1
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Rylands C, Calabrese P. Transport and Entanglement across Integrable Impurities from Generalized Hydrodynamics. PHYSICAL REVIEW LETTERS 2023; 131:156303. [PMID: 37897777 DOI: 10.1103/physrevlett.131.156303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Accepted: 09/06/2023] [Indexed: 10/30/2023]
Abstract
Quantum impurity models (QIMs) are ubiquitous throughout physics. As simplified toy models they provide crucial insights for understanding more complicated strongly correlated systems, while in their own right are accurate descriptions of many experimental platforms. In equilibrium, their physics is well understood and have proven a testing ground for many powerful theoretical tools, both numerical and analytical, in use today. Their nonequilibrium physics is much less studied and understood. However, the recent advancements in nonequilibrium integrable quantum systems through the development of generalized hydrodynamics (GHD) coupled with the fact that many archetypal QIMs are in fact integrable presents an enticing opportunity to enhance our understanding of these systems. We take a step towards this by expanding the framework of GHD to incorporate integrable interacting QIMs. We present a set of Bethe-Boltzmann type equations which incorporate the effects of impurity scattering and discuss the new aspects which include entropy production. These impurity GHD equations are then used to study a bipartioning quench wherein a relevant backscattering impurity is included at the location of the bipartition. The density and current profiles are studied as a function of the impurity strength and expressions for the entanglement entropy and full counting statistics are derived.
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Affiliation(s)
- Colin Rylands
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
| | - Pasquale Calabrese
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
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2
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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.
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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.
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3
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Transport in helical Luttinger liquids in the fractional quantum Hall regime. Nat Commun 2021; 12:5312. [PMID: 34493723 PMCID: PMC8423831 DOI: 10.1038/s41467-021-25631-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2021] [Accepted: 08/20/2021] [Indexed: 11/10/2022] Open
Abstract
Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations1–3. Here we investigate transport properties of hDWs in the ν = 2/3 fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the naïve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity. Previous work has shown that helical domain walls can form between states of different spin-polarization during a ferromagnetic spin transition in the fractional quantum Hall regime. Here, the authors study the transport through a single helical domain wall and find strong deviations from a simplified theory of weakly interacting edge channels.
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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: 15] [Impact Index Per Article: 5.0] [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.
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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
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5
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Béri B. Exact Nonequilibrium Transport in the Topological Kondo Effect. PHYSICAL REVIEW LETTERS 2017; 119:027701. [PMID: 28753367 DOI: 10.1103/physrevlett.119.027701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Indexed: 06/07/2023]
Abstract
A leading candidate for the experimental confirmation of the nonlocal quantum dynamics of Majorana fermions is the topological Kondo effect, predicted for mesoscopic superconducting islands connected to metallic leads. We identify an anisotropic, Toulouse-like, limit of the topological Kondo problem where the full nonequilibrium conductance and shot noise can be calculated exactly. Near the Kondo fixed point, we find novel asymptotic features including a universal conductance scaling function and fractional charge quantization observable via the Fano factor. In the universal regime, our results apply for generic anisotropy and even away from the Kondo limit as long as the system supports an emergent topological Kondo fixed point. Our approach thus provides key new qualitative insights and exact expressions for quantitative comparisons to future experimental data.
