking fields such as mechanical strain, or electric or magnetic fields, can tune the valley polarization of these materials, making them suitable candidates for "valleytronics." Here we study a quantum well of AlAs, where the two-dimensional electrons reside in two energetically degenerate valleys. By fabricating a strain-inducing grating on the sample surface, we engineer a spatial modulation of the electron population in different valleys, i.e., a "valley superlattice" in the quantum well plane. Our results establish a novel manipulation technique of the valley degree of freedom, paving the way to realizing a valley-selective layered structure in multivalley materials, with potential application in valleytronics.
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Affiliation(s)
- M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Md Shafayat Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - I Jo
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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34
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Hossain MS, Ma MK, Mueed MA, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Direct Observation of Composite Fermions and Their Fully-Spin-Polarized Fermi Sea near ν=5/2. Phys Rev Lett 2018; 120:256601. [PMID: 29979050 DOI: 10.1103/physrevlett.120.256601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2018] [Indexed: 06/08/2023]
Abstract
The enigmatic even-denominator fractional quantum Hall state at Landau level filling factor ν=5/2 is arguably the most promising candidate for harboring Majorana quasiparticles with non-Abelian statistics and, thus, of potential use for topological quantum computing. The theoretical description of the ν=5/2 state is generally believed to involve a topological p-wave pairing of fully-spin-polarized composite fermions through their condensation into a non-Abelian Moore-Read Pfaffian state. There is, however, no direct and conclusive experimental evidence for the existence of composite fermions near ν=5/2 or for an underlying fully-spin-polarized Fermi sea. Here, we report the observation of composite fermions very near ν=5/2 through geometric resonance measurements and find that the measured Fermi wave vector provides direct demonstration of a Fermi sea with full spin polarization. This lends crucial credence to the model of 5/2 fractional quantum Hall effect as a topological p-wave paired state of composite fermions.
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Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Meng K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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35
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Schreiber KA, Samkharadze N, Gardner GC, Lyanda-Geller Y, Manfra MJ, Pfeiffer LN, West KW, Csáthy GA. Electron-electron interactions and the paired-to-nematic quantum phase transition in the second Landau level. Nat Commun 2018; 9:2400. [PMID: 29921969 PMCID: PMC6008478 DOI: 10.1038/s41467-018-04879-1] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2018] [Accepted: 05/23/2018] [Indexed: 11/12/2022] Open
Abstract
In spite of its ubiquity in strongly correlated systems, the competition of paired and nematic ground states remains poorly understood. Recently such a competition was reported in the two-dimensional electron gas at filling factor ν = 5/2. At this filling factor a pressure-induced quantum phase transition was observed from the paired fractional quantum Hall state to the quantum Hall nematic. Here we show that the pressure-induced paired-to-nematic transition also develops at ν = 7/2, demonstrating therefore this transition in both spin branches of the second orbital Landau level. However, we find that pressure is not the only parameter controlling this transition. Indeed, ground states consistent with those observed under pressure also develop in a sample measured at ambient pressure, but in which the electron-electron interaction was tuned close to its value at the quantum critical point. Our experiments suggest that electron-electron interactions play a critical role in driving the paired-to-nematic transition.
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Affiliation(s)
- K A Schreiber
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - N Samkharadze
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Lorentzweg 1, 2628 CJ, Delft, Netherlands
| | - G C Gardner
- School of Materials Engineering, Purdue University, West Lafayette, IN, 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - Y Lyanda-Geller
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - M J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, IN, 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - G A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA.
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA.
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36
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Bennaceur K, Lupien C, Reulet B, Gervais G, Pfeiffer LN, West KW. Competing Charge Density Waves Probed by Nonlinear Transport and Noise in the Second and Third Landau Levels. Phys Rev Lett 2018; 120:136801. [PMID: 29694212 DOI: 10.1103/physrevlett.120.136801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2017] [Indexed: 06/08/2023]
Abstract
Charge density waves (CDWs) in the second and third Landau levels (LLs) are investigated by both nonlinear electronic transport and noise. The use of a Corbino geometry ensures that only bulk properties are probed, with no contribution from edge states. Sliding transport of CDWs is revealed by narrow band noise in reentrant quantum Hall states R2a and R2c of the second LL, as well as in pinned CDWs of the third LL. Competition between various phases-stripe, pinned CDW, or fractional quantum Hall liquid-in both LLs are clearly revealed by combining noise data with maps of conductivity versus magnetic field and bias voltage.
