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Rosen IT, Andersen MP, Rodenbach LK, Tai L, Zhang P, Wang KL, Kastner MA, Goldhaber-Gordon D. Measured Potential Profile in a Quantum Anomalous Hall System Suggests Bulk-Dominated Current Flow. PHYSICAL REVIEW LETTERS 2022; 129:246602. [PMID: 36563259 DOI: 10.1103/physrevlett.129.246602] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2022] [Revised: 09/20/2022] [Accepted: 11/04/2022] [Indexed: 06/17/2023]
Abstract
Ideally, quantum anomalous Hall systems should display zero longitudinal resistance. Yet in experimental quantum anomalous Hall systems elevated temperature can make the longitudinal resistance finite, indicating dissipative flow of electrons. Here, we show that the measured potentials at multiple locations within a device at elevated temperature are well described by solution of Laplace's equation, assuming spatially uniform conductivity, suggesting nonequilibrium current flows through the two-dimensional bulk. Extrapolation suggests that at even lower temperatures current may still flow primarily through the bulk rather than, as had been assumed, through edge modes. An argument for bulk current flow previously applied to quantum Hall systems supports this picture.
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Affiliation(s)
- Ilan T Rosen
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Molly P Andersen
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
| | - Linsey K Rodenbach
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Lixuan Tai
- Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Peng Zhang
- Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Kang L Wang
- Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - M A Kastner
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - David Goldhaber-Gordon
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Department of Physics, Stanford University, Stanford, California 94305, USA
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2
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Ella L, Rozen A, Birkbeck J, Ben-Shalom M, Perello D, Zultak J, Taniguchi T, Watanabe K, Geim AK, Ilani S, Sulpizio JA. Simultaneous voltage and current density imaging of flowing electrons in two dimensions. NATURE NANOTECHNOLOGY 2019; 14:480-487. [PMID: 30858521 DOI: 10.1038/s41565-019-0398-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Accepted: 01/31/2019] [Indexed: 06/09/2023]
Abstract
A variety of physical phenomena associated with nanoscale electron transport often results in non-trivial spatial voltage and current patterns, particularly in nonlocal transport regimes. While numerous techniques have been devised to image electron flows, the need remains for a nanoscale probe capable of simultaneously imaging current and voltage distributions with high sensitivity and minimal invasiveness, in a magnetic field, across a broad range of temperatures and beneath an insulating surface. Here we present a technique for spatially mapping electron flows based on a nanotube single-electron transistor, which achieves high sensitivity for both voltage and current imaging. In a series of experiments using high-mobility graphene devices, we demonstrate the ability of our technique to visualize local aspects of intrinsically nonlocal transport, as in ballistic flows, which are not easily resolvable via existing methods. This technique should aid in understanding the physics of two-dimensional electronic devices and enable new classes of experiments that image electron flow through buried nanostructures in the quantum and interaction-dominated regimes.
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Affiliation(s)
- Lior Ella
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Asaf Rozen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - John Birkbeck
- School of Physics and Astronomy, University of Manchester, Manchester, UK
- National Graphene Institute, University of Manchester, Manchester, UK
| | - Moshe Ben-Shalom
- School of Physics and Astronomy, University of Manchester, Manchester, UK
- National Graphene Institute, University of Manchester, Manchester, UK
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel
| | - David Perello
- School of Physics and Astronomy, University of Manchester, Manchester, UK
- National Graphene Institute, University of Manchester, Manchester, UK
| | - Johanna Zultak
- School of Physics and Astronomy, University of Manchester, Manchester, UK
- National Graphene Institute, University of Manchester, Manchester, UK
| | | | - Kenji Watanabe
- National Institute for Materials Science, Tsukuba, Japan
| | - Andre K Geim
- School of Physics and Astronomy, University of Manchester, Manchester, UK
- National Graphene Institute, University of Manchester, Manchester, UK
| | - Shahal Ilani
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Joseph A Sulpizio
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel.