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Affiliation(s)
- B Béri
- School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
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6
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Bi Z, Zhang R, You YZ, Young A, Balents L, Liu CX, Xu C. Bilayer Graphene as a Platform for Bosonic Symmetry-Protected Topological States. PHYSICAL REVIEW LETTERS 2017; 118:126801. [PMID: 28388187 DOI: 10.1103/physrevlett.118.126801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2016] [Indexed: 06/07/2023]
Abstract
Bosonic symmetry protected topological (BSPT) states, the bosonic analogue of topological insulators, have attracted enormous theoretical interest in the last few years. Although BSPT states have been classified by various approaches, there is so far no successful experimental realization of any BSPT state in two or higher dimensions. In this paper, we propose that a two-dimensional BSPT state with U(1)×U(1) symmetry can be realized in bilayer graphene in a magnetic field. Here the two U(1) symmetries represent total spin S^{z} and total charge conservation, respectively. The Coulomb interaction plays a central role in this proposal-it gaps out all the fermions at the boundary, so that only bosonic charge and spin degrees of freedom are gapless and protected at the edge. Based on the above conclusion, we propose that the bulk quantum phase transition between the BSPT and trivial phase, which can be driven by applying both magnetic and electric fields, can become a "bosonic phase transition" with interactions. That is, only bosonic modes close their gap at the transition, which is fundamentally different from all the well-known topological insulator to trivial insulator transitions that occur for free fermion systems. We discuss various experimental consequences of this proposal.
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Affiliation(s)
- Zhen Bi
- Department of physics, University of California, Santa Barbara, California 93106, USA
| | - Ruixing Zhang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
| | - Yi-Zhuang You
- Department of physics, University of California, Santa Barbara, California 93106, USA
| | - Andrea Young
- Department of physics, University of California, Santa Barbara, California 93106, USA
| | - Leon Balents
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
| | - Chao-Xing Liu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
| | - Cenke Xu
- Department of physics, University of California, Santa Barbara, California 93106, USA
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7
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Hashisaka M, Ota T, Muraki K, Fujisawa T. Shot-noise evidence of fractional quasiparticle creation in a local fractional quantum Hall state. PHYSICAL REVIEW LETTERS 2015; 114:056802. [PMID: 25699462 DOI: 10.1103/physrevlett.114.056802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2014] [Indexed: 06/04/2023]
Abstract
We experimentally identify fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T(1)(1-T(1)) over a wide range of T(1), where T(1) is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process enables us to elucidate the dynamics of Laughlin quasiparticles in FQH systems.
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Affiliation(s)
- Masayuki Hashisaka
- Department of Physics, Tokyo Institute of Technology, 2-12-1-H81 Ookayama, Meguro, Tokyo 152-8551, Japan
| | - Tomoaki Ota
- Department of Physics, Tokyo Institute of Technology, 2-12-1-H81 Ookayama, Meguro, Tokyo 152-8551, 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-H81 Ookayama, Meguro, Tokyo 152-8551, Japan
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8
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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.
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Affiliation(s)
- Igor V Yurkevich
- Nonlinearity and Complexity Research Group, Aston University, Birmingham B4 7ET, United Kingdom
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9
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Wang C, Feldman DE. Chirality, causality, and fluctuation-dissipation theorems in nonequilibrium steady states. PHYSICAL REVIEW LETTERS 2013; 110:030602. [PMID: 23373909 DOI: 10.1103/physrevlett.110.030602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2012] [Indexed: 06/01/2023]
Abstract
Edges of some quantum Hall liquids and a number of other systems exhibit chiral transport: excitations can propagate in one direction only, e.g., clockwise. We derive a family of fluctuation-dissipation relations in nonequilibrium steady states of such chiral systems. The theorems connect nonlinear response with fluctuations far from thermal equilibrium and hold only in case of chiral transport. They can be used to test the chiral or nonchiral character of the system.
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Affiliation(s)
- Chenjie Wang
- Department of Physics, Brown University, Providence, Rhode Island 02912, USA
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10
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Branschädel A, Boulat E, Saleur H, Schmitteckert P. Shot noise in the self-dual interacting resonant level model. PHYSICAL REVIEW LETTERS 2010; 105:146805. [PMID: 21230859 DOI: 10.1103/physrevlett.105.146805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2010] [Indexed: 05/30/2023]
Abstract
By using two independent and complementary approaches, we compute exactly the shot noise in an out-of-equilibrium interacting impurity model, the interacting resonant level model at its self-dual point. An analytical approach based on the thermodynamical Bethe ansatz allows us to obtain the density matrix in the presence of a bias voltage, which in turn allows for the computation of any observable. A time-dependent density matrix renormalization group technique that has proven to yield the correct result for a free model (the resonant level model) is shown to be in perfect agreement with the former method.