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Affiliation(s)
- K Bennaceur
- Département de Physique et Institut Quantique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
- Department of Physics, Amrita Vishwa Vidyapeetham, Amritapuri 690525, India
- Department of Physics, McGill University, Montréal, Québec H3A 2T8, Canada
| | - C Lupien
- Département de Physique et Institut Quantique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - B Reulet
- Département de Physique et Institut Quantique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - G Gervais
- Department of Physics, McGill University, Montréal, Québec H3A 2T8, Canada
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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37
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Jo I, Deng H, Liu Y, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Cyclotron Orbits of Composite Fermions in the Fractional Quantum Hall Regime. Phys Rev Lett 2018; 120:016802. [PMID: 29350938 DOI: 10.1103/physrevlett.120.016802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Indexed: 06/07/2023]
Abstract
We study a bilayer GaAs hole system that hosts two distinct many-body phases at low temperatures and high perpendicular magnetic fields. The higher-density (top) layer develops a Fermi sea of composite fermions (CFs) in its half-filled lowest Landau level, while the lower-density (bottom) layer forms a Wigner crystal (WC) as its filling becomes very small. Owing to the interlayer interaction, the CFs in the top layer feel the periodic Coulomb potential of the WC in the bottom layer. We measure the magnetoresistance of the top layer while changing the bottom-layer density. As the WC layer density increases, the resistance peaks separating the adjacent fractional quantum Hall states in the top layer change nonmonotonically and attain maximum values when the cyclotron orbit of the CFs encloses one WC lattice point. These features disappear at T=275 mK when the WC melts. The observation of such geometric resonance features is unprecedented and surprising as it implies that the CFs retain a well-defined cyclotron orbit and Fermi wave vector even deep in the fractional quantum Hall regime, far from half-filling.
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Affiliation(s)
- Insun Jo
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Hao Deng
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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38
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Jang J, Yoo HM, Pfeiffer LN, West KW, Baldwin KW, Ashoori RC. Full momentum- and energy-resolved spectral function of a 2D electronic system. Science 2017; 358:901-906. [PMID: 29146806 DOI: 10.1126/science.aam7073] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2017] [Accepted: 10/05/2017] [Indexed: 11/02/2022]
Abstract
The single-particle spectral function measures the density of electronic states in a material as a function of both momentum and energy, providing central insights into strongly correlated electron phenomena. Here we demonstrate a high-resolution method for measuring the full momentum- and energy-resolved electronic spectral function of a two-dimensional (2D) electronic system embedded in a semiconductor. The technique remains operational in the presence of large externally applied magnetic fields and functions even for electronic systems with zero electrical conductivity or with zero electron density. Using the technique on a prototypical 2D system, a GaAs quantum well, we uncover signatures of many-body effects involving electron-phonon interactions, plasmons, polarons, and a phonon analog of the vacuum Rabi splitting in atomic systems.
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Affiliation(s)
- Joonho Jang
- Department of Physics, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA.
| | - Heun Mo Yoo
- Department of Physics, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Raymond C Ashoori
- Department of Physics, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA.
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39
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Jo I, Rosales KAV, Mueed MA, Pfeiffer LN, West KW, Baldwin KW, Winkler R, Padmanabhan M, Shayegan M. Transference of Fermi Contour Anisotropy to Composite Fermions. Phys Rev Lett 2017; 119:016402. [PMID: 28731746 DOI: 10.1103/physrevlett.119.016402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2017] [Indexed: 06/07/2023]
Abstract
There has been a surge of recent interest in the role of anisotropy in interaction-induced phenomena in two-dimensional (2D) charged carrier systems. A fundamental question is how an anisotropy in the energy-band structure of the carriers at zero magnetic field affects the properties of the interacting particles at high fields, in particular of the composite fermions (CFs) and the fractional quantum Hall states (FQHSs). We demonstrate here tunable anisotropy for holes and hole-flux CFs confined to GaAs quantum wells, via applying in situ in-plane strain and measuring their Fermi wave vector anisotropy through commensurability oscillations. For strains on the order of 10^{-4} we observe significant deformations of the shapes of the Fermi contours for both holes and CFs. The measured Fermi contour anisotropy for CFs at high magnetic field (α_{CF}) is less than the anisotropy of their low-field hole (fermion) counterparts (α_{F}), and closely follows the relation α_{CF}=sqrt[α_{F}]. The energy gap measured for the ν=2/3 FQHS, on the other hand, is nearly unaffected by the Fermi contour anisotropy up to α_{F}∼3.3, the highest anisotropy achieved in our experiments.
