1
|
Moosavi P. Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids. PHYSICAL REVIEW LETTERS 2023; 131:100401. [PMID: 37739371 DOI: 10.1103/physrevlett.131.100401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 06/01/2023] [Accepted: 07/12/2023] [Indexed: 09/24/2023]
Abstract
We study inhomogeneous 1+1-dimensional quantum many-body systems described by Tomonaga-Luttinger-liquid theory with general propagation velocity and Luttinger parameter varying smoothly in space, equivalent to an inhomogeneous compactification radius for free boson conformal field theory. This model appears prominently in low-energy descriptions, including for trapped ultracold atoms, while here we present an application to quantum Hall edges with inhomogeneous interactions. The dynamics is shown to be governed by a pair of coupled continuity equations identical to inhomogeneous Dirac-Bogoliubov-de Gennes equations with a local gap and solved by analytical means. We obtain their exact Green's functions and scattering matrix using a Magnus expansion, which generalize previous results for conformal interfaces and quantum wires coupled to leads. Our results explicitly describe the late-time evolution following quantum quenches, including inhomogeneous interaction quenches, and Andreev reflections between coupled quantum Hall edges, revealing remarkably universal dependence on details at stationarity or at late times out of equilibrium.
Collapse
Affiliation(s)
- Per Moosavi
- Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland
| |
Collapse
|
2
|
Glidic P, Maillet O, Piquard C, Aassime A, Cavanna A, Jin Y, Gennser U, Anthore A, Pierre F. Quasiparticle Andreev scattering in the ν = 1/3 fractional quantum Hall regime. Nat Commun 2023; 14:514. [PMID: 36720855 PMCID: PMC9889737 DOI: 10.1038/s41467-023-36080-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 01/12/2023] [Indexed: 02/02/2023] Open
Abstract
The scattering of exotic quasiparticles may follow different rules than electrons. In the fractional quantum Hall regime, a quantum point contact (QPC) provides a source of quasiparticles with field effect selectable charges and statistics, which can be scattered on an 'analyzer' QPC to investigate these rules. Remarkably, for incident quasiparticles dissimilar to those naturally transmitted across the analyzer, electrical conduction conserves neither the nature nor the number of the quasiparticles. In contrast with standard elastic scattering, theory predicts the emergence of a mechanism akin to the Andreev reflection at a normal-superconductor interface. Here, we observe the predicted Andreev-like reflection of an e/3 quasiparticle into a - 2e/3 hole accompanied by the transmission of an e quasielectron. Combining shot noise and cross-correlation measurements, we independently determine the charge of the different particles and ascertain the coincidence of quasielectron and fractional hole. The present work advances our understanding on the unconventional behavior of fractional quasiparticles, with implications toward the generation of novel quasi-particles/holes and non-local entanglements.
Collapse
Affiliation(s)
- P Glidic
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - O Maillet
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - C Piquard
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - A Aassime
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - A Cavanna
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - Y Jin
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - U Gennser
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - A Anthore
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France.
- Université Paris Cité, CNRS, Centre de Nanosciences et de Nanotechnologies, F-91120, Palaiseau, France.
| | - F Pierre
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France.
| |
Collapse
|
3
|
Kane CL. Quantized Nonlinear Conductance in Ballistic Metals. PHYSICAL REVIEW LETTERS 2022; 128:076801. [PMID: 35244424 DOI: 10.1103/physrevlett.128.076801] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2021] [Revised: 01/11/2022] [Accepted: 01/12/2022] [Indexed: 06/14/2023]
Abstract
We introduce a nonlinear frequency-dependent D+1 terminal conductance that characterizes a D-dimensional Fermi gas, generalizing the Landauer conductance in D=1. For a 2D ballistic conductor, we show that this conductance is quantized and probes the Euler characteristic of the Fermi sea. We critically address the roles of electrical contacts and Fermi liquid interactions, and we propose experiments on 2D Dirac materials, such as graphene, using a triple point contact geometry.
Collapse
Affiliation(s)
- C L Kane
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| |
Collapse
|
4
|
Yutushui M, Stern A, Mross DF. Identifying the ν=5/2 Topological Order through Charge Transport Measurements. PHYSICAL REVIEW LETTERS 2022; 128:016401. [PMID: 35061467 DOI: 10.1103/physrevlett.128.016401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2021] [Accepted: 10/27/2021] [Indexed: 06/14/2023]
Abstract
We propose an experiment to identify the topological order of the ν=5/2 state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing ν=2,5/2, and 3 in the same device. Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measurements. Additionally, it distinguishes between the Moore-Read and anti-Pfaffian topological orders, which are favored by numerical calculations.
Collapse
Affiliation(s)
- Misha Yutushui
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - David F Mross
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| |
Collapse
|
5
|
Feldman DE, Halperin BI. Fractional charge and fractional statistics in the quantum Hall effects. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:076501. [PMID: 34015771 DOI: 10.1088/1361-6633/ac03aa] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 05/20/2021] [Indexed: 06/12/2023]
Abstract
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.
Collapse
Affiliation(s)
- D E Feldman
- Brown Theoretical Physics Center and Department of Physics, Brown University, Providence, RI 02912, United States of America
| | - Bertrand I Halperin
- Department of Physics, Harvard University, Cambridge, MA 02138, United States of America
| |
Collapse
|
6
|
Lin C, Hashisaka M, Akiho T, Muraki K, Fujisawa T. Quantized charge fractionalization at quantum Hall Y junctions in the disorder dominated regime. Nat Commun 2021; 12:131. [PMID: 33408325 PMCID: PMC7788083 DOI: 10.1038/s41467-020-20395-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2020] [Accepted: 12/02/2020] [Indexed: 11/09/2022] Open
Abstract
Fractionalization is a phenomenon where an elementary excitation partitions into several pieces. This picture explains non-trivial transport through a junction of one-dimensional edge channels defined by topologically distinct quantum Hall states, for example, a hole-conjugate state at Landau-level filling factor ν = 2/3. Here we employ a time-resolved scheme to identify an elementary fractionalization process; injection of charge q from a non-interaction region into an interacting and scattering region of one-dimensional channels results in the formation of a collective excitation with charge (1-r)q by reflecting fractionalized charge rq. The fractionalization factors, r = 0.34 ± 0.03 for ν = 2/3 and r = 0.49 ± 0.03 for ν = 2, are consistent with the quantized values of 1/3 and 1/2, respectively, which are expected in the disorder dominated regime. The scheme can be used for generating and transporting fractionalized charges with a well-defined time course along a well-defined path.
Collapse
Affiliation(s)
- Chaojing Lin
- Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo, 152-8551, Japan.
