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Das S, Das S, Mandal SS. Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength. PHYSICAL REVIEW LETTERS 2023; 131:056202. [PMID: 37595232 DOI: 10.1103/physrevlett.131.056202] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 06/26/2023] [Indexed: 08/20/2023]
Abstract
A successful probing of the neutral Majorana mode in recent thermal Hall conductivity measurements opines in favor of the particle-hole symmetric Pfaffian (PH-Pf) topological order, contrasting the theoretical predictions of Pfaffian or anti-Pfaffian phases. Here we report a reentrant anomalous quantized phase that is found to be gapped in the thermodynamic limit, distinct from the conventional Pfaffian, anti-Pfaffian, or PH-Pf phases, at an intermediate strength of Landau level mixing. Our proposed wave function consistent with the PH-Pf shift in spherical geometry rightly captures the topological order of this phase, as its overlap with the exact ground state is very high and it reproduces low-lying entanglement spectra. A unique topological order, irrespective of the flux shifts, found for this phase, possibly corroborates the experimentally found topological order.
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Affiliation(s)
- Sudipto Das
- Department of Physics, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Sahana Das
- Department of Physics, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Sudhansu S Mandal
- Department of Physics, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
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2
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Pu S, Balram AC, Fremling M, Gromov A, Papić Z. Signatures of Supersymmetry in the ν=5/2 Fractional Quantum Hall Effect. PHYSICAL REVIEW LETTERS 2023; 130:176501. [PMID: 37172226 DOI: 10.1103/physrevlett.130.176501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Accepted: 04/10/2023] [Indexed: 05/14/2023]
Abstract
The Moore-Read state, one of the leading candidates for describing the fractional quantum Hall effect at filling factor ν=5/2, is a paradigmatic p-wave superconductor with non-Abelian topological order. Among its many exotic properties, the state hosts two collective modes: a bosonic density wave and a neutral fermion mode that arises from an unpaired electron in the condensate. It has recently been proposed that the descriptions of the two modes can be unified by postulating supersymmetry (SUSY) that relates them in the long-wavelength limit. Here we extend the SUSY description to construct wave functions of the two modes on closed surfaces, such as the sphere and torus, and we test the resulting states in large-scale numerical simulations. We demonstrate the equivalence in the long-wavelength limit between SUSY wave functions and previous descriptions of collective modes based on the Girvin-MacDonald-Platzman ansatz, Jack polynomials, and bipartite composite fermions. Leveraging the first-quantized form of the SUSY wave functions, we study their energies using the Monte Carlo method and show that realistic ν=5/2 systems are close to the putative SUSY point, where the two collective modes become degenerate in energy.
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Affiliation(s)
- Songyang Pu
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Ajit C Balram
- Institute of Mathematical Sciences, CIT Campus, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India
| | - Mikael Fremling
- Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - Andrey Gromov
- Department of Physics and Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20740, USA
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
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3
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Yang B. Fractional Quantum Hall Effect from Frustration-Free Hamiltonians. PHYSICAL REVIEW LETTERS 2020; 125:176402. [PMID: 33156656 DOI: 10.1103/physrevlett.125.176402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 09/24/2020] [Indexed: 05/06/2023]
Abstract
We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalized set of few-body coherent states. In particular, model Hamiltonians of the FQH effect (FQHE) are equivalent to the real-space von Neumann lattice of local projection operators imposed on a continuous system in the thermodynamic limit. It can be analytically derived that tuning local one-body potentials in such lattices amounts to the tuning of individual two- or few-body pseudopotentials. For some cases, we can realize pure few-body pseudopotentials important for stabilizing exotic non-Abelian topological phases. Thus, this new approach can potentially lead to the experimental realization of coveted non-Abelian quantum fluids including the Moore-Read state and the Fibonacci state. The reformulation of the FQHE as a sum of local projections opens up new paths for rigorously proving the incompressibility of microscopic Hamiltonians in the thermodynamic limit.