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Affiliation(s)
- A Branschädel
- Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
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11
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Ferraro D, Braggio A, Merlo M, Magnoli N, Sassetti M. Relevance of multiple quasiparticle tunneling between edge states at nu=p/(2np+1). PHYSICAL REVIEW LETTERS 2008; 101:166805. [PMID: 18999702 DOI: 10.1103/physrevlett.101.166805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2008] [Indexed: 05/27/2023]
Abstract
We present an explanation for the anomalous behavior in tunneling conductance and noise through a point contact between edge states in the Jain series nu=p/(2np+1), for extremely weak backscattering and low temperatures [Y. C. Chung, M. Heiblum, and V. Umansky, Phys. Rev. Lett. 91, 216804 (2003)10.1103/PhysRevLett.91.216804]. We consider edge states with neutral modes propagating at finite velocity, and we show that the activation of their dynamics causes the unexpected change in the temperature power law of the conductance. Even more importantly, we demonstrate that multiple-quasiparticle tunneling at low energies becomes the most relevant process. This result will be used to explain the experimental data on current noise where tunneling particles have a charge that can reach p times the single-quasiparticle charge. In this Letter, we analyze the conductance and the shot noise to substantiate quantitatively the proposed scenario.
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Affiliation(s)
- D Ferraro
- Dipartimento di Fisica & INFN, Università di Genova, Via Dodecaneso 33, Genoa, Italy
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12
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Gutman DB, Gefen Y, Mirlin AD. Nonequilibrium Luttinger liquid: zero-bias anomaly and dephasing. PHYSICAL REVIEW LETTERS 2008; 101:126802. [PMID: 18851399 DOI: 10.1103/physrevlett.101.126802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2008] [Indexed: 05/26/2023]
Abstract
A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left and right movers yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.
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Affiliation(s)
- D B Gutman
- Institut für Theorie der kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany
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13
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Clerk AA. Backaction noise in strongly interacting systems: the dc SQUID and the interacting quantum point contact. PHYSICAL REVIEW LETTERS 2006; 96:056801. [PMID: 16486968 DOI: 10.1103/physrevlett.96.056801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2005] [Indexed: 05/06/2023]
Abstract
We study the backaction noise and measurement the efficiency (i.e., noise temperature) of a dc SQUID amplifier and, equivalently, a quantum point-contact detector formed in a Luttinger liquid. Using a mapping to a dissipative tight-binding model, we show that these systems are able to reach the quantum limit even in regimes where several independent transport processes contribute to the current. We suggest how this is related to the underlying integrability of these systems.
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Affiliation(s)
- A A Clerk
- Department of Physics, McGill University, Montréal, Québec H3A 2T8, Canada
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14
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Kindermann M, Trauzettel B. Current fluctuations in an interacting quantum dot. PHYSICAL REVIEW LETTERS 2005; 94:166803. [PMID: 15904259 DOI: 10.1103/physrevlett.94.166803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2004] [Indexed: 05/02/2023]
Abstract
We calculate the counting statistics of electron transfer through an open quantum dot with charging interaction. A dot that is connected to leads by two single-channel quantum point contacts in an in-plane magnetic field is described by a Luttinger liquid with impurity at the Toulouse point. We find that the fluctuations of the current through this conductor exhibit distinctive interaction effects. Fluctuations saturate at high voltages, while the mean current increases linearly with the bias voltage. All cumulants higher than the second one reach at large bias a temperature independent limit.