- Tokyo Tech Academy for Super Smart Society, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo, 152-8551, Japan.
| | - Masayuki Hashisaka
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa, 243-0198, Japan
| | - Takafumi Akiho
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa, 243-0198, Japan
| | - Koji Muraki
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa, 243-0198, Japan
| | - Toshimasa Fujisawa
- Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo, 152-8551, Japan.
| |
Collapse
|
7
|
Di Carli A, Henderson G, Flannigan S, Colquhoun CD, Mitchell M, Oppo GL, Daley AJ, Kuhr S, Haller E. Collisionally Inhomogeneous Bose-Einstein Condensates with a Linear Interaction Gradient. PHYSICAL REVIEW LETTERS 2020; 125:183602. [PMID: 33196233 DOI: 10.1103/physrevlett.125.183602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2019] [Accepted: 09/23/2020] [Indexed: 06/11/2023]
Abstract
We study the evolution of a collisionally inhomogeneous matter wave in a spatial gradient of the interaction strength. Starting with a Bose-Einstein condensate with weak repulsive interactions in quasi-one-dimensional geometry, we monitor the evolution of a matter wave that simultaneously extends into spatial regions with attractive and repulsive interactions. We observe the formation and the decay of solitonlike density peaks, counterpropagating self-interfering wave packets, and the creation of cascades of solitons. The matter-wave dynamics is well reproduced in numerical simulations based on the nonpolynomial Schrödinger equation with three-body loss, allowing us to better understand the underlying behavior based on a wavelet transformation. Our analysis provides new understanding of collapse processes for solitons, and opens interesting connections to other nonlinear instabilities.
Collapse
Affiliation(s)
- Andrea Di Carli
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Grant Henderson
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Stuart Flannigan
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Craig D Colquhoun
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Matthew Mitchell
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Gian-Luca Oppo
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Andrew J Daley
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Stefan Kuhr
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Elmar Haller
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| |
Collapse
|
8
|
Filippone M, Marguerite A, Le Hur K, Fève G, Mora C. Phase-Coherent Dynamics of Quantum Devices with Local Interactions. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E847. [PMID: 33286618 PMCID: PMC7517448 DOI: 10.3390/e22080847] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Revised: 06/21/2020] [Accepted: 07/02/2020] [Indexed: 11/16/2022]
Abstract
This review illustrates how Local Fermi Liquid (LFL) theories describe the strongly correlated and coherent low-energy dynamics of quantum dot devices. This approach consists in an effective elastic scattering theory, accounting exactly for strong correlations. Here, we focus on the mesoscopic capacitor and recent experiments achieving a Coulomb-induced quantum state transfer. Extending to out-of-equilibrium regimes, aimed at triggered single electron emission, we illustrate how inelastic effects become crucial, requiring approaches beyond LFLs, shedding new light on past experimental data by showing clear interaction effects in the dynamics of mesoscopic capacitors.
Collapse
Affiliation(s)
- Michele Filippone
- Department of Quantum Matter Physics, University of Geneva 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
| | - Arthur Marguerite
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel;
| | - Karyn Le Hur
- CPHT, CNRS, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France;
| | - Gwendal Fève
- Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France;
| | - Christophe Mora
- Laboratoire Matériaux et Phénomènes Quantiques, CNRS, Université de Paris, F-75013 Paris, France;
| |
Collapse
|
9
|
Acciai M, Calzona A, Carrega M, Sassetti M. Spectral features of voltage pulses in interacting helical channels. EPJ WEB OF CONFERENCES 2020. [DOI: 10.1051/epjconf/202023000009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the interplay of voltage-driven excitations and electron-electron interactions in a pair of counterpropagating helical channels capacitively coupled to a time-dependent gate. By focusing on the non-equilibrium spectral properties of the system, we show how the spectral function is modified by external drives with different time profile in presence of Coulomb interactions. In particular, we focus on a Lorentzian drive and a square single pulse. In presence of strong enough electron-electron interactions, we find that both drives can result in minimal excitations, i.e. characterized by an excess spectral function with a definite sign. This is in contrast with what happens in the non-interacting case, where only properly quantized Lorentzian pulses are able to produce minimal excitations.
Collapse
|
10
|
Väyrynen JI, Goldstein M, Gefen Y. Superconducting Correlations Out of Repulsive Interactions on a Fractional Quantum Hall Edge. PHYSICAL REVIEW LETTERS 2019; 122:236802. [PMID: 31298920 DOI: 10.1103/physrevlett.122.236802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Revised: 05/06/2019] [Indexed: 06/10/2023]
Abstract
We consider a fractional quantum Hall bilayer system with an interface between quantum Hall states of filling fractions (ν_{top},ν_{bottom})=(1,1) and (1/3,2), motivated by a recent approach to engineering artificial edges [Y. Ronen et al., Nat. Phys. 14, 411 (2018)NPAHAX1745-247310.1038/s41567-017-0035-2]. We show that random tunneling and strong repulsive interactions within one of the layers will drive the system to a stable fixed point with two counterpropagating charge modes which have attractive interactions. As a result, slowly decaying correlations on the edge become predominantly superconducting. We discuss the resulting observable effects and derive general requirements for electron attraction in Abelian quantum Hall states. The broader interest in fractional quantum Hall edge with quasi-long-range superconducting order lies in the prospects of hosting exotic anyonic boundary excitations, which may serve as a platform for topological quantum computation.
Collapse
Affiliation(s)
- Jukka I Väyrynen
- Microsoft Quantum, Microsoft Station Q, University of California, Santa Barbara, California 93106-6105, USA
| | - Moshe Goldstein
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| |
Collapse
|
11
|
Štrkalj A, Ferguson MS, Wolf TMR, Levkivskyi I, Zilberberg O. Tunneling into a Finite Luttinger Liquid Coupled to Noisy Capacitive Leads. PHYSICAL REVIEW LETTERS 2019; 122:126802. [PMID: 30978091 DOI: 10.1103/physrevlett.122.126802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2018] [Revised: 01/11/2019] [Indexed: 06/09/2023]
Abstract
Tunneling spectroscopy of one-dimensional interacting wires can be profoundly sensitive to the boundary conditions of the wire. Here, we analyze the tunneling spectroscopy of a wire coupled to capacitive metallic leads. Strikingly, with increasing many-body interactions in the wire, the impact of the boundary noise becomes more prominent. This interplay allows for a smooth crossover from standard 1D tunneling signatures into a regime where the tunneling is dominated by the fluctuations at the leads. This regime is characterized by an elevated zero-bias tunneling alongside a universal power-law decay at high energies. Furthermore, local tunneling measurements in this regime show a unique spatial dependence that marks the formation of plasmonic standing waves in the wire. Our result offers a tunable method by which to control the boundary effects and measure the interaction strength (Luttinger parameter) within the wire.