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Affiliation(s)
- Insun Jo
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - Medini Padmanabhan
- Physical Sciences Department, Rhode Island College, Providence, Rhode Island 02908, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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40
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Abstract
Double layer two-dimensional electron systems at high perpendicular magnetic field are used to realize magnetic tunnel junctions in which the electrons at the Fermi level in the two layers have either parallel or antiparallel spin magnetizations. In the antiparallel case the tunnel junction, at low temperatures, behaves as a nearly ideal spin diode. At elevated temperatures the diode character degrades as long-wavelength spin waves are thermally excited. These tunnel junctions provide a demonstration that the spin polarization of the electrons in the N=1 Landau level at filling factors ν=5/2 and 7/2 is essentially complete, and, with the aid of an in-plane magnetic field component, that Landau level mixing at these filling factors is weak in the samples studied.
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Affiliation(s)
- J P Eisenstein
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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41
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Uchida K, Otobe T, Mochizuki T, Kim C, Yoshita M, Akiyama H, Pfeiffer LN, West KW, Tanaka K, Hirori H. Subcycle Optical Response Caused by a Terahertz Dressed State with Phase-Locked Wave Functions. Phys Rev Lett 2016; 117:277402. [PMID: 28084756 DOI: 10.1103/physrevlett.117.277402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2016] [Indexed: 06/06/2023]
Abstract
The coherent interaction of light with matter imprints the phase information of the light field on the wave function of the photon-dressed electronic state. A driving electric field, together with a stable phase that is associated with the optical probe pulses, enables the role of the dressed state in the optical response to be investigated. We observed optical absorption strengths modulated on a subcycle time scale in a GaAs quantum well in the presence of a multicycle terahertz driving pulse using a near-infrared probe pulse. The measurements were in good agreement with the analytical formula that accounts for the optical susceptibilities caused by the dressed state of the excitons, which indicates that the output probe intensity was coherently reshaped by the excitonic sideband emissions.
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Affiliation(s)
- K Uchida
- Institute for Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
- Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
| | - T Otobe
- Kansai Photon Science Institute, National Institutes for Quantum and Radiological Science and Technology, Kizugawa, Kyoto 619-0615, Japan
| | - T Mochizuki
- Fukushima Renewable Energy Institute, National Institute of Advanced Industrial Science and Technology, Koriyama, Fukushima 963-0298, Japan
| | - C Kim
- Institute for Solid State Physics, the University of Tokyo, and JST-CREST, Kashiwa, Chiba 277-8581, Japan
| | - M Yoshita
- Institute for Solid State Physics, the University of Tokyo, and JST-CREST, Kashiwa, Chiba 277-8581, Japan
| | - H Akiyama
- Institute for Solid State Physics, the University of Tokyo, and JST-CREST, Kashiwa, Chiba 277-8581, Japan
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K Tanaka
- Institute for Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
- Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
| | - H Hirori
- Institute for Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
- Precursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
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42
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Mueed MA, Kamburov D, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States. Phys Rev Lett 2016; 117:246801. [PMID: 28009213 DOI: 10.1103/physrevlett.117.246801] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 06/06/2023]
Abstract
Via the application of a parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells and study the geometric resonance of composite fermions (CFs) with a periodic density modulation in our samples. The measurements reveal that CFs exist close to bilayer quantum Hall states, formed at Landau level filling factors ν=1 and 1/2. Near ν=1, the geometric resonance features are consistent with half the total electron density in the bilayer system, implying that CFs prefer to stay in separate layers and exhibit a two-component behavior. In contrast, close to ν=1/2, CFs appear single-layer-like (single component) as their resonance features correspond to the total density.
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Affiliation(s)
- M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D Kamburov
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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43
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Liu Y, Hasdemir S, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Observation of an Anisotropic Wigner Crystal. Phys Rev Lett 2016; 117:106802. [PMID: 27636486 DOI: 10.1103/physrevlett.117.106802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2016] [Indexed: 06/06/2023]
Abstract
We report a new correlated phase of two-dimensional charged carriers in high magnetic fields, manifested by an anisotropic insulating behavior at low temperatures. It appears in a large range of low Landau level fillings 1/3≲ν≲2/3 in hole systems confined to wide GaAs quantum wells when the sample is tilted in magnetic field to an intermediate angle. The parallel field component (B_{∥}) leads to a crossing of the lowest two Landau levels, and an elongated hole wave function in the direction of B_{∥}. Under these conditions, the in-plane resistance exhibits an insulating behavior, with the resistance along B_{∥} about 10 times smaller than the resistance perpendicular to B_{∥}. We interpret this anisotropic insulating phase as a two-component, striped Wigner crystal.