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Affiliation(s)
- Markus Kindermann
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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15
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Course 5 Noise in mesoscopic physics. NANOPHYSICS: COHERENCE AND TRANSPORT, ÉCOLE D'ÉTÉ DE PHYSIQUE DES HOUCHES SESSION LXXXI 2005. [DOI: 10.1016/s0924-8099(05)80047-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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16
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Papa E, MacDonald AH. Interactions suppress quasiparticle tunneling at Hall bar constrictions. PHYSICAL REVIEW LETTERS 2004; 93:126801. [PMID: 15447295 DOI: 10.1103/physrevlett.93.126801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2004] [Indexed: 05/24/2023]
Abstract
Tunneling of fractionally charged quasiparticles across a two-dimensional electron system on a fractional quantum Hall plateau is expected to be strongly enhanced at low temperatures. This theoretical prediction is at odds with recent experimental studies of samples with weakly pinched quantum-point-contact constrictions in which the opposite behavior is observed. We argue here that this unexpected finding is a consequence of electron-electron interactions near the point contact.
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Affiliation(s)
- Emiliano Papa
- Department of Physics, The University of Texas, Austin, TX 78712, USA
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17
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Roddaro S, Pellegrini V, Beltram F, Biasiol G, Sorba L. Interedge strong-to-weak scattering evolution at a constriction in the fractional quantum Hall regime. PHYSICAL REVIEW LETTERS 2004; 93:046801. [PMID: 15323783 DOI: 10.1103/physrevlett.93.046801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2004] [Indexed: 05/24/2023]
Abstract
Gate-voltage control of interedge tunneling at a split-gate constriction in the fractional quantum Hall regime is reported. Quantitative agreement with the behavior predicted for out-of-equilibrium quasiparticle transport between chiral Luttinger liquids is shown at low temperatures at specific values of the backscattering strength. When the latter is lowered by changing the gate voltage, the zero-bias peak of the tunneling conductance evolves into a minimum, and a nonlinear quasiholelike characteristic emerges. Our analysis emphasizes the role of the local filling factor in the split-gate constriction region.
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Affiliation(s)
- Stefano Roddaro
- NEST-INFM, Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
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18
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Koutouza A, Saleur H, Trauzettel B. How irrelevant operators affect the determination of fractional charge. PHYSICAL REVIEW LETTERS 2003; 91:026801. [PMID: 12906498 DOI: 10.1103/physrevlett.91.026801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2002] [Indexed: 05/24/2023]
Abstract
We show that the inclusion of irrelevant terms in the Hamiltonian describing tunneling between edge states in the fractional quantum Hall effect can lead to a variety of nonperturbative behaviors in intermediate energy regimes and, in particular, affect crucially the determination of charge through shot noise measurements. We show, for instance, that certain combinations of relevant and irrelevant terms can lead to an effective measured charge nue in the strong backscattering limit and an effective measured charge e in the weak backscattering limit, in sharp contrast with standard perturbative expectations. This provides a possible scenario to explain the experimental observations by Comforti et al. [Nature (London) 416, 515 (2002)]], which are so far not understood.
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Affiliation(s)
- A Koutouza
- Department of Physics, University of Southern California, Los Angeles, California 90089-0484, USA
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19
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Trauzettel B, Egger R, Grabert H. Coulomb drag shot noise in coupled Luttinger liquids. PHYSICAL REVIEW LETTERS 2002; 88:116401. [PMID: 11909416 DOI: 10.1103/physrevlett.88.116401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2001] [Indexed: 05/23/2023]
Abstract
Coulomb drag shot noise has been studied theoretically for 1D interacting electron systems, which are realized, e.g., in single-wall nanotubes. We show that under adiabatic coupling to external leads, the Coulomb drag shot noise of two coupled or crossed nanotubes contains surprising effects, in particular, a complete locking of the shot noise in the tubes. In contrast to Coulomb drag of the average current, the noise locking is based on a symmetry of the underlying Hamiltonian and is not limited to asymptotically small energy scales.