Collapse
Affiliation(s)
- Antonio Štrkalj
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | | | - Tobias M R Wolf
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Ivan Levkivskyi
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Oded Zilberberg
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| |
Collapse
|
12
|
Horovitz B, Giamarchi T, Le Doussal P. Transconducting Transition for a Dynamic Boundary Coupled to Several Luttinger Liquids. PHYSICAL REVIEW LETTERS 2018; 121:166803. [PMID: 30387677 DOI: 10.1103/physrevlett.121.166803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2018] [Indexed: 06/08/2023]
Abstract
We study a dynamic boundary, e.g., a mobile impurity, coupled to N independent Tomonaga-Luttinger liquids (TLLs) each with interaction parameter K. We demonstrate that for N≥2 there is a quantum phase transition at K≥1/2, where the TLL phases lock together at the particle position, resulting in a nonzero transconductance equal to e^{2}/Nh. The transition line terminates for strong coupling at K=1-(1/N), consistent with results at large N. Another type of a dynamic boundary is a superconducting (or a Bose-Einstein condensate) grain coupled to N≥2 TLLs; here the transition signals also the onset of a relevant Josephson coupling.
Collapse
Affiliation(s)
- B Horovitz
- Department of Physics, Ben Gurion University, Beer Sheva 84105, Israel
| | - T Giamarchi
- DPMC-MaNEP, University of Geneva, 24 Quai Ernest Ansermet, 1211 Geneva 4, Switzerland
| | - P Le Doussal
- Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, PSL University CNRS, Sorbonne Universités, 24 rue Lhomond, 75231 Paris Cedex 05, France
| |
Collapse
|
13
|
Roussely G, Arrighi E, Georgiou G, Takada S, Schalk M, Urdampilleta M, Ludwig A, Wieck AD, Armagnat P, Kloss T, Waintal X, Meunier T, Bäuerle C. Unveiling the bosonic nature of an ultrashort few-electron pulse. Nat Commun 2018; 9:2811. [PMID: 30022067 PMCID: PMC6052057 DOI: 10.1038/s41467-018-05203-7] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Accepted: 06/12/2018] [Indexed: 11/09/2022] Open
Abstract
Quantum dynamics is very sensitive to dimensionality. While two-dimensional electronic systems form Fermi liquids, one-dimensional systems—Tomonaga–Luttinger liquids—are described by purely bosonic excitations, even though they are initially made of fermions. With the advent of coherent single-electron sources, the quantum dynamics of such a liquid is now accessible at the single-electron level. Here, we report on time-of-flight measurements of ultrashort few-electron charge pulses injected into a quasi one-dimensional quantum conductor. By changing the confinement potential we can tune the system from the one-dimensional Tomonaga–Luttinger liquid limit to the multi-channel Fermi liquid and show that the plasmon velocity can be varied over almost an order of magnitude. These results are in quantitative agreement with a parameter-free theory and demonstrate a powerful probe for directly investigating real-time dynamics of fractionalisation phenomena in low-dimensional conductors. Electronic excitations in low-dimensional quantum nanoelectronic devices are collective waves that are strongly affected by the Coulomb interaction. Here, the authors demonstrate that they are able to prepare these collective excitations down to the single electron level and control their propagation.
Collapse
Affiliation(s)
- Gregoire Roussely
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Everton Arrighi
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Giorgos Georgiou
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.,Univ. Savoie Mont-Blanc, CNRS, IMEP-LAHC, 73370, Le Bourget du Lac, France
| | - Shintaro Takada
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.,National Institute of Advanced Industrial Science and Technology (AIST), National Metrology Institute of Japan (NMIJ), Tsukuba, Ibaraki, 305-8563, Japan
| | - Martin Schalk
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Matias Urdampilleta
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Arne Ludwig
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780, Bochum, Germany
| | - Andreas D Wieck
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780, Bochum, Germany
| | - Pacome Armagnat
- Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France
| | - Thomas Kloss
- Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France
| | - Xavier Waintal
- Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France
| | - Tristan Meunier
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Christopher Bäuerle
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.
| |
Collapse
|
14
|
Bäuerle C, Christian Glattli D, Meunier T, Portier F, Roche P, Roulleau P, Takada S, Waintal X. Coherent control of single electrons: a review of current progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:056503. [PMID: 29355831 DOI: 10.1088/1361-6633/aaa98a] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.
Collapse
Affiliation(s)
- Christopher Bäuerle
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | | | | | | | | | | | | | | |
Collapse
|
15
|
Lutchyn RM, Glazman LI. Transport through a Majorana Island in the Strong Tunneling Regime. PHYSICAL REVIEW LETTERS 2017; 119:057002. [PMID: 28949747 DOI: 10.1103/physrevlett.119.057002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Indexed: 06/07/2023]
Abstract
In the presence of Rashba spin-orbit coupling, a magnetic field can drive a proximitized nanowire into a topological superconducting phase [R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010).PRLTAO0031-900710.1103/PhysRevLett.105.077001 and Y. Oreg, G. Refael, and F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010).PRLTAO0031-900710.1103/PhysRevLett.105.177002]. We study the transport properties of such nanowires in the Coulomb blockade regime. The associated with topological superconductivity Majorana modes significantly modify transport and lead to single-electron coherent transmission through the nanowire-a nonlocal signature of topological superconductivity. In this Letter, we focus on the case of strong hybridization of the Majorana modes with normal leads. The induced by hybridization broadening of the Majorana zero-energy states competes with the charging energy, leading to a considerable modification of the Coulomb blockade in a nanowire contacted by two normal leads. We evaluate the two-terminal conductance as a function of the gate voltage, junctions transmission coefficients, and the geometric capacitance of and the induced superconducting gap in the nanowire.
Collapse
Affiliation(s)
- Roman M Lutchyn
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
| | - Leonid I Glazman
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| |
Collapse
|
16
|
Uchino S, Ueda M. Anomalous Transport in the Superfluid Fluctuation Regime. PHYSICAL REVIEW LETTERS 2017; 118:105303. [PMID: 28339264 DOI: 10.1103/physrevlett.118.105303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2016] [Indexed: 06/06/2023]
Abstract
Motivated by a recent experiment in ultracold atoms [S. Krinner et al., Proc. Natl. Acad. Sci. U.S.A. 113, 8144 (2016)PNASA60027-842410.1073/pnas.1601812113], we analyze transport of attractively interacting fermions through a one-dimensional wire near the superfluid transition. We show that in a ballistic regime where the conductance is quantized in the absence of interaction, the conductance is renormalized by superfluid fluctuations in reservoirs. In particular, the particle conductance is strongly enhanced, and the conductance plateau is blurred by emergent bosonic pair transport. For spin transport, in addition to the contact resistance, the wire itself is resistive, leading to a suppression of the measured spin conductance. Our results are qualitatively consistent with the experimental observations.
