1
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Cohen LA, Samuelson NL, Wang T, Taniguchi T, Watanabe K, Zaletel MP, Young AF. Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact. Science 2023; 382:542-547. [PMID: 37917688 DOI: 10.1126/science.adf9728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 09/29/2023] [Indexed: 11/04/2023]
Abstract
One-dimensional conductors are described by Luttinger liquid theory, which predicts a power-law suppression of the single-electron tunneling density of states at low voltages. The scaling exponent is predicted to be quantized when tunneling into a single isolated chiral edge state of the fractional quantum Hall effect. We report conductance measurements across a point contact linking integer and fractional quantum Hall edge states (at fillings 1 and [Formula: see text], respectively). At weak coupling, we observe the predicted universal quadratic scaling with temperature and voltage. At strong coupling, we demonstrate perfect Andreev reflection of fractionalized quasiparticles at the point contact. We use the strong coupling physics to realize a nearly dissipationless direct current voltage step-up transformer, whose gain arises directly from topological fractionalization of electrical charge.
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Affiliation(s)
- Liam A Cohen
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Noah L Samuelson
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Taige Wang
- Department of Physics, University of California, Berkeley, CA 94720, USA
- Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Michael P Zaletel
- Department of Physics, University of California, Berkeley, CA 94720, USA
- Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Andrea F Young
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
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2
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Ma KKW, Wang R, Yang K. Realization of Supersymmetry and Its Spontaneous Breaking in Quantum Hall Edges. PHYSICAL REVIEW LETTERS 2021; 126:206801. [PMID: 34110185 DOI: 10.1103/physrevlett.126.206801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2021] [Accepted: 04/28/2021] [Indexed: 06/12/2023]
Abstract
Supersymmetry (SUSY) relating bosons and fermions plays an important role in unifying different fundamental interactions in particle physics. Since no superpartners of elementary particles have been observed, SUSY, if present, must be broken at low-energy. This makes it important to understand how SUSY is realized and broken, and study their consequences. We show that an N=(1,0) SUSY, arguably the simplest type, can be realized at the edge of the Moore-Read quantum Hall state. Depending on the absence or presence of edge reconstruction, both SUSY-preserving and SUSY broken phases can be realized in the same system, allowing for their unified description. The significance of the gapless fermionic Goldstino mode in the SUSY broken phase is discussed.
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Affiliation(s)
- Ken K W Ma
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Ruojun Wang
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Kun Yang
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
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3
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Zhu W, Sheng DN, Yang K. Topological Interface between Pfaffian and Anti-Pfaffian Order in ν=5/2 Quantum Hall Effect. PHYSICAL REVIEW LETTERS 2020; 125:146802. [PMID: 33064527 DOI: 10.1103/physrevlett.125.146802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Accepted: 09/01/2020] [Indexed: 06/11/2023]
Abstract
A recent thermal Hall experiment triggered renewed interest in the problem of ν=5/2 quantum Hall effect, which motivated novel interpretations based on the formation of mesoscopic puddles made of Pfaffian and anti-Pfaffian topological orders. Here, we study an interface between the Pfaffian and anti-Pfaffian states, which may play crucial roles in thermal transport, by means of state-of-the-art, density-matrix renormalization group simulations. We demonstrate that an intrinsic electric dipole moment emerges at the interface, similar to the "p-n" junction sandwiched between N-type and P-type semiconductor. Importantly, we elucidate the topological origin of this dipole moment, whose formation is to counterbalance the mismatch of guiding-center Hall viscosity of bulk Pfaffian and anti-Pfaffian states. In addition, these results imply that the formation of a dipole moment could be helpful to stabilize the puddles made of Pfaffian and anti-Pfaffian states in experimental conditions.
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Affiliation(s)
- W Zhu
- Institute of Natural Sciences, Westlake Institute of Advanced Study, Hangzhou, 030024, China and School of Science, Westlake University, Hangzhou, 030024, China
| | - D N Sheng
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Kun Yang
- National High Magnetic Field Laboratory and Physics Department, Florida State University, Tallahassee, Florida 32306, USA
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4
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Bandyopadhyay S, Ortiz G, Nussinov Z, Seidel A. Local Two-Body Parent Hamiltonians for the Entire Jain Sequence. PHYSICAL REVIEW LETTERS 2020; 124:196803. [PMID: 32469535 DOI: 10.1103/physrevlett.124.196803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Accepted: 04/27/2020] [Indexed: 06/11/2023]
Abstract
Using an algebra of second-quantized operators, we develop local two-body parent Hamiltonians for all unprojected Jain states at filling factor n/(2np+1), with integer n and (half-)integer p. We rigorously establish that these states are uniquely stabilized and that zero mode counting reproduces mode counting in the associated edge conformal field theory. We further establish the organizing "entangled Pauli principle" behind the resulting zero mode paradigm and unveil an emergent SU(n) symmetry characteristic of the fixed point physics of the Jain quantum Hall fluid.
