1
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Wang C, Gupta A, Singh SK, Madathil PT, Chung YJ, Pfeiffer LN, Baldwin KW, Winkler R, Shayegan M. Fractional Quantum Hall State at Filling Factor ν=1/4 in Ultra-High-Quality GaAs Two-Dimensional Hole Systems. PHYSICAL REVIEW LETTERS 2023; 131:266502. [PMID: 38215363 DOI: 10.1103/physrevlett.131.266502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 12/01/2023] [Indexed: 01/14/2024]
Abstract
Single-component fractional quantum Hall states (FQHSs) at even-denominator filling factors may host non-Abelian quasiparticles that are considered to be building blocks of topological quantum computers. Such states, however, are rarely observed in the lowest-energy Landau level, namely at filling factors ν<1. Here, we report evidence for an even-denominator FQHS at ν=1/4 in ultra-high-quality two-dimensional hole systems confined to modulation-doped GaAs quantum wells. We observe a deep minimum in the longitudinal resistance at ν=1/4, superimposed on a highly insulating background, suggesting a close competition between the ν=1/4 FQHS and the magnetic-field-induced, pinned Wigner solid states. Our experimental observations are consistent with the very recent theoretical calculations that predict that substantial Landau level mixing, caused by the large hole effective mass, can induce composite fermion pairing and lead to a non-Abelian FQHS at ν=1/4. Our results demonstrate that Landau level mixing can provide a very potent means for tuning the interaction between composite fermions and creating new non-Abelian FQHSs.
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Affiliation(s)
- Chengyu Wang
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S K Singh
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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2
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Zhao T, Balram AC, Jain JK. Composite Fermion Pairing Induced by Landau Level Mixing. PHYSICAL REVIEW LETTERS 2023; 130:186302. [PMID: 37204896 DOI: 10.1103/physrevlett.130.186302] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 04/10/2023] [Indexed: 05/21/2023]
Abstract
Pairing of composite fermions provides a possible mechanism for fractional quantum Hall effect at even denominator fractions and is believed to serve as a platform for realizing quasiparticles with non-Abelian braiding statistics. We present results from fixed-phase diffusion Monte Carlo calculations which predict that substantial Landau level mixing can induce a pairing of composite fermions at filling factors ν=1/2 and ν=1/4 in the l=-3 relative angular momentum channel, thereby destabilizing the composite-fermion Fermi seas to produce non-Abelian fractional quantum Hall states.
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Affiliation(s)
- Tongzhou Zhao
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Ajit C Balram
- Institute of Mathematical Sciences, CIT Campus, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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3
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Yuzhu W, Bo Y. Geometric fluctuation of conformal Hilbert spaces and multiple graviton modes in fractional quantum Hall effect. Nat Commun 2023; 14:2317. [PMID: 37085543 PMCID: PMC10121662 DOI: 10.1038/s41467-023-38036-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2022] [Accepted: 04/06/2023] [Indexed: 04/23/2023] Open
Abstract
Neutral excitations in fractional quantum Hall (FQH) fluids define the incompressibility of topological phases, a species of which can show graviton-like behaviors and are thus called the graviton modes (GMs). Here, we develop the microscopic theory for multiple GMs in FQH fluids and show explicitly that they are associated with the geometric fluctuation of well-defined conformal Hilbert spaces (CHSs), which are hierarchical subspaces within a single Landau level, each with emergent conformal symmetry and continuously parameterized by a unimodular metric. This leads to several statements about the number and the merging/splitting of GMs, which are verified numerically with both model and realistic interactions. We also discuss how the microscopic theory can serve as the basis for the additional Haldane modes in the effective field theory description and their experimental relevance to realistic electron-electron interactions.
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Affiliation(s)
- Wang Yuzhu
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798, Singapore
| | - Yang Bo
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798, Singapore.
- Institute of High Performance Computing, A*STAR, Singapore, 138632, Singapore.
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4
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Hossain MS, Ma MK, Chung YJ, Singh SK, Gupta A, West KW, Baldwin KW, Pfeiffer LN, Winkler R, Shayegan M. Valley-Tunable Even-Denominator Fractional Quantum Hall State in the Lowest Landau Level of an Anisotropic System. PHYSICAL REVIEW LETTERS 2023; 130:126301. [PMID: 37027870 DOI: 10.1103/physrevlett.130.126301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 02/22/2023] [Indexed: 06/19/2023]
Abstract
Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors (ν) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at ν=1/2 in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multivalley degree of freedom offer an unprecedented tunability of the ν=1/2 FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the ν=1/2 FQHS depend strongly on valley occupancy.
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Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Meng K Ma
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S K Singh
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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5
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Sharma A, Pu S, Balram AC, Jain JK. Fractional Quantum Hall Effect with Unconventional Pairing in Monolayer Graphene. PHYSICAL REVIEW LETTERS 2023; 130:126201. [PMID: 37027884 DOI: 10.1103/physrevlett.130.126201] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 02/24/2023] [Indexed: 06/19/2023]
Abstract
Motivated by the observation of even denominator fractional quantum Hall effect in the n=3 Landau level of monolayer graphene [Kim et al., Nat. Phys. 15, 154 (2019)NPAHAX1745-247310.1038/s41567-018-0355-x], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an f-wave pairing. Analogous calculation suggests the possibility of a p-wave pairing of composite fermions at half filling in the n=2 graphene Landau level, whereas no pairing instability is found at half filling in the n=0 and n=1 graphene Landau levels. The relevance of these results to experiments is discussed.
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Affiliation(s)
- Anirban Sharma
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Songyang Pu
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
- 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
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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6
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Wang C, Gupta A, Singh SK, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Winkler R, Shayegan M. Even-Denominator Fractional Quantum Hall State at Filling Factor ν=3/4. PHYSICAL REVIEW LETTERS 2022; 129:156801. [PMID: 36269975 DOI: 10.1103/physrevlett.129.156801] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 08/17/2022] [Indexed: 06/16/2023]
Abstract
Fractional quantum Hall states (FQHSs) exemplify exotic phases of low-disorder two-dimensional (2D) electron systems when electron-electron interaction dominates over the thermal and kinetic energies. Particularly intriguing among the FQHSs are those observed at even-denominator Landau level filling factors, as their quasiparticles are generally believed to obey non-Abelian statistics and be of potential use in topological quantum computing. Such states, however, are very rare and fragile, and are typically observed in the excited Landau level of 2D electron systems with the lowest amount of disorder. Here we report the observation of a new and unexpected even-denominator FQHS at filling factor ν=3/4 in a GaAs 2D hole system with an exceptionally high quality (mobility). Our magnetotransport measurements reveal a strong minimum in the longitudinal resistance at ν=3/4, accompanied by a developing Hall plateau centered at (h/e^{2})/(3/4). This even-denominator FQHS is very unusual as it is observed in the lowest Landau level and in a 2D hole system. While its origin is unclear, it is likely a non-Abelian state, emerging from the residual interaction between composite fermions.
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Affiliation(s)
- Chengyu Wang
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S K Singh
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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7
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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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