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Affiliation(s)
- Bo Yang
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371 and Institute of High Performance Computing, A*STAR, Singapore, 138632
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4
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Zhu W, Sheng DN. Disorder-Driven Transition in the ν=5/2 Fractional Quantum Hall Effect. PHYSICAL REVIEW LETTERS 2019; 123:056804. [PMID: 31491310 DOI: 10.1103/physrevlett.123.056804] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2018] [Revised: 05/09/2019] [Indexed: 06/10/2023]
Abstract
The fractional quantum Hall (FQH) effect at the filling number ν=5/2 is a primary candidate for non-Abelian topological order, while the fate of such a state in the presence of random disorder has not been resolved. We address this open question by implementing an unbiased diagnosis based on numerical exact diagonalization. We calculate the disorder averaged Hall conductance and the associated statistical distribution of the topological invariant Chern number, which unambiguously characterize the disorder-driven collapse of the FQH state. As the disorder strength increases towards a critical value, a continuous phase transition is detected based on the disorder configuration averaged wave function fidelity and the entanglement entropy. In the strong disorder regime, we identify a composite Fermi liquid phase with fluctuating Chern numbers, in striking contrast to the well-known ν=1/3 case where an Anderson insulator appears. Interestingly, the lowest Landau level projected a local density profile, the wave function overlap, and the entanglement entropy as a function of disorder strength simultaneously signal an intermediate phase, which may be relevant to the recent proposal of a particle-hole Pfaffian state or Pfaffian-anti-Pfaffian puddle state.
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Affiliation(s)
- W Zhu
- Institute of Natural Sciences, Westlake Institute of Advanced Study and School of Science, Westlake University, Hangzhou 030024, China
- Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - D N Sheng
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
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Lee CH, Ho WW, Yang B, Gong J, Papić Z. Floquet Mechanism for Non-Abelian Fractional Quantum Hall States. PHYSICAL REVIEW LETTERS 2018; 121:237401. [PMID: 30576179 DOI: 10.1103/physrevlett.121.237401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2018] [Revised: 09/17/2018] [Indexed: 06/09/2023]
Abstract
Three-body correlations, which arise between spin-polarized electrons in the first excited Landau level, are believed to play a key role in the emergence of enigmatic non-Abelian fractional quantum Hall (FQH) effects. Inspired by recent advances in Floquet engineering, we investigate periodic driving of anisotropic two-body interactions as a route for controllably creating and tuning effective three-body interactions in the FQH regime. We develop an analytic formalism to describe this Floquet-FQH protocol, which is distinct from previous approaches that instead focus on band structure engineering via modulation of single-particle hopping terms. By systematically analyzing the resulting interactions using generalized pseudopotentials, we show that our Floquet-FQH approach leads to repulsive as well as attractive three-body interactions that are highly tunable and support a variety of non-Abelian multicomponent FQH states. Finally, we propose an implementation of the protocol in optically dressed ultracold polar molecules with modulated Rabi frequencies.
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Affiliation(s)
- Ching Hua Lee
- Institute of High Performance Computing, A*STAR, Singapore, 138632
- Department of Physics, National University of Singapore, Singapore, 117542
| | - Wen Wei Ho
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Bo Yang
- Institute of High Performance Computing, A*STAR, Singapore, 138632
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore, 637371
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore, 117542
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
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6
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Balram AC, Mukherjee S, Park K, Barkeshli M, Rudner MS, Jain JK. Fractional Quantum Hall Effect at ν=2+6/13: The Parton Paradigm for the Second Landau Level. PHYSICAL REVIEW LETTERS 2018; 121:186601. [PMID: 30444400 DOI: 10.1103/physrevlett.121.186601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Indexed: 06/09/2023]
Abstract
The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν=2+6/13 [A. Kumar et al., Phys. Rev. Lett. 105, 246808 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.246808] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a "3[over ¯]2[over ¯]111" parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the 3[over ¯]2[over ¯]111 state to be a good candidate for the ν=2+6/13 FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the "n[over ¯]2[over ¯]111" family of parton states naturally describes many observed SLL FQHE plateaus.
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Affiliation(s)
- Ajit C Balram
- Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Sutirtha Mukherjee
- Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Kwon Park
- Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Maissam Barkeshli
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20472, USA
| | - Mark S Rudner
- Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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7
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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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8
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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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9
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Wang YF, Yao H, Gu ZC, Gong CD, Sheng DN. Non-abelian quantum Hall effect in topological flat bands. PHYSICAL REVIEW LETTERS 2012; 108:126805. [PMID: 22540612 DOI: 10.1103/physrevlett.108.126805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2011] [Indexed: 05/31/2023]
Abstract
Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable ν=1 bosonic non-abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read pfaffian state.