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Affiliation(s)
- Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S Hasdemir
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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44
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Deng H, Liu Y, Jo I, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Commensurability Oscillations of Composite Fermions Induced by the Periodic Potential of a Wigner Crystal. Phys Rev Lett 2016; 117:096601. [PMID: 27610870 DOI: 10.1103/physrevlett.117.096601] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2016] [Indexed: 06/06/2023]
Abstract
When the kinetic energy of a collection of interacting two-dimensional (2D) electrons is quenched at very high magnetic fields so that the Coulomb repulsion dominates, the electrons are expected to condense into an ordered array, forming a quantum Wigner crystal (WC). Although this exotic state has long been suspected in high-mobility 2D electron systems at very low Landau level fillings (ν≪1), its direct observation has been elusive. Here we present a new technique and experimental results directly probing the magnetic-field-induced WC. We measure the magnetoresistance of a bilayer electron system where one layer has a very low density and is in the WC regime (ν≪1), while the other ("probe") layer is near ν=1/2 and hosts a sea of composite fermions (CFs). The data exhibit commensurability oscillations in the magnetoresistance of the CF layer, induced by the periodic potential of WC electrons in the other layer, and provide a unique, direct glimpse at the symmetry of the WC, its lattice constant, and melting. They also demonstrate a striking example of how one can probe an exotic many-body state of 2D electrons using equally exotic quasiparticles of another many-body state.
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Affiliation(s)
- H Deng
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - Y Liu
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - I Jo
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
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45
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Mueed MA, Hossain MS, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Reorientation of the Stripe Phase of 2D Electrons by a Minute Density Modulation. Phys Rev Lett 2016; 117:076803. [PMID: 27563985 DOI: 10.1103/physrevlett.117.076803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2016] [Indexed: 06/06/2023]
Abstract
Interacting two-dimensional electrons confined in a GaAs quantum well exhibit isotropic transport when the Fermi level resides in the first excited (N=1) Landau level. Adding an in-plane magnetic field (B_{||}) typically leads to an anisotropic, stripelike (nematic) phase of electrons with the stripes oriented perpendicular to the B_{||} direction. Our experimental data reveal how a periodic density modulation, induced by a surface strain grating from strips of negative electron-beam resist, competes against the B_{||}-induced orientational order of the stripe phase. Even a minute (<0.25%) density modulation is sufficient to reorient the stripes along the direction of the surface grating.
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Affiliation(s)
- M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Md Shafayat Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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46
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Levy AL, Wurstbauer U, Kuznetsova YY, Pinczuk A, Pfeiffer LN, West KW, Manfra MJ, Gardner GC, Watson JD. Optical Emission Spectroscopy Study of Competing Phases of Electrons in the Second Landau Level. Phys Rev Lett 2016; 116:016801. [PMID: 26799037 DOI: 10.1103/physrevlett.116.016801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2015] [Indexed: 06/05/2023]
Abstract
Quantum phases of electrons in the filling factor range 2≤ν≤3 are probed by the weak optical emission from the partially populated second Landau level and spin wave measurements. Observations of optical emission include a multiplet of sharp peaks that exhibit a strong filling factor dependence. Spin wave measurements by resonant inelastic light scattering probe breaking of spin rotational invariance and are used to link this optical emission with collective phases of electrons. A remarkably rapid interplay between emission peak intensities manifests phase competition in the second Landau level.