Collapse
Affiliation(s)
- Shun Uchino
- RIKEN Center for Emergent Matter Science, Wako, Saitama 351-0198, Japan
| | - Masahito Ueda
- RIKEN Center for Emergent Matter Science, Wako, Saitama 351-0198, Japan
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| |
Collapse
|
17
|
Abstract
We study particle and spin transport in a single-mode quantum point contact, using a charge neutral, quantum degenerate Fermi gas with tunable, attractive interactions. This yields the spin and particle conductance of the point contact as a function of chemical potential or confinement. The measurements cover a regime from weak attraction, where quantized conductance is observed, to the resonantly interacting superfluid. Spin conductance exhibits a broad maximum when varying the chemical potential at moderate interactions, which signals the emergence of Cooper pairing. In contrast, the particle conductance is unexpectedly enhanced even before the gas is expected to turn into a superfluid, continuously rising from the plateau at [Formula: see text] for weak interactions to plateau-like features at nonuniversal values as high as [Formula: see text] for intermediate interactions. For strong interactions, the particle conductance plateaus disappear and the spin conductance gets suppressed, confirming the spin-insulating character of a superfluid. Our observations document the breakdown of universal conductance quantization as many-body correlations appear. The observed anomalous quantization challenges a Fermi liquid description of the normal phase, shedding new light on the nature of the strongly attractive Fermi gas.
Collapse
|
18
|
Xie HY, Li H, Chou YZ, Foster MS. Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid. PHYSICAL REVIEW LETTERS 2016; 116:086603. [PMID: 26967434 DOI: 10.1103/physrevlett.116.086603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2016] [Indexed: 06/05/2023]
Abstract
The combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrability-breaking terms.
Collapse
Affiliation(s)
- Hong-Yi Xie
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Heqiu Li
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Yang-Zhi Chou
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| |
Collapse
|
19
|
Husmann D, Uchino S, Krinner S, Lebrat M, Giamarchi T, Esslinger T, Brantut JP. Connecting strongly correlated superfluids by a quantum point contact. Science 2015; 350:1498-501. [DOI: 10.1126/science.aac9584] [Citation(s) in RCA: 87] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
|
20
|
Chou YZ, Levchenko A, Foster MS. Helical Quantum Edge Gears in 2D Topological Insulators. PHYSICAL REVIEW LETTERS 2015; 115:186404. [PMID: 26565481 DOI: 10.1103/physrevlett.115.186404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2015] [Indexed: 06/05/2023]
Abstract
We show that two-terminal transport can measure the Luttinger liquid (LL) parameter K, in helical LLs at the edges of two-dimensional topological insulators (TIs) with Rashba spin-orbit coupling. We consider a Coulomb drag geometry with two coplanar TIs and short-ranged spin-flip interedge scattering. Current injected into one edge loop induces circulation in the second, which floats without leads. In the low-temperature (T→0) perfect drag regime, the conductance is (e^{2}/h)(2K+1)/(K+1). At higher T, we predict a conductivity ~T^{-4K+3}. The conductivity for a single edge is also computed.
Collapse
Affiliation(s)
- Yang-Zhi Chou
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Alex Levchenko
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| |
Collapse
|
21
|
Dóra B, Pollmann F. Absence of Orthogonality Catastrophe after a Spatially Inhomogeneous Interaction Quench in Luttinger Liquids. PHYSICAL REVIEW LETTERS 2015; 115:096403. [PMID: 26371667 DOI: 10.1103/physrevlett.115.096403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2014] [Indexed: 06/05/2023]
Abstract
We investigate the Loschmidt echo, the overlap of the initial and final wave functions of Luttinger liquids after a spatially inhomogeneous interaction quench. In studying the Luttinger model, we obtain an analytic solution of the bosonic Bogoliubov-de Gennes equations after quenching the interactions within a finite spatial region. As opposed to the power-law temporal decay following a potential quench, the interaction quench in the Luttinger model leads to a finite, hardly time-dependent overlap; therefore, no orthogonality catastrophe occurs. The steady state value of the Loschmidt echo after a sudden inhomogeneous quench is the square of the respective adiabatic overlaps. Our results are checked and validated numerically on the XXZ Heisenberg chain.
Collapse
Affiliation(s)
- Balázs Dóra
- Department of Physics and BME-MTA Exotic Quantum Phases Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
| | - Frank Pollmann
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| |
Collapse
|
22
|
Al-Hassanieh KA, Rincón J, Alvarez G, Dagotto E. Spin Andreev-like reflection in metal-Mott insulator heterostructures. PHYSICAL REVIEW LETTERS 2015; 114:066401. [PMID: 25723231 DOI: 10.1103/physrevlett.114.066401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2014] [Indexed: 06/04/2023]
Abstract
Using the time-dependent density-matrix renormalization group (tDMRG), we study the time evolution of electron wave packets in one-dimensional (1D) metal-superconductor heterostructures. The results show Andreev reflection at the interface, as expected. By combining these results with the well-known single-spin-species electron-hole transformation in the Hubbard model, we predict an analogous spin Andreev reflection in metal-Mott insulator heterostructures. This effect is numerically confirmed using 1D tDMRG, but it is expected to also be present in higher dimensions, as well as in more general Hamiltonians. We present an intuitive picture of the spin reflection, analogous to that of Andreev reflection at metal-superconductor interfaces. This allows us to discuss a novel antiferromagnetic proximity effect. Possible experimental realizations are discussed.
Collapse
Affiliation(s)
- K A Al-Hassanieh
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Julián Rincón
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - G Alvarez
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA and Computer Science & Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - E Dagotto
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA and Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
| |
Collapse
|
23
|
Schroer A, Braunecker B, Levy Yeyati A, Recher P. Detection of spin entanglement via spin-charge separation in crossed Tomonaga-Luttinger liquids. PHYSICAL REVIEW LETTERS 2014; 113:266401. [PMID: 25615359 DOI: 10.1103/physrevlett.113.266401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2014] [Indexed: 06/04/2023]
Abstract
We investigate tunneling between two spinful Tomonaga-Luttinger liquids (TLLs) realized, e.g., as two crossed nanowires or quantum Hall edge states. When injecting into each TLL one electron of opposite spin, the dc current measured after the crossing differs for singlet, triplet, or product states. This is a striking new non-Fermi liquid feature because the (mean) current in a noninteracting beam splitter is insensitive to spin entanglement. It can be understood in terms of collective excitations subject to spin-charge separation. This behavior may offer an easier alternative to traditional entanglement detection schemes based on current noise, which we show to be suppressed by the interactions.
