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Le HA, Lee IH, Kim YH, Eric Yang SR. Phase diagram and crossover phases of topologically ordered graphene zigzag nanoribbons: role of localization effects. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:265604. [PMID: 38547530 DOI: 10.1088/1361-648x/ad38f9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2024] [Accepted: 03/28/2024] [Indexed: 04/06/2024]
Abstract
We computed the phase diagram of zigzag graphene nanoribbons as a function of on-site repulsion, doping, and disorder strength. The topologically ordered phase undergoes topological phase transitions into crossover phases, which are new disordered phases with non-universal topological entanglement entropy that exhibits significant variance. We explored the nature of non-local correlations in both the topologically ordered and crossover phases. In the presence of localization effects, strong on-site repulsion and/or doping weaken non-local correlations between the opposite zigzag edges of the topologically ordered phase. In one of the crossover phases, bothe-/2solitonic fractional charges and spin-charge separation were absent; however, charge-transfer correlations between the zigzag edges were possible. Another crossover phase contains solitonice-/2fractional charges but lacks charge transfer correlations. We also observed properties of non-topological, strongly disordered, and strongly repulsive phases. Each phase on the phase diagram exhibits a different zigzag-edge structure. Additionally, we investigated the tunneling of solitonic fractional charges under an applied voltage between the zigzag edges of undoped topologically ordered zigzag ribbons, and found that it may lead to a zero-bias tunneling anomaly.
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Affiliation(s)
- Hoang-Anh Le
- Department of Physics, Korea University, Seoul 02841, Republic of Korea
| | - In-Hwan Lee
- Department of Physics, Korea University, Seoul 02841, Republic of Korea
| | - Young Heon Kim
- Department of Physics, Korea University, Seoul 02841, Republic of Korea
| | - S-R Eric Yang
- Department of Physics, Korea University, Seoul 02841, Republic of Korea
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Kim YH, Lee HJ, Lee HY, Yang SRE. New disordered anyon phase of doped graphene zigzag nanoribbon. Sci Rep 2022; 12:14551. [PMID: 36008453 PMCID: PMC9411593 DOI: 10.1038/s41598-022-18731-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Accepted: 08/18/2022] [Indexed: 11/28/2022] Open
Abstract
We investigate interacting disordered zigzag nanoribbons at low doping, using the Hubbard model to treat electron interactions within the density matrix renormalization group and Hartree-Fock method. Extra electrons that are inserted into an interacting disordered zigzag nanoribbon divide into anyons. Furthermore, the fractional charges form a new disordered anyon phase with a highly distorted edge spin density wave, containing numerous localized magnetic moments residing on the zigzag edges, thereby displaying spin-charge separation and a strong non-local correlation between the opposite zigzag edges. We make the following new predictions, which can be experimentally tested: (1) In the low doping case and weak disorder regime, the soft gap in the tunneling density of states is replaced by a sharp peak at the midgap energy with two accompanying peaks. The [Formula: see text] fractional charges that reside on the boundary of the zigzag edges are responsible for these peaks. (2) We find that the midgap peak disappears as the doping concentration increases. The presence of [Formula: see text] fractional charges will be strongly supported by the detection of these peaks. Doped zigzag ribbons may also exhibit unusual transport, magnetic, and inter-edge tunneling properties.
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Affiliation(s)
- Young Heon Kim
- Department of Physics, Korea University, Seoul, 02855, South Korea
| | - Hye Jeong Lee
- Department of Physics, Korea University, Seoul, 02855, South Korea
| | - Hyun-Yong Lee
- Department of Applied Physics, Graduate School, Korea University, Sejong, 30019, South Korea
- Division of Display and Semiconductor Physics, Korea University, Sejong, 30019, South Korea
- Interdisciplinary Program in E.ICT-Culture-Sports Convergence, Korea University, Sejong, 30019, South Korea
| | - S-R Eric Yang
- Department of Physics, Korea University, Seoul, 02855, South Korea.
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3
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Interplay between topological valley and quantum Hall edge transport. Nat Commun 2022; 13:4187. [PMID: 35858959 PMCID: PMC9300606 DOI: 10.1038/s41467-022-31680-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 06/21/2022] [Indexed: 11/08/2022] Open
Abstract
An established way of realising topologically protected states in a two-dimensional electron gas is by applying a perpendicular magnetic field thus creating quantum Hall edge channels. In electrostatically gapped bilayer graphene intriguingly, even in the absence of a magnetic field, topologically protected electronic states can emerge at naturally occurring stacking domain walls. While individually both types of topologically protected states have been investigated, their intriguing interplay remains poorly understood. Here, we focus on the interplay between topological domain wall states and quantum Hall edge transport within the eight-fold degenerate zeroth Landau level of high-quality suspended bilayer graphene. We find that the two-terminal conductance remains approximately constant for low magnetic fields throughout the distinct quantum Hall states since the conduction channels are traded between domain wall and device edges. For high magnetic fields, however, we observe evidence of transport suppression at the domain wall, which can be attributed to the emergence of spectral minigaps. This indicates that stacking domain walls potentially do not correspond to a topological domain wall in the order parameter.