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Affiliation(s)
- Yi-Fei Wang
- Center for Statistical and Theoretical Condensed Matter Physics, and Department of Physics, Zhejiang Normal University, Jinhua 321004, China
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10
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Deng N, Kumar A, Manfra MJ, Pfeiffer LN, West KW, Csáthy GA. Collective nature of the reentrant integer quantum Hall states in the second Landau level. PHYSICAL REVIEW LETTERS 2012; 108:086803. [PMID: 22463555 DOI: 10.1103/physrevlett.108.086803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2011] [Indexed: 05/31/2023]
Abstract
We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature.
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Affiliation(s)
- N Deng
- Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA
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11
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Rezayi EH, Simon SH. Breaking of particle-hole symmetry by Landau level mixing in the ν=5/2 quantized Hall state. PHYSICAL REVIEW LETTERS 2011; 106:116801. [PMID: 21469885 DOI: 10.1103/physrevlett.106.116801] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2010] [Indexed: 05/30/2023]
Abstract
We perform numerical studies to determine if the fractional quantum Hall state observed at a filling factor of ν=5/2 is the Moore-Read wave function or its particle-hole conjugate, the so-called anti-Pfaffian. Using a truncated Hilbert space approach we find that, for realistic interactions, including Landau-level mixing, the ground state remains fully polarized and the anti-Pfaffian is strongly favored.
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Affiliation(s)
- Edward H Rezayi
- Department of Physics, California State University, Los Angeles, California 90032, USA
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Kumar A, Csáthy GA, Manfra MJ, Pfeiffer LN, West KW. Nonconventional odd-denominator fractional quantum Hall states in the second Landau level. PHYSICAL REVIEW LETTERS 2010; 105:246808. [PMID: 21231551 DOI: 10.1103/physrevlett.105.246808] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2010] [Indexed: 05/30/2023]
Abstract
We report the observation of a new fractional quantum Hall state in the second Landau level of a two-dimensional electron gas at the Landau level filling factor ν=2+6/13. We find that the model of noninteracting composite fermions can explain the magnitude of gaps of the prominent 2+1/3 and 2+2/3 states. The same model fails, however, to account for the gaps of the 2+2/5 and the newly observed 2+6/13 states suggesting that these two states are of exotic origin.
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Affiliation(s)
- A Kumar
- Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA
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Wójs A, Toke C, Jain JK. Landau-level mixing and the emergence of Pfaffian excitations for the 5/2 fractional quantum Hall effect. PHYSICAL REVIEW LETTERS 2010; 105:096802. [PMID: 20868183 DOI: 10.1103/physrevlett.105.096802] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2010] [Indexed: 05/29/2023]
Abstract
We report on exact diagonalization studies for fully spin polarized 5/2 fractional quantum Hall effect, incorporating Landau-level mixing through the Bishara-Nayak effective interaction. We find that there is an experimentally accessible region in the phase diagram where the Pfaffian model accurately describes not only the ground state but also the neutral and charged excitations. These results are consistent with the observed persistence of the 5/2 Hall effect down to very low magnetic fields; they are also relevant to the experimental attempts to detect non-Abelian braid statistics.
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Affiliation(s)
- Arkadiusz Wójs
- TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
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Zhang C, Knuuttila T, Dai Y, Du RR, Pfeiffer LN, West KW. Nu = 5/2 fractional quantum Hall effect at 10 T: implications for the Pfaffian state. PHYSICAL REVIEW LETTERS 2010; 104:166801. [PMID: 20482071 DOI: 10.1103/physrevlett.104.166801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2009] [Indexed: 05/29/2023]
Abstract
We report on the magnetotransport (including tilt fields) around Landau level filling factor nu=5/2 in a high-purity modulation-doped GaAs/AlGaAs quantum well with twice the electron density of standard samples. A quantized 5/2 Hall plateau is observed at B approximately = 10 T, with an activation gap approximately 125 mK; the plateau can persist up to approximately 25 degree tilt field. This finding is discussed in the context of a proposed Moore-Read Pfaffian (or anti-Pfaffian) wave function being a possible ground state at 5/2. The tilt fields induce a background resistance at 5/2 that could be either isotropic or anisotropic, depending simply on the in-plane magnetic field direction with respect to the GaAs crystalline axis. Such data indicate a substantial coupling between the 5/2 collective phases and the GaAs crystal.
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Affiliation(s)
- Chi Zhang
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251, USA
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