Collapse
Affiliation(s)
- Alexander Schroer
- Institut für Mathematische Physik, Technische Universität Braunschweig, D-38106 Braunschweig, Germany
| | - Bernd Braunecker
- Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, United Kingdom
| | - Alfredo Levy Yeyati
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC), and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Patrik Recher
- Institut für Mathematische Physik, Technische Universität Braunschweig, D-38106 Braunschweig, Germany and Interactive Research Center of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan
| |
Collapse
|
24
|
Inoue H, Grivnin A, Ofek N, Neder I, Heiblum M, Umansky V, Mahalu D. Charge fractionalization in the integer quantum Hall effect. PHYSICAL REVIEW LETTERS 2014; 112:166801. [PMID: 24815662 DOI: 10.1103/physrevlett.112.166801] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2014] [Indexed: 06/03/2023]
Abstract
We report an observation, via sensitive shot noise measurements, of charge fractionalization of chiral edge electrons in the integer quantum Hall effect regime. Such fractionalization results solely from interchannel Coulomb interaction, leading electrons to decompose to excitations carrying fractional charges. The experiment was performed by guiding a partitioned current carrying edge channel in proximity to another unbiased edge channel, leading to shot noise in the unbiased edge channel without net current, which exhibited an unconventional dependence on the partitioning. The determination of the fractional excitations, as well as the relative velocities of the two original (prior to the interaction) channels, relied on a recent theory pertaining to this measurement. Our result exemplifies the correlated nature of multiple chiral edge channels in the integer quantum Hall effect regime.
Collapse
Affiliation(s)
- Hiroyuki Inoue
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
| | - Anna Grivnin
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
| | - Nissim Ofek
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Izhar Neder
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, 69978 Tel Aviv, Israel
| | - Moty Heiblum
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
| | - Vladimir Umansky
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
| | - Diana Mahalu
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
| |
Collapse
|
25
|
Kamata H, Kumada N, Hashisaka M, Muraki K, Fujisawa T. Fractionalized wave packets from an artificial Tomonaga-Luttinger liquid. NATURE NANOTECHNOLOGY 2014; 9:177-181. [PMID: 24509659 DOI: 10.1038/nnano.2013.312] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2013] [Accepted: 12/20/2013] [Indexed: 06/03/2023]
Abstract
The model of interacting fermion systems in one dimension known as a Tomonaga-Luttinger liquid (TLL) provides a simple and exactly solvable theoretical framework that predicts various intriguing physical properties. Evidence of a TLL has been observed as power-law behaviour in electronic transport on various types of one-dimensional conductor. However, these measurements, which rely on d.c. transport involving electron tunneling processes, cannot identify the long-awaited hallmark of charge fractionalization, in which an injection of elementary charge e from a non-interacting lead is divided into the non-trivial effective charge e* and the remainder, e-e* (refs 6, 7, 8). Here, we report time-resolved transport measurements on an artificial TLL composed of coupled integer quantum Hall edge channels, in which we successfully identify single charge fractionalization processes. A wave packet of charge q incident from a non-interacting region breaks up into several fractionalized charge wave packets at the edges of the artificial TLL, from which transport eigenmodes can be evaluated directly. These results are informative for elucidating the nature of TLLs and low-energy excitations in the edge channels.
Collapse
Affiliation(s)
- H Kamata
- Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan
| | - N Kumada
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - M Hashisaka
- Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan
| | - K Muraki
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - T Fujisawa
- Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan
| |
Collapse
|
26
|
Scheller CP, Liu TM, Barak G, Yacoby A, Pfeiffer LN, West KW, Zumbühl DM. Possible evidence for helical nuclear spin order in GaAs quantum wires. PHYSICAL REVIEW LETTERS 2014; 112:066801. [PMID: 24580700 DOI: 10.1103/physrevlett.112.066801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2013] [Indexed: 06/03/2023]
Abstract
We present transport measurements of cleaved edge overgrowth GaAs quantum wires. The conductance of the first mode reaches 2e(2)/h at high temperatures T≳10 K, as expected. As T is lowered, the conductance is gradually reduced to 1e(2)/h, becoming T independent at T≲0.1 K, while the device cools far below 0.1 K. This behavior is seen in several wires, is independent of density, and not altered by moderate magnetic fields B. The conductance reduction by a factor of 2 suggests lifting of the electron spin degeneracy in the absence of B. Our results are consistent with theoretical predictions for helical nuclear magnetism in the Luttinger liquid regime.
Collapse
Affiliation(s)
- C P Scheller
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - T-M Liu
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - 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
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| |
Collapse
|
27
|
Milletarì M, Rosenow B. Shot-noise signatures of charge fractionalization in the ν=2 quantum Hall edge. PHYSICAL REVIEW LETTERS 2013; 111:136807. [PMID: 24116806 DOI: 10.1103/physrevlett.111.136807] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2012] [Revised: 07/30/2013] [Indexed: 06/02/2023]
Abstract
We investigate the effect of interactions on shot noise in ν=2 quantum Hall edges, where a repulsive coupling between copropagating edge modes is expected to give rise to charge fractionalization. Using the method of nonequilibrium bosonization, we find that even asymptotically the edge distribution function depends in a sensitive way on the interaction strength between the edge modes. We compute shot noise and the Fano factor from the asymptotic distribution function, and from comparison with a reference model of fractionalized excitations, we find that the Fano factor can be close to the value of the fractionalized charge.
Collapse
Affiliation(s)
- Mirco Milletarì
- Institut für Theoretische Physik, Universität Leipzig, Brüderstrasse 14, D-04103 Leipzig, Germany and Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | | |
Collapse
|
28
|
Altshuler BL, Aleiner IL, Yudson VI. Localization at the edge of a 2D topological insulator by Kondo impurities with random anisotropies. PHYSICAL REVIEW LETTERS 2013; 111:086401. [PMID: 24010457 DOI: 10.1103/physrevlett.111.086401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2013] [Indexed: 06/02/2023]
Abstract
We consider chiral electrons moving along the one-dimensional helical edge of a two-dimensional topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states.