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Affiliation(s)
- Sumanta Bandyopadhyay
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
| | - Gerardo Ortiz
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
- Department of Physics, Indiana University, Bloomington, Indiana 47405-7105, USA
| | - Zohar Nussinov
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Alexander Seidel
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
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5
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Macaluso E, Comparin T, Mazza L, Carusotto I. Fusion Channels of Non-Abelian Anyons from Angular-Momentum and Density-Profile Measurements. PHYSICAL REVIEW LETTERS 2019; 123:266801. [PMID: 31951460 DOI: 10.1103/physrevlett.123.266801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Indexed: 06/10/2023]
Abstract
We present a method to characterize non-Abelian anyons that is based only on static measurements and that does not rely on any form of interference. For geometries where the anyonic statistics can be revealed by rigid rotations of the anyons, we link this property to the angular momentum of the initial state. We test our method on the paradigmatic example of the Moore-Read state that is known to support excitations with non-Abelian statistics of Ising type. As an example, we reveal the presence of different fusion channels for two such excitations, a defining feature of non-Abelian anyons. This is obtained by measuring density-profile properties, like the mean square radius of the system or the depletion generated by the anyons. Our study paves the way to novel methods for characterizing non-Abelian anyons, both in the experimental and theoretical domains.
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Affiliation(s)
- E Macaluso
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Trento, Italy
| | - T Comparin
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Trento, Italy
| | - L Mazza
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - I Carusotto
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Trento, Italy
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6
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Hu Y, Venderbos JWF, Kane CL. Fractional Excitonic Insulator. PHYSICAL REVIEW LETTERS 2018; 121:126601. [PMID: 30296161 DOI: 10.1103/physrevlett.121.126601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2018] [Indexed: 06/08/2023]
Abstract
We argue that a correlated fluid of electrons and holes can exhibit a fractional quantum Hall effect at zero magnetic field analogous to the Laughlin state at filling 1/m. We introduce a variant of the Laughlin wave function for electrons and holes and show that for m=1 it is the exact ground state of a free fermion model that describes p_{x}+ip_{y} excitonic pairing. For m>1 we develop a simple composite fermion mean field theory, and we present evidence that our wave function correctly describes this phase. We derive an interacting Hamiltonian for which our wave function is the exact ground state, and we present physical arguments that the m=3 state can be realized in a system in which energy bands with angular momentum that differ by 3 cross at the Fermi energy. This leads to a gapless state with (p_{x}+ip_{y})^{3} excitonic pairing, which we argue is conducive to forming the fractional excitonic insulator in the presence of interactions. Prospects for numerics on model systems and band structure engineering to realize this phase in real materials are discussed.
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Affiliation(s)
- Yichen Hu
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Jörn W F Venderbos
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - C L Kane
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
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7
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Ghazaryan A, Graß T, Gullans MJ, Ghaemi P, Hafezi M. Light-Induced Fractional Quantum Hall Phases in Graphene. PHYSICAL REVIEW LETTERS 2017; 119:247403. [PMID: 29286754 DOI: 10.1103/physrevlett.119.247403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Indexed: 06/07/2023]
Abstract
We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at nonzero relative angular momentum can become dominant, resembling a hollow-core pseudopotential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν=1/2 and ν=2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.
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Affiliation(s)
- Areg Ghazaryan
- Department of Physics, City College, City University of New York, New York, New York 10031, USA
| | - Tobias Graß
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, College Park, Maryland 20742, USA
| | - Michael J Gullans
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Pouyan Ghaemi
- Department of Physics, City College, City University of New York, New York, New York 10031, USA
- Department of Physics, Graduate Center, City University of New York, New York, New York 10016, USA
| | - Mohammad Hafezi
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, College Park, Maryland 20742, USA
- Department of Electrical Engineering and IREAP, University of Maryland, College Park, Maryland 20742, USA
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8
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Lin X, Du R, Xie X. Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene. Natl Sci Rev 2014. [DOI: 10.1093/nsr/nwu071] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Abstract
The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.