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Affiliation(s)
- B Trauzettel
- Fakultät für Physik, Albert-Ludwigs-Universität, D-79104 Freiburg, Germany
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20
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Rosenow B, Halperin BI. Nonuniversal behavior of scattering between fractional quantum Hall edges. PHYSICAL REVIEW LETTERS 2002; 88:096404. [PMID: 11864038 DOI: 10.1103/physrevlett.88.096404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2001] [Indexed: 05/23/2023]
Abstract
In a fractional quantum Hall system with a narrow constriction, tunneling of quasiparticles between states at different edges can lead to resistance and to shot noise. The ratio of the shot noise to the backscattered current, in the weak scattering regime, measures the fractional charge of the quasiparticle, which has been confirmed in several experiments. However, the predicted nonlinearity of the resistance was apparently not observed in some of these cases. As a possible explanation, we consider a model where coupling between the current carrying edge mode and additional phononlike edge modes can lead to nonuniversal exponents in the current-voltage characteristic.
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Affiliation(s)
- Bernd Rosenow
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany
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21
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Safi I, Devillard P, Martin T. Partition noise and statistics in the fractional quantum hall effect. PHYSICAL REVIEW LETTERS 2001; 86:4628-4631. [PMID: 11384300 DOI: 10.1103/physrevlett.86.4628] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2000] [Indexed: 05/23/2023]
Abstract
A microscopic theory of current partition in fractional quantum Hall liquids, described by chiral Luttinger liquids, is developed to compute the noise correlations, using the Keldysh technique. In this Hanbury-Brown and Twiss geometry, at Laughlin filling factors nu = 1/3, the real time noise correlator exhibits oscillations which persist over larger time scales than that of an uncorrelated Hall fluid. The zero frequency noise correlations are negative at filling factor 1/3 as for bare electrons (antibunching), but are strongly reduced in amplitude. These correlations become positive (bunching) for nu < or = 1/5, suggesting a tendency towards bosonic behavior.
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Affiliation(s)
- I Safi
- Centre de Physique Théorique, Case 907 Luminy, 13288 Marseille Cedex 9, France
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22
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Griffiths TG, Comforti E, Heiblum M, Stern A, Umansky V. Evolution of quasiparticle charge in the fractional quantum hall regime. PHYSICAL REVIEW LETTERS 2000; 85:3918-3921. [PMID: 11041960 DOI: 10.1103/physrevlett.85.3918] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2000] [Indexed: 05/23/2023]
Abstract
The charge of quasiparticles in a fractional quantum Hall (FQH) liquid, tunneling through a partly reflecting constriction with transmission t, was determined via shot noise measurements. In the nu = 1/3 FQH state, a charge smoothly evolving from e(*) = e/3 for t(1/3) congruent with 1 to e(*) = e for t(1/3)<<1 was determined, agreeing with chiral Luttinger liquid theory. In the nu = 2/5 FQH state the quasiparticle charge evolves smoothly from e(*) = e/5 at t(2/5) congruent with 1 to a maximum charge less than e(*) = e/3 at t(2/5)<<1. Thus it appears that quasiparticles with an approximate charge e/5 pass a barrier they see as almost opaque.
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Affiliation(s)
- TG Griffiths
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100, USA
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Martin T, Ouvry S. Martin and ouvry reply:. PHYSICAL REVIEW LETTERS 2000; 85:223. [PMID: 10991200 DOI: 10.1103/physrevlett.85.223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2000] [Indexed: 05/23/2023]
Affiliation(s)
- T Martin
- Centre de Physique Theorique, Case 907 13009 Marseille, France
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Fendley P, Saleur H. Nonequilibrium dc noise in a Luttinger liquid with an impurity. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:10845-10854. [PMID: 9984882 DOI: 10.1103/physrevb.54.10845] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lesage F, Saleur H, Skorik S. Time correlations in 1D quantum impurity problems. PHYSICAL REVIEW LETTERS 1996; 76:3388-3391. [PMID: 10060954 DOI: 10.1103/physrevlett.76.3388] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Lee H, Levitov LS. Current fluctuations in a single tunnel junction. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:7383-7391. [PMID: 9982185 DOI: 10.1103/physrevb.53.7383] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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