Collapse
Affiliation(s)
- B L Altshuler
- Physics Department, Columbia University, New York, New York 10027, USA
| | | | | |
Collapse
|
29
|
Protopopov IV, Gutman DB, Mirlin AD. Correlations in nonequilibrium Luttinger liquid and singular Fredholm determinants. PHYSICAL REVIEW LETTERS 2013; 110:216404. [PMID: 23745901 DOI: 10.1103/physrevlett.110.216404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2012] [Indexed: 06/02/2023]
Abstract
We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants det(1+ÂB[over ^]), where A(ε) and B(t) have multiple discontinuities in energy and time spaces. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish nonequilibrium Fermi-edge singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing genuinely nonequilibrium quantum correlations between left- and right-moving fermions that have left the interaction region.
Collapse
Affiliation(s)
- I V Protopopov
- Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | | | | |
Collapse
|
30
|
Bocquillon E, Freulon V, Berroir J.M, Degiovanni P, Plaçais B, Cavanna A, Jin Y, Fève G. Separation of neutral and charge modes in one-dimensional chiral edge channels. Nat Commun 2013; 4:1839. [DOI: 10.1038/ncomms2788] [Citation(s) in RCA: 100] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2012] [Accepted: 03/22/2013] [Indexed: 11/09/2022] Open
|
31
|
Jezouin S, Albert M, Parmentier FD, Anthore A, Gennser U, Cavanna A, Safi I, Pierre F. Tomonaga-Luttinger physics in electronic quantum circuits. Nat Commun 2013; 4:1802. [PMID: 23653214 PMCID: PMC3644111 DOI: 10.1038/ncomms2810] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2012] [Accepted: 03/26/2013] [Indexed: 12/02/2022] Open
Abstract
In one-dimensional conductors, interactions result in correlated electronic systems. At low energy, a hallmark signature of the so-called Tomonaga–Luttinger liquids is the universal conductance curve predicted in presence of an impurity. A seemingly different topic is the quantum laws of electricity, when distinct quantum conductors are assembled in a circuit. In particular, the conductances are suppressed at low energy, a phenomenon called dynamical Coulomb blockade. Here we investigate the conductance of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance, and demonstrate a proposed link to Tomonaga–Luttinger physics. We reformulate and establish experimentally a recently derived phenomenological expression for the conductance using a wide range of circuits, including carbon nanotube data obtained elsewhere. By confronting both conductance data and phenomenological expression with the universal Tomonaga–Luttinger conductance curve, we demonstrate experimentally the predicted mapping between dynamical Coulomb blockade and the transport across a Tomonaga–Luttinger liquid with an impurity. When physicists study the characteristics of quantum conductors they usually take great pains to limit the resistance of other elements in the system. But Jezouin et al. show that when a single quantum channel is measured in series with a resistor, it exhibits analogous characteristics to a Tomonaga–Luttinger liquid.
Collapse
Affiliation(s)
- S Jezouin
- CNRS/Univ Paris Diderot (Sorbonne Paris Cité), Laboratoire de Photonique et de Nanostructures, route de Nozay, 91460 Marcoussis, France
| | | | | | | | | | | | | | | |
Collapse
|
32
|
Yurkevich IV, Galda A, Yevtushenko OM, Lerner IV. Duality of weak and strong scatterer in a Luttinger liquid coupled to massless bosons. PHYSICAL REVIEW LETTERS 2013; 110:136405. [PMID: 23581351 DOI: 10.1103/physrevlett.110.136405] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2012] [Indexed: 06/02/2023]
Abstract
We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, ΔWSΔWL=1, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.
Collapse
Affiliation(s)
- Igor V Yurkevich
- Nonlinearity and Complexity Research Group, Aston University, Birmingham B4 7ET, United Kingdom
| | | | | | | |
Collapse
|
33
|
DeGottardi W, Lal S, Vishveshwara S. Charge fractionalization in a mesoscopic ring. PHYSICAL REVIEW LETTERS 2013; 110:026402. [PMID: 23383924 DOI: 10.1103/physrevlett.110.026402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2012] [Indexed: 06/01/2023]
Abstract
We study the fractionalization of an electron tunneling into a strongly interacting electronic one-dimensional ring. As a complement to transport measurements in quantum wires connected to leads, we propose noninvasive measures involving the magnetic field profile around the ring to probe this fractionalization. In particular, we show that the magnetic field squared produced by the electron and the power that it would induce in a detector exhibit anisotropic profiles that depend on the degree of fractionalization. We contrast true fractionalization with two other scenarios which could mimic it-quantum superposition and classical probabilistic electron insertion. We show that the proposed field-dependent measures and those of the persistent current can distinguish between these three scenarios.
Collapse
Affiliation(s)
- Wade DeGottardi
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St., Urbana, Illinois 61801-3080, USA
| | | | | |
Collapse
|
34
|
Ilan R, Cayssol J, Bardarson JH, Moore JE. Nonequilibrium transport through a gate-controlled barrier on the quantum spin Hall edge. PHYSICAL REVIEW LETTERS 2012; 109:216602. [PMID: 23215605 DOI: 10.1103/physrevlett.109.216602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2012] [Indexed: 06/01/2023]
Abstract
The quantum spin Hall insulator is characterized by the presence of gapless helical edge states where the spin of the charge carriers is locked to their direction of motion. In order to probe the properties of the edge modes, we propose a design of a tunable quantum impurity realized by a local gate under an external magnetic field. Using the integrability of the impurity model, the conductance is computed for arbitrary interactions, temperatures and voltages, including the effect of Fermi liquid leads. The result can be used to infer the strength of interactions from transport experiments.
Collapse
Affiliation(s)
- Roni Ilan
- Department of Physics, University of California, Berkeley, California 94720, USA
| | | | | | | |
Collapse
|
35
|
Micklitz T, Levchenko A, Rosch A. Nonlinear conductance of long quantum wires at a conductance plateau transition: where does the voltage drop? PHYSICAL REVIEW LETTERS 2012; 109:036405. [PMID: 22861879 DOI: 10.1103/physrevlett.109.036405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2012] [Indexed: 06/01/2023]
Abstract
We calculate the linear and nonlinear conductance of spinless fermions in clean, long quantum wires, where short-ranged interactions lead locally to equilibration. Close to the quantum phase transition, where the conductance jumps from zero to one conductance quantum, the conductance obtains a universal form governed by the ratios of temperature, bias voltage, and gate voltage. Asymptotic analytic results are compared to solutions of a Boltzmann equation which includes the effects of three-particle scattering. Surprisingly, we find that for long wires the voltage predominantly drops close to one end of the quantum wire due to a thermoelectric effect.