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Affiliation(s)
- Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ruirui Du
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xincheng Xie
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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9
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Papić Z, Haldane FDM, Rezayi EH. Quantum phase transitions and the ν=5/2 fractional Hall state in wide quantum wells. PHYSICAL REVIEW LETTERS 2012; 109:266806. [PMID: 23368602 DOI: 10.1103/physrevlett.109.266806] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2012] [Indexed: 06/01/2023]
Abstract
We study the nature of the ν=5/2 quantum Hall state in wide quantum wells under the mixing of electronic subbands and Landau levels. A general method is introduced to analyze the Moore-Read pfaffian state and its particle-hole conjugate, the anti-pfaffian state, under periodic boundary conditions in a "quartered" Brillouin zone scheme containing both even and odd numbers of electrons. By examining the rotational quantum numbers on the torus, we show spontaneous breaking of the particle-hole symmetry can be observed in finite-size systems. In the presence of electronic-subband and Landau-level mixing, the particle-hole symmetry is broken in such a way that the anti-pfaffian state is unambiguously favored, and becomes more robust in the vicinity of a transition to the compressible phase, in agreement with recent experiments.
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Affiliation(s)
- Z Papić
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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10
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Rodríguez ID, Simon SH, Slingerland JK. Evaluation of ranks of real space and particle entanglement spectra for large systems. PHYSICAL REVIEW LETTERS 2012; 108:256806. [PMID: 23004635 DOI: 10.1103/physrevlett.108.256806] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2011] [Indexed: 06/01/2023]
Abstract
We devise a way to calculate the dimensions of symmetry sectors appearing in the particle entanglement spectrum (PES) and real space entanglement spectrum (RSES) of multiparticle systems from their real space wave functions. We first note that these ranks in the entanglement spectra equal the dimensions of spaces of wave functions with a number of particles fixed. This also yields equality of the multiplicities in the PES and the RSES. Our technique allows numerical calculations for much larger systems than were previously feasible. For somewhat smaller systems, we can find approximate entanglement energies as well as multiplicities. We illustrate the method with results on the RSES and PES multiplicities for integer quantum Hall states, Laughlin and Jain composite fermion states, and for the Moore-Read state at filling ν = 5/2 for system sizes up to 70 particles.
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Affiliation(s)
- Iván D Rodríguez
- Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland
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11
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Dubail J, Read N. Entanglement spectra of complex paired superfluids. PHYSICAL REVIEW LETTERS 2011; 107:157001. [PMID: 22107314 DOI: 10.1103/physrevlett.107.157001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2011] [Indexed: 05/31/2023]
Abstract
We study the entanglement in various fully gapped complex paired states of fermions in two dimensions, focusing on the entanglement spectrum (ES), and using the Bardeen-Cooper-Schrieffer (BCS) form of the ground-state wave function on a cylinder. Certain forms of the pairing functions allow a simple and explicit exact solution for the ES. In the weak-pairing phase of ℓ-wave paired spinless fermions (ℓ odd), the universal low-lying part of the ES consists of |ℓ| chiral Majorana fermion modes [or 2|ℓ| (ℓ even) for spin-singlet states]. For |ℓ|>1, the pseudoenergies of the modes are split in general, but for all ℓ there is a zero-pseudoenergy mode at a zero wave vector if the number of modes is odd. This ES agrees with the perturbed conformal field theory of the edge excitations. For more general BCS states, we show how the entanglement gap diverges as a model pairing function is approached.
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Affiliation(s)
- J Dubail
- Department of Physics, Yale University, P.O. Box 208120, New Haven, Connecticut 06520-8120, USA
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12
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Bid A, Ofek N, Inoue H, Heiblum M, Kane CL, Umansky V, Mahalu D. Observation of neutral modes in the fractional quantum Hall regime. Nature 2010; 466:585-90. [DOI: 10.1038/nature09277] [Citation(s) in RCA: 162] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2010] [Accepted: 06/17/2010] [Indexed: 11/09/2022]
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13
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14
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Grosfeld E, Das S. Probing the neutral edge modes in transport across a point contact via thermal effects in the Read-Rezayi non-Abelian quantum Hall states. PHYSICAL REVIEW LETTERS 2009; 102:106403. [PMID: 19392135 DOI: 10.1103/physrevlett.102.106403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2008] [Indexed: 05/27/2023]
Abstract
Non-Abelian quantum Hall states are characterized by the simultaneous appearance of charge and neutral gapless edge modes, with the structure of the latter being intricately related to the existence of bulk quasiparticle excitations obeying non-Abelian statistics. Here we propose a scenario for detecting the neutral modes by having two point contacts in series separated by a distance set by the thermal equilibration length of the charge mode. We show that by using the first point contact as a heating device, the excess charge noise measured at the second point contact carries a nontrivial signature of the presence of the neutral mode. We also obtain explicit expressions for the thermal conductance and corresponding Lorentz number for transport across a quantum point contact between two edges held at different temperatures and chemical potentials.