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Lin X, Du R, Xie X. Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene. Natl Sci Rev 2014. [DOI: 10.1093/nsr/nwu071] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Abstract
The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.
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Affiliation(s)
- Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ruirui Du
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xincheng Xie
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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4
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Martin AM, Benedict KA, Sheard FW, Eaves L. Model for the voltage steps in the breakdown of the integer quantum Hall effect. PHYSICAL REVIEW LETTERS 2003; 91:126803. [PMID: 14525386 DOI: 10.1103/physrevlett.91.126803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2002] [Revised: 03/12/2003] [Indexed: 05/24/2023]
Abstract
In samples used to maintain the U.S. resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the generation of magnetoexcitons when the quantum Hall fluid flows past an ionized impurity above a critical velocity. The calculated generation rate gives a voltage step height in good agreement with measurements on both electron and hole gases. We also compare this model to a hydrodynamic description of breakdown.
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Affiliation(s)
- A M Martin
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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Abstract
The edge of a two-dimensional electron system in a magnetic field consists of one-dimensional channels that arise from the confining electric field at the edge of the system. The crossed electric and magnetic fields cause electrons to drift parallel to the sample boundary, creating a chiral current that travels along the edge in only one direction. In an ideal two-dimensional electron system in the quantum Hall regime, all the current flows along the edge. Quantization of the Hall resistance arises from occupation of N one-dimensional edge channels, each contributing a conductance of e2/h. Here we report differential conductance measurements, in the integer quantum Hall regime, of tunnelling between the edges of a pair of two-dimensional electron systems that are separated by an atomically precise, high-quality, tunnel barrier. The resultant interaction between the edge states leads to the formation of new energy gaps and an intriguing dispersion relation for electrons travelling along the barrier: for example, we see a persistent conductance peak at zero bias voltage and an absence of tunnelling features due to electron spin. These features are unexpected and are not consistent with a model of weakly interacting edge states. Remnant disorder along the barrier and charge screening may each play a role, although detailed numerical studies will be required to elucidate these effects.
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Rahman M, Davies JH, Larkin IA, Holland MC, Long AR, Williamson JG. Edge and bulk transport in variably connected quantum Hall conductor. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:16409-16412. [PMID: 9985756 DOI: 10.1103/physrevb.54.16409] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Blom FA, Wolter JH. Imaging of edge channels in the integer quantum Hall regime by the lateral photoelectric effect. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:5760-5766. [PMID: 9981763 DOI: 10.1103/physrevb.52.5760] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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8
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Blom FA, Wolter JH. Direct observation of edge channels in the integer quantum hall regime. PHYSICAL REVIEW LETTERS 1995; 74:1198-1201. [PMID: 10058959 DOI: 10.1103/physrevlett.74.1198] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Mao JM, Xie SS, Gu BY, Yang GZ. Far-infrared radiation-induced inter-edge-channel scattering in a high magnetic field. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:10924-10931. [PMID: 9975196 DOI: 10.1103/physrevb.50.10924] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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10
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Takagaki Y, Friedland KJ, Herfort J, Kostial H, Ploog K. Inter-edge-state scattering in the spin-polarized quantum Hall regime with current injection into inner states. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:4456-4462. [PMID: 9976747 DOI: 10.1103/physrevb.50.4456] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Maessen RT, Blom FA, Wolter JH. Edge-channel transport in the presence of a lateral concentration gradient in the two-dimensional electron gas. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:17897-17901. [PMID: 10008423 DOI: 10.1103/physrevb.48.17897] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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12
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Blom FA, Wolter JH. Separation of edge channels by a macroscopic distance in a half-gated GaAs/AlxGa1-xAs heterostructure. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:15700-15704. [PMID: 10005964 DOI: 10.1103/physrevb.47.15700] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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13
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Merz R, Keilmann F, Haug RJ, Ploog K. Nonequilibrium edge-state transport resolved by far-infrared microscopy. PHYSICAL REVIEW LETTERS 1993; 70:651-653. [PMID: 10054168 DOI: 10.1103/physrevlett.70.651] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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