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Affiliation(s)
- A L Levy
- Department of Physics, Columbia University, New York, New York 10027, USA
| | - U Wurstbauer
- Walter Schottky Institut and Physik-Department, Technische Universität München, Am Coulombwall 4a, 85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Munich, Germany
| | - Y Y Kuznetsova
- Department of Physics, Columbia University, New York, New York 10027, USA
| | - A Pinczuk
- Department of Physics, Columbia University, New York, New York 10027, USA
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M J Manfra
- Department of Physics and Astronomy, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - G C Gardner
- School of Materials Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - J D Watson
- Department of Physics and Astronomy, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
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47
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Hatke AT, Liu Y, Engel LW, Shayegan M, Pfeiffer LN, West KW, Baldwin KW. Microwave spectroscopy of the low-filling-factor bilayer electron solid in a wide quantum well. Nat Commun 2015; 6:7071. [PMID: 25947282 PMCID: PMC4432649 DOI: 10.1038/ncomms8071] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2014] [Accepted: 03/28/2015] [Indexed: 11/30/2022] Open
Abstract
At the low Landau filling factor termination of the fractional quantum Hall effect series, two-dimensional electron systems exhibit an insulating phase that is understood as a form of pinned Wigner solid. Here we use microwave spectroscopy to probe the transition to the insulator for a wide quantum well sample that can support single-layer or bilayer states depending on its overall carrier density. We find that the insulator exhibits a resonance which is characteristic of a bilayer solid. The resonance also reveals a pair of transitions within the solid, which are not accessible to dc transport measurements. As density is biased deeper into the bilayer solid regime, the resonance grows in specific intensity, and the transitions within the insulator disappear. These behaviours are suggestive of a picture of the insulating phase as an emulsion of liquid and solid components. In 2D electron gases, insulating behaviour at low fractional quantum Hall filling factors is understood by the formation of an electronic Wigner solid. Here, the authors use microwave spectroscopy to evidence an electron liquid–solid mixed phase in bilayer states of GaAs/AlGaAs wide quantum wells.
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Affiliation(s)
- A T Hatke
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - Y Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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48
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Mueed MA, Kamburov D, Liu Y, Shayegan M, Pfeiffer LN, West KW, Baldwin KW, Winkler R. Composite fermions with a warped Fermi contour. Phys Rev Lett 2015; 114:176805. [PMID: 25978251 DOI: 10.1103/physrevlett.114.176805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2014] [Indexed: 06/04/2023]
Abstract
Via measurements of commensurability features near the Landau filling factor ν=1/2, we probe the shape of the Fermi contour for hole-flux composite fermions confined to a wide GaAs quantum well. The data reveal that the composite fermions are strongly influenced by the characteristics of the Landau level in which they are formed. In particular, their Fermi contour is warped when their Landau level originates from a hole band with significant warping.
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Affiliation(s)
- M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D Kamburov
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
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49
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Dorozhkin SI, Umansky V, Pfeiffer LN, West KW, Baldwin K, von Klitzing K, Smet JH. Random flips of electric field in microwave-induced states with spontaneously broken symmetry. Phys Rev Lett 2015; 114:176808. [PMID: 25978254 DOI: 10.1103/physrevlett.114.176808] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2014] [Indexed: 06/04/2023]
Abstract
In a two-dimensional electron system subject to microwaves and a magnetic field, photovoltages emerge. They can be separated into two components originating from built-in electric fields and electric field domains arising from spontaneous symmetry breaking. The latter occurs in the zero resistance regime only and manifests itself in pulsed behavior, synchronous across the sample. The pulses show sign reversal. This implies a flip of the field in each domain, consistent with the existence of two equally probable electric field domain configurations due to the spontaneous symmetry breaking.
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Affiliation(s)
- S I Dorozhkin
- Institute of Solid State Physics, Chernogolovka, Moscow District 142432, Russia
| | - V Umansky
- Department of Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
| | - L N Pfeiffer
- Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974, USA
| | - K W West
- Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974, USA
| | - K Baldwin
- Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974, USA
| | - K von Klitzing
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - J H Smet
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
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50
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Kleinbaum E, Kumar A, Pfeiffer LN, West KW, Csáthy GA. Gap reversal at filling factors 3+1/3 and 3+1/5: towards novel topological order in the fractional quantum Hall regime. Phys Rev Lett 2015; 114:076801. [PMID: 25763967 DOI: 10.1103/physrevlett.114.076801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Indexed: 06/04/2023]
Abstract
In the region of the second Landau level several theories predict fractional quantum Hall states with novel topological order. We report the opening of an energy gap at the filling factor ν=3+1/3, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the ν=3+1/3 and 3+1/5 states from the upper spin branch are reversed when compared to the ν=2+1/3 and 2+1/5 counterpart states in the lower spin branch. Our findings raise the possibility that at least one of the former states is of an unusual topological order.
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Affiliation(s)
- Ethan Kleinbaum
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Ashwani Kumar
- Department of Physics, Monmouth College, Monmouth, Illinois 61462, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - G A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
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