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Patlatiuk T, Scheller CP, Hill D, Tserkovnyak Y, Egues JC, Barak G, Yacoby A, Pfeiffer LN, West KW, Zumbühl DM. Edge-State Wave Functions from Momentum-Conserving Tunneling Spectroscopy. PHYSICAL REVIEW LETTERS 2020; 125:087701. [PMID: 32909808 DOI: 10.1103/physrevlett.125.087701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2020] [Accepted: 07/21/2020] [Indexed: 06/11/2023]
Abstract
We perform momentum-conserving tunneling spectroscopy using a GaAs cleaved-edge overgrowth quantum wire to investigate adjacent quantum Hall edge states. We use the lowest five wire modes with their distinct wave functions to probe each edge state and apply magnetic fields to modify the wave functions and their overlap. This reveals an intricate and rich tunneling conductance fan structure which is succinctly different for each of the wire modes. We self-consistently solve the Poisson-Schrödinger equations to simulate the spectroscopy, reproducing the striking fans in great detail, thus, confirming the calculations. Further, the model predicts hybridization between wire states and Landau levels, which is also confirmed experimentally. This establishes momentum-conserving tunneling spectroscopy as a powerful technique to probe edge state wave functions.
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Affiliation(s)
- T Patlatiuk
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - C P Scheller
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - D Hill
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
| | - Y Tserkovnyak
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
| | - J C Egues
- Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil
| | - G Barak
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - A Yacoby
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D M Zumbühl
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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Li J, Wen H, Watanabe K, Taniguchi T, Zhu J. Gate-Controlled Transmission of Quantum Hall Edge States in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2018; 120:057701. [PMID: 29481178 DOI: 10.1103/physrevlett.120.057701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Revised: 12/01/2017] [Indexed: 06/08/2023]
Abstract
The edge states of the quantum Hall and fractional quantum Hall effect of a two-dimensional electron gas carry key information of the bulk excitations. Here we demonstrate gate-controlled transmission of edge states in bilayer graphene through a potential barrier with tunable height. The backscattering rate is continuously varied from 0 to close to 1, with fractional quantized values corresponding to the sequential complete backscattering of individual modes. Our experiments demonstrate the feasibility to controllably manipulate edge states in bilayer graphene, thus opening the door to more complex experiments.
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Affiliation(s)
- Jing Li
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Hua Wen
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Kenji Watanabe
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Jun Zhu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Kadigrobov AM, Fistul MV. Bound states induced giant oscillations of the conductance in the quantum Hall regime. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:255301. [PMID: 27166511 DOI: 10.1088/0953-8984/28/25/255301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We theoretically studied the quasiparticle transport in a 2D electron gas biased in the quantum Hall regime and in the presence of a lateral potential barrier. The lateral junction hosts the specific magnetic field dependent quasiparticle states highly localized in the transverse direction. The quantum tunnelling across the barrier provides a complex bands structure of a one-dimensional energy spectrum of these bound states, [Formula: see text], where p y is the electron momentum in the longitudinal direction y. Such a spectrum manifests itself by a large number of peaks and drops in the dependence of the magnetic edge states transmission coefficient D(E ) on the electron energy E. E.g. the high value of D occurs as soon as the electron energy E reaches gaps in the spectrum. These peaks and drops of D(E) result in giant oscillations of the transverse conductance G x with the magnetic field and/or the transport voltage. Our theoretical analysis, based on the coherent macroscopic quantum superposition of the bound states and the magnetic edge states propagating along the system boundaries, is in a good accord with the experimental observations found in Kang et al (2000 Lett. Nat. 403 59).
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Affiliation(s)
- A M Kadigrobov
- Theoretische Physik III, Ruhr-Universität Bochum, D-44801 Bochum, Germany
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Jiang P, Chien CC, Yang I, Kang W, Baldwin KW, Pfeiffer LN, West KW. Zero-bias anomalies in narrow tunnel junctions in the quantum Hall regime. PHYSICAL REVIEW LETTERS 2010; 105:246801. [PMID: 21231544 DOI: 10.1103/physrevlett.105.246801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2010] [Indexed: 05/30/2023]
Abstract
We report on the study of cleaved-edge-overgrown line junctions with a serendipitously created narrow opening in an otherwise thin, precise line barrier. Two sets of zero-bias anomalies are observed with an enhanced conductance for filling factors ν>1 and a strongly suppressed conductance for ν<1. A transition between the two behaviors is found near ν≈1. The zero-bias anomaly (ZBA) line shapes find explanation in Luttinger liquid models of tunneling between quantum Hall edge states. The ZBA for ν<1 occurs from strong backscattering induced by suppression of quasiparticle tunneling between the edge channels for the n=0 Landau levels. The ZBA for ν>1 arises from weak tunneling of quasiparticles between the n=1 edge channels.