Collapse
Affiliation(s)
- T Micklitz
- Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | | |
Collapse
|
36
|
Aita H, Arrachea L, Naón C. Four-terminal resistance of an interacting quantum wire with weakly invasive contacts. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:475601. [PMID: 22067546 DOI: 10.1088/0953-8984/23/47/475601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We analyze the behavior of the four-terminal resistance, relative to the two-terminal resistance of an interacting quantum wire with an impurity, taking into account the invasiveness of the voltage probes. We consider a one-dimensional Luttinger model of spinless fermions for the wire. We treat the coupling to the voltage probes perturbatively, within the framework of non-equilibrium Green function techniques. Our investigation unveils the combined effect of impurities, electron-electron interactions and invasiveness of the probes on the possible occurrence of negative resistance.
Collapse
Affiliation(s)
- Hugo Aita
- Departamento de Física and IFLP, FCE, Universidad Nacional de La Plata, cc 67 (1900) La Plata, Argentina
| | | | | |
Collapse
|
37
|
Karzig T, Refael G, Glazman LI, von Oppen F. Energy partitioning of tunneling currents into Luttinger liquids. PHYSICAL REVIEW LETTERS 2011; 107:176403. [PMID: 22107546 DOI: 10.1103/physrevlett.107.176403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2011] [Indexed: 05/31/2023]
Abstract
Tunneling of electrons of definite chirality into a quantum wire creates counterpropagating excitations, carrying both charge and energy. We find that the partitioning of energy is qualitatively different from that of charge. The partition ratio of energy depends on the excess energy of the tunneling electrons (controlled by the applied bias) and on the interaction strength within the wire (characterized by the Luttinger-liquid parameter κ), while the partitioning of charge is fully determined by κ. Moreover, unlike for charge currents, the partitioning of energy current should manifest itself in dc experiments on wires contacted by conventional (Fermi-liquid) leads.
Collapse
Affiliation(s)
- Torsten Karzig
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | | | | |
Collapse
|
38
|
Schmidt TL. Current correlations in quantum spin Hall insulators. PHYSICAL REVIEW LETTERS 2011; 107:096602. [PMID: 21929258 DOI: 10.1103/physrevlett.107.096602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2011] [Indexed: 05/31/2023]
Abstract
We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the interedge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross correlations, which could be exploited in experiments to elucidate the interplay between electron-electron interactions and the helical nature of the edge states.
Collapse
Affiliation(s)
- Thomas L Schmidt
- Department of Physics, Yale University, 217 Prospect Street, New Haven, Connecticut 06520, USA
| |
Collapse
|
39
|
Matveev KA, Andreev AV. Equilibration of Luttinger liquid and conductance of quantum wires. PHYSICAL REVIEW LETTERS 2011; 107:056402. [PMID: 21867082 DOI: 10.1103/physrevlett.107.056402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2010] [Indexed: 05/31/2023]
Abstract
Luttinger liquid theory describes one-dimensional electron systems in terms of noninteracting bosonic excitations. In this approximation thermal excitations are decoupled from the current flowing through a quantum wire, and the conductance is quantized. We show that relaxation processes not captured by the Luttinger liquid theory lead to equilibration of the excitations with the current and give rise to a temperature-dependent correction to the conductance. In long wires, the magnitude of the correction is expressed in terms of the velocities of bosonic excitations. In shorter wires it is controlled by the relaxation rate.
Collapse
Affiliation(s)
- K A Matveev
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | | |
Collapse
|
40
|
Chen W, Andreev AV, Glazman LI. Quantum criticality in a Mott pn junction in an armchair carbon nanotube. PHYSICAL REVIEW LETTERS 2011; 106:216801. [PMID: 21699326 DOI: 10.1103/physrevlett.106.216801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2011] [Indexed: 05/31/2023]
Abstract
In an armchair carbon nanotube pn junction the p and n regions are separated by a region of a Mott insulator, which can backscatter electrons only in pairs. We predict a quantum-critical behavior in such a pn junction. Depending on the junction's built-in electric field E, its conductance G scales either to zero or to 4e(2)/h as the temperature T is lowered. The two types of the G(T) dependence indicate the existence, at some special value of E, of an intermediate quantum-critical point with a finite conductance G<4e(2)/h. This makes the pn junction drastically different from a simple potential barrier in a Luttinger liquid.
Collapse
Affiliation(s)
- Wei Chen
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
| | | | | |
Collapse
|
41
|
Schmeltzer D. Dirac's method for constraints: an application to quantum wires. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:155601. [PMID: 21460427 DOI: 10.1088/0953-8984/23/15/155601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We investigate the Hubbard model in the limit U = ∞, which is equivalent to the statistical condition of exclusion of double occupancy. We solve this problem using Dirac's method for constraints. The constraints are solved within the bosonization method. We find that the constraints modify the anomalous commutator. We apply this theory to quantum wires at finite temperatures where the Hubbard interaction is U = ∞. We find that the anomalous commutator induced by the constraints gives rise to the 0.7 anomalous conductance.
Collapse
Affiliation(s)
- D Schmeltzer
- Department of Physics, City College of the City University of New York, New York, NY 10031, USA
| |
Collapse
|
42
|
Gutman DB, Gefen Y, Mirlin AD. Full counting statistics of a Luttinger liquid conductor. PHYSICAL REVIEW LETTERS 2010; 105:256802. [PMID: 21231608 DOI: 10.1103/physrevlett.105.256802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2010] [Indexed: 05/30/2023]
Abstract
Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.
Collapse
Affiliation(s)
- D B Gutman
- Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel
| | | | | |
Collapse
|
43
|
Sato K, Loss D, Tserkovnyak Y. Cooper-pair injection into quantum spin Hall insulators. PHYSICAL REVIEW LETTERS 2010; 105:226401. [PMID: 21231401 DOI: 10.1103/physrevlett.105.226401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2010] [Indexed: 05/30/2023]
Abstract
We theoretically study tunneling of Cooper pairs from a superconductor spanning a two-dimensional topological insulator strip into its helical edge states. The coherent low-energy electron-pair tunneling sets off positive current cross correlations along the edges, which reflect an interplay of two quantum-entanglement processes. Most importantly, superconducting spin pairing dictates a Cooper pair partitioning into the helical edge liquids, which transport electrons in opposite directions for opposite spin orientations. At the same time, Luttinger-liquid correlations fractionalize electrons injected at a given edge into counterpropagating charge pulses carrying definite fractions of the elementary electron charge.