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Affiliation(s)
- Eytan Grosfeld
- Department of Physics, University of Illinois, 1110 West Green Street, Urbana Illinois 61801-3080, USA
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15
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Radu IP, Miller JB, Marcus CM, Kastner MA, Pfeiffer LN, West KW. Quasi-Particle Properties from Tunneling in the
v
= 5/2 Fractional Quantum Hall State. Science 2008; 320:899-902. [DOI: 10.1126/science.1157560] [Citation(s) in RCA: 267] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Iuliana P. Radu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - J. B. Miller
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - C. M. Marcus
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - M. A. Kastner
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - L. N. Pfeiffer
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - K. W. West
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
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16
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Lee SS, Ryu S, Nayak C, Fisher MPA. Particle-hole symmetry and the nu=5/2 quantum Hall state. PHYSICAL REVIEW LETTERS 2007; 99:236807. [PMID: 18233397 DOI: 10.1103/physrevlett.99.236807] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2007] [Indexed: 05/06/2023]
Abstract
We discuss the implications of approximate particle-hole symmetry in a half-filled Landau level in which a paired quantum Hall state forms. We note that the Pfaffian state is not particle-hole symmetric. Therefore, in the limit of vanishing Landau-level mixing, in which particle-hole transformation is an exact symmetry, the Pfaffian spontaneously breaks this symmetry. There is a particle-hole conjugate state, which we call the anti-Pfaffian, which is degenerate with the Pfaffian in this limit. We observe that strong Landau-level mixing should favor the Pfaffian, but it is an open problem which state is favored for the moderate Landau-level mixing which is present in experiments. We discuss the bulk and edge physics of the anti-Pfaffian. We analyze a simplified model in which transitions between analogs of the two states can be studied in detail. Finally, we discuss experimental implications.
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Affiliation(s)
- Sung-Sik Lee
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
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17
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Wan X, Yang K, Rezayi EH. Edge excitations and non-Abelian statistics in the moore-read state: A numerical study in the presence of coulomb interaction and edge confinement. PHYSICAL REVIEW LETTERS 2006; 97:256804. [PMID: 17280380 DOI: 10.1103/physrevlett.97.256804] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2006] [Indexed: 05/13/2023]
Abstract
We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at a filling fraction nu = 5/2, with Coulomb interaction and a background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge +e/4 quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Majorana fermions, clearly indicating the non-Abelian nature of the quasihole.
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Affiliation(s)
- Xin Wan
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
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18
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Fendley P, Fisher MPA, Nayak C. Dynamical disentanglement across a point contact in a non-Abelian quantum Hall state. PHYSICAL REVIEW LETTERS 2006; 97:036801. [PMID: 16907526 DOI: 10.1103/physrevlett.97.036801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2006] [Indexed: 05/11/2023]
Abstract
We analyze the tunneling of non-Abelian quasiparticles between the edges of a quantum Hall droplet at the Landau level filling fraction nu=5/2, assuming that the electrons in the first excited Landau level organize themselves in the non-Abelian Moore-Read Pfaffian state. By bosonizing the edge theory, we show that an effective spin-1/2 degree of freedom emerges in the description of a point contact. We show how the crossover from the high-temperature regime of weak quasiparticle tunneling between the edges of the droplet, with the 4-terminal Rxx approximately T(-3/2), to the low-temperature limit, with Rxx(-1/10)(h/e2) approximately-T4, is closely related to the two-channel Kondo effect. We give a physical interpretation for the entropy loss of ln(2[square root of 2) in this crossover.
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Affiliation(s)
- Paul Fendley
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904-4714, USA
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19
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Ino K. Field theory of spin-singlet quantum Hall states. PHYSICAL REVIEW LETTERS 2001; 86:882-885. [PMID: 11177964 DOI: 10.1103/physrevlett.86.882] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2000] [Indexed: 05/23/2023]
Abstract
We formulate a field theory for the Haldane-Rezayi quantum Hall state and its variants. A new essential ingredient is a class of super Chern-Simons field.
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Affiliation(s)
- K Ino
- Nomura Research Institute, Hongo 2-2-9, Bunkyo-ku, Tokyo, 113-0033, Japan
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20
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Read N, Rezayi E. Quasiholes and fermionic zero modes of paired fractional quantum Hall states: The mechanism for non-Abelian statistics. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:16864-16887. [PMID: 9985816 DOI: 10.1103/physrevb.54.16864] [Citation(s) in RCA: 110] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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