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Affiliation(s)
- P Jiang
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
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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.
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Affiliation(s)
- Amit Agarwal
- Center for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India
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9
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Ristivojevic Z, Nattermann T. Transport in a dissipative Luttinger liquid. PHYSICAL REVIEW LETTERS 2008; 101:016405. [PMID: 18764132 DOI: 10.1103/physrevlett.101.016405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2008] [Indexed: 05/26/2023]
Abstract
We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (Ohmic) bath. For nonzero dissipation, the single impurity is always a relevant perturbation which suppresses transport strongly. At zero temperature, the current voltage relation of the link is I approximately exp(-E0/eV), where E0 approximately eta/kappa and kappa denotes the compressibility. At nonzero temperature T, the linear conductance is proportional to exp(-sqrt(CE0/kBT)). The decay of Friedel oscillation saturates for a distance larger than L(eta) approximately 1/eta from the impurity.
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Affiliation(s)
- Zoran Ristivojevic
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany
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10
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Nattermann T, Petković A, Ristivojevic Z, Schütze F. Absence of the Mott glass phase in 1D disordered fermionic systems. PHYSICAL REVIEW LETTERS 2007; 99:186402. [PMID: 17995424 DOI: 10.1103/physrevlett.99.186402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2007] [Indexed: 05/25/2023]
Abstract
We study the competition between the Mott and the Anderson insulating state in a one-dimensional disordered fermionic system. The notorious difficulties associated with strong coupling phases are avoided by using a new description in terms of the kink energies (or instanton surface tension) of the electronic displacement pattern. The approach has some similarities to the description of the flat phase of surfaces undergoing a roughening transition. Tracing back both a finite compressibility and a nonzero ac conductivity to vanishing kink energy we exclude the existence of an intermediate Mott-glass phase in systems with short range interaction only. In systems with long range interaction the Anderson insulating phase exhibits the features of a Mott glass however. The phase diagram is constructed from combining the information from the renormalization group flow, the kink energy, and simple rescaling analysis.
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Affiliation(s)
- Thomas Nattermann
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany
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Papa E, Stroh T. Metal-insulator transition tuned by external gates in Hall systems with constrictions. PHYSICAL REVIEW LETTERS 2006; 97:046801. [PMID: 16907604 DOI: 10.1103/physrevlett.97.046801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2005] [Indexed: 05/11/2023]
Abstract
The nature of a metal-insulator transition tuned by external gates in quantum Hall systems with point constrictions, as reported in recent experiments [S. Roddaro, Phys. Rev. Lett. 95, 156804 (2005)10.1103/PhysRevLett.95.156804], is examined. We attribute this phenomenon to a splitting of the integer edge into conducting and insulating stripes, the latter wide enough to allow for the stability of the edge structure. Interchannel impurity scattering and interchannel Coulomb interactions do not destabilize this picture.
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Affiliation(s)
- Emiliano Papa
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904-4714, USA
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12
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Jiang P, Yang I, Kang W, Pfeiffer LN, Baldwin KW, West KW. Interaction effects and pseudogap in two-dimensional lateral tunnel junctions. PHYSICAL REVIEW LETTERS 2006; 96:126804. [PMID: 16605941 DOI: 10.1103/physrevlett.96.126804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2005] [Indexed: 05/08/2023]
Abstract
Tunneling characteristics of a two-dimensional lateral tunnel junction are reported. A pseudogap on the order of Coulomb energy is detected in the tunneling density of states (TDOS) when two identical two-dimensional electron systems are laterally separated by a thin energy barrier. The Coulombic pseudogap remains robust well into the quantum Hall regime until it is overshadowed by the cyclotron gap in the TDOS. The pseudogap is modified by the in-plane magnetic field, demonstrating a nontrivial effect of the in-plane magnetic field on the electron-electron interaction.
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Affiliation(s)
- P Jiang
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
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Gornyi IV, Mirlin AD, Polyakov DG. Dephasing and weak localization in disordered Luttinger liquid. PHYSICAL REVIEW LETTERS 2005; 95:046404. [PMID: 16090828 DOI: 10.1103/physrevlett.95.046404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2004] [Indexed: 05/03/2023]
Abstract
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit.