Collapse
Affiliation(s)
- Koji Sato
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
| | | | | |
Collapse
|
44
|
Goldstein M, Berkovits R. Duality between different geometries of a resonant level in a Luttinger liquid. PHYSICAL REVIEW LETTERS 2010; 104:106403. [PMID: 20366441 DOI: 10.1103/physrevlett.104.106403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2009] [Indexed: 05/29/2023]
Abstract
We prove an exact duality between the side-coupled and embedded geometries of a single level quantum dot attached to a quantum wire in a Luttinger liquid phase by a tunneling term and interactions. This is valid even in the presence of a finite bias voltage. Under this relation the Luttinger liquid parameter g goes into its inverse, and transmittance maps onto reflectance. We then demonstrate how this duality is revealed by the transport properties of the side-coupled case. Conductance is found to exhibit an antiresonance as a function of the level energy, whose width vanishes (enhancing transport) as a power law for low temperature and bias voltage whenever g > 1, and diverges (suppressing transport) for g < 1. On-resonance transmission is always destroyed, unless g is large enough.
Collapse
Affiliation(s)
- Moshe Goldstein
- The Minerva Center, Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | | |
Collapse
|
45
|
Schmeltzer D, Kuklov A, Malard M. A scaling approach for interacting quantum wires--a possible explanation for the 0.7 anomalous conductance. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:095301. [PMID: 21389411 DOI: 10.1088/0953-8984/22/9/095301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We consider a weakly interacting finite wire with short and long range interactions. The long range interactions enhance the 4k(F) scattering and renormalize the wire to a strongly interacting limit. For large screening lengths, the renormalized charge stiffness Luttinger parameter K(eff) decreases to [Formula: see text], giving rise to a Wigner crystal at T=0 with an anomalous conductance at finite temperatures. For short screening lengths, the renormalized Luttinger parameter K(eff) is restricted to ½≤K(eff)≤1. As a result, at temperatures larger than the magnetic exchange energy we find an interacting metal which, for K(eff)≈½, is equivalent to the Hubbard U−>∞ model, with the anomalous conductance G≈e(2)/h.
Collapse
Affiliation(s)
- D Schmeltzer
- Department of Physics, City College of the CUNY, USA
| | | | | |
Collapse
|
46
|
Ristivojevic Z, Japaridze GI, Nattermann T. Spin filtering by field-dependent resonant tunneling. PHYSICAL REVIEW LETTERS 2010; 104:076401. [PMID: 20366899 DOI: 10.1103/physrevlett.104.076401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2009] [Indexed: 05/29/2023]
Abstract
We consider theoretically transport in a spinful one-channel interacting quantum wire placed in an external magnetic field. For the case of two pointlike impurities embedded in the wire, under a small voltage bias the spin-polarized current occurs at special points in the parameter space, tunable by a single parameter. At sufficiently low temperatures complete spin polarization may be achieved, provided repulsive interaction between electrons is not too strong.
Collapse
Affiliation(s)
- Zoran Ristivojevic
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany
| | | | | |
Collapse
|
47
|
Agarwal A, Sen D. AC conductivity of a quantum Hall line junction. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:375601. [PMID: 21832349 DOI: 10.1088/0953-8984/21/37/375601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We present a microscopic model for calculating the AC conductivity of a finite length line junction made up of two counter- or co-propagating single mode quantum Hall edges with possibly different filling fractions. The effect of density-density interactions and a local tunneling conductance (σ) between the two edges is considered. Assuming that σ is independent of the frequency ω, we derive expressions for the AC conductivity as a function of ω, the length of the line junction and other parameters of the system. We reproduce the results of Sen and Agarwal (2008 Phys. Rev. B 78 085430) in the DC limit ([Formula: see text]), and generalize those results for an interacting system. As a function of ω, the AC conductivity shows significant oscillations if σ is small; the oscillations become less prominent as σ increases. A renormalization group analysis shows that the system may be in a metallic or an insulating phase depending on the strength of the interactions. We discuss the experimental implications of this for the behavior of the AC conductivity at low temperatures.
Collapse
Affiliation(s)
- Amit Agarwal
- Center for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India
| | | |
Collapse
|
48
|
Berg E, Oreg Y, Kim EA, von Oppen F. Fractional charges on an integer quantum Hall edge. PHYSICAL REVIEW LETTERS 2009; 102:236402. [PMID: 19658953 DOI: 10.1103/physrevlett.102.236402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2008] [Indexed: 05/28/2023]
Abstract
We propose ways to create and detect fractionally charged excitations in integer quantum Hall edge states. The charge fractionalization occurs due to the Coulomb interaction between electrons propagating on different edge channels. The fractional charge of the solitonlike collective excitations can be observed in time-resolved or frequency-dependent shot noise measurements.
Collapse
Affiliation(s)
- E Berg
- Department of Physics, Stanford University, Stanford, CA 94305-4045, USA
| | | | | | | |
Collapse
|
49
|
Wächter P, Meden V, Schönhammer K. Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:215608. [PMID: 21825557 DOI: 10.1088/0953-8984/21/21/215608] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We study electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (two-dimensional) leads, thereby bringing theory closer towards systems resembling set-ups realized in experiments. In particular, we compute the temperature dependence of the linear conductance G of a system without bulk impurities on the temperature T. The appearance of new temperature scales introduced by the lengths of overhanging parts of the leads and the wire implies a G(T) which is much more complex than the power-law behavior described so far for end-coupled wires. Depending on the precise set-up the wide temperature regime of power-law scaling found in the end-coupled case is broken up into up to five fairly narrow regimes interrupted by extended crossover regions. Our results can be used to optimize the experimental set-ups designed for a verification of Luttinger liquid power-law scaling.
Collapse
Affiliation(s)
- P Wächter
- Institut für Theoretische Physik, Universität Göttingen, D-37077 Göttingen, Germany
| | | | | |
Collapse
|
50
|
Rech J, Micklitz T, Matveev KA. Conductance of fully equilibrated quantum wires. PHYSICAL REVIEW LETTERS 2009; 102:116402. [PMID: 19392220 DOI: 10.1103/physrevlett.102.116402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2009] [Indexed: 05/27/2023]
Abstract
We study the conductance of a quantum wire in the presence of weak electron-electron scattering. In a sufficiently long wire the scattering leads to full equilibration of the electron distribution function in the frame moving with the electric current. At nonzero temperature this equilibrium distribution differs from the one supplied by the leads. As a result the contact resistance increases, and the quantized conductance of the wire acquires a quadratic in temperature correction. The magnitude of the correction is found by analysis of the conservation laws of the system and does not depend on the details of the interaction mechanism responsible for equilibration.
Collapse
Affiliation(s)
- Jérôme Rech
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | | | | |
Collapse
|