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Affiliation(s)
- I V Gornyi
- Institut für Nanotechnologie, Forschungszentrum Karlsruhe, Germany
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14
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Huber M, Grayson M, Rother M, Biberacher W, Wegscheider W, Abstreiter G. Structure of a single sharp quantum Hall edge probed by momentum-resolved tunneling. PHYSICAL REVIEW LETTERS 2005; 94:016805. [PMID: 15698115 DOI: 10.1103/physrevlett.94.016805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2004] [Indexed: 05/24/2023]
Abstract
Momentum-resolved magnetotunneling spectroscopy is performed at a single sharp quantum Hall (QH) edge to probe the structure of integer QH edge modes. An epitaxially overgrown cleaved edge is shown to realize the sharp-edge limit with interchannel distances smaller than both the magnetic length and the Bohr radius where the Chklovskii soft-edge picture is no longer valid. The line shape of principal conductance peaks is explained, and an edge filling factor is determined from the peak position. A step in the dispersion is attributed to fluctuations in the QH ground energy.
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Affiliation(s)
- M Huber
- Walter Schottky Institut, Technische Universität München, D-85748 Garching, Germany
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15
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Yang I, Kang W, Baldwin KW, Pfeiffer LN, West KW. Cascade of quantum phase transitions in tunnel-coupled edge states. PHYSICAL REVIEW LETTERS 2004; 92:056802. [PMID: 14995327 DOI: 10.1103/physrevlett.92.056802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2003] [Indexed: 05/24/2023]
Abstract
We report on the cascade of quantum phase transitions exhibited by tunnel-coupled edge states across a quantum Hall line junction. We identify a series of quantum critical points between successive strong and weak tunneling regimes in the zero-bias conductance. Scaling analysis shows that the conductance near the critical magnetic fields B(c) is a function of a single scaling argument /B-B(c)/T(-kappa), where the exponent kappa=0.42. This puzzling resemblance to a quantum Hall-insulator transition points to the importance of interedge correlation between the coupled edge states.
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Affiliation(s)
- I Yang
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
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16
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Kim EA, Fradkin E. Double point contact in quantum Hall line junctions. PHYSICAL REVIEW LETTERS 2003; 91:156801. [PMID: 14611485 DOI: 10.1103/physrevlett.91.156801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2003] [Indexed: 05/24/2023]
Abstract
We show that multiple point contacts on a barrier separating two laterally coupled quantum Hall fluids induce Aharonov-Bohm (AB) oscillations in the tunneling conductance. These quantum coherence effects provide new evidence for the Luttinger liquid behavior of the edge states of quantum Hall fluids. For a two point contact, we identify coherent and incoherent regimes determined by the relative magnitude of their separation and the temperature. We analyze both regimes in the strong and weak tunneling amplitude limits as well as their temperature dependence. We find that the tunneling conductance should exhibit AB oscillations in the coherent regime, both at strong and weak tunneling amplitudes with the same period but with different functional form.
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Affiliation(s)
- Eun-Ah Kim
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green Street, Urbana, Illinois 61801-3080, USA
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Zülicke U, Shimshoni E. Strongly correlated fractional quantum Hall line junctions. PHYSICAL REVIEW LETTERS 2003; 90:026802. [PMID: 12570567 DOI: 10.1103/physrevlett.90.026802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2002] [Indexed: 05/24/2023]
Abstract
We have studied a clean finite-length line junction between interacting counterpropagating single-branch fractional quantum Hall edge channels. Exact solutions for low-lying excitations and transport properties are obtained when the two edges belong to quantum Hall systems with different filling factors and interact via the long-range Coulomb interaction. Charging effects due to the coupling to external edge-channel leads are fully taken into account. Conductances and power laws in the current-voltage characteristics of tunneling are strongly affected by interedge correlations.
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Affiliation(s)
- U Zülicke
- Institut für Theoretische Festkörperphysik, Universität Karlsruhe, D-76128 Karlsruhe, Germany
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18
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Auslaender OM, Yacoby A, de Picciotto R, Baldwin KW, Pfeiffer LN, West KW. Tunneling spectroscopy of the elementary excitations in a one-dimensional wire. Science 2002; 295:825-8. [PMID: 11823634 DOI: 10.1126/science.1066266] [Citation(s) in RCA: 267] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The collective excitation spectrum of interacting electrons in one dimension has been measured by controlling the energy and momentum of electrons tunneling between two closely spaced, parallel quantum wires in a GaAs/AlGaAs heterostructure while measuring the resulting conductance. The excitation spectrum deviates from the noninteracting spectrum, attesting to the importance of Coulomb interactions. An observed 30% enhancement of the excitation velocity relative to noninteracting electrons with the same density, a parameter determined experimentally, is consistent with theories on interacting electrons in one dimension. In short wires, 6 and 2 micrometers long, finite size effects, resulting from the breaking of translational invariance, are observed.
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Affiliation(s)
- O M Auslaender
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
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