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Huang H, Hussain W, Myers SA, Pfeiffer LN, West KW, Baldwin KW, Csáthy GA. Evidence for Topological Protection Derived from Six-Flux Composite Fermions. Nat Commun 2024; 15:1461. [PMID: 38368413 PMCID: PMC10874392 DOI: 10.1038/s41467-024-45860-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 02/05/2024] [Indexed: 02/19/2024] Open
Abstract
The composite fermion theory opened a new chapter in understanding many-body correlations through the formation of emergent particles. The formation of two-flux and four-flux composite fermions is well established. While there are limited data linked to the formation of six-flux composite fermions, topological protection associated with them is conspicuously lacking. Here we report evidence for the formation of a quantized and gapped fractional quantum Hall state at the filling factor ν = 9/11, which we associate with the formation of six-flux composite fermions. Our result provides evidence for the most intricate composite fermion with six fluxes and expands the already diverse family of highly correlated topological phases with a new member that cannot be characterized by correlations present in other known members. Our observations pave the way towards the study of higher order correlations in the fractional quantum Hall regime.
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Affiliation(s)
- Haoyun Huang
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - Waseem Hussain
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - S A Myers
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - G A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA.
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2
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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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3
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Madathil PT, Rosales KAV, Chung YJ, West KW, Baldwin KW, Pfeiffer LN, Engel LW, Shayegan M. Moving Crystal Phases of a Quantum Wigner Solid in an Ultra-High-Quality 2D Electron System. PHYSICAL REVIEW LETTERS 2023; 131:236501. [PMID: 38134784 DOI: 10.1103/physrevlett.131.236501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 10/24/2023] [Indexed: 12/24/2023]
Abstract
In low-disorder, two-dimensional electron systems (2DESs), the fractional quantum Hall states at very small Landau level fillings (ν) terminate in a Wigner solid (WS) phase, where electrons arrange themselves in a periodic array. The WS is typically pinned by the residual disorder sites and manifests an insulating behavior, with nonlinear current-voltage (I-V) and noise characteristics. We report here measurements on an ultralow-disorder, dilute 2DES, confined to a GaAs quantum well. In the ν<1/5 range, superimposed on a highly insulating longitudinal resistance, the 2DES exhibits a developing fractional quantum Hall state at ν=1/7, attesting to its exceptional high quality and dominance of electron-electron interaction in the low filling regime. In the nearby insulating phases, we observe remarkable nonlinear I-V and noise characteristics as a function of increasing current, with current thresholds delineating three distinct phases of the WS: a pinned phase (P1) with very small noise, a second phase (P2) in which dV/dI fluctuates between positive and negative values and is accompanied by very high noise, and a third phase (P3) where dV/dI is nearly constant and small, and noise is about an order of magnitude lower than in P2. In the depinned (P2 and P3) phases, the noise spectrum also reveals well-defined peaks at frequencies that vary linearly with the applied current, suggestive of washboard frequencies. We discuss the data in light of a recent theory that proposes different dynamic phases for a driven WS.
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Affiliation(s)
- P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- 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
| | - 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
| | - L W Engel
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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4
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Zhao L, Lin W, Chung YJ, Gupta A, Baldwin KW, Pfeiffer LN, Liu Y. Dynamic Response of Wigner Crystals. PHYSICAL REVIEW LETTERS 2023; 130:246401. [PMID: 37390428 DOI: 10.1103/physrevlett.130.246401] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Accepted: 05/26/2023] [Indexed: 07/02/2023]
Abstract
The Wigner crystal, an ordered array of electrons, is one of the very first proposed many-body phases stabilized by the electron-electron interaction. We examine this quantum phase with simultaneous capacitance and conductance measurements, and observe a large capacitive response while the conductance vanishes. We study one sample with four devices whose length scale is comparable with the crystal's correlation length, and deduce the crystal's elastic modulus, permittivity, pinning strength, etc. Such a systematic quantitative investigation of all properties on a single sample has a great promise to advance the study of Wigner crystals.
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Affiliation(s)
- Lili Zhao
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
| | - Wenlu Lin
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
| | - Yoon Jang Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Adbhut Gupta
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Kirk W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Loren N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Yang Liu
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
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Hossain MS, Ma MK, Villegas-Rosales KA, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Anisotropic Two-Dimensional Disordered Wigner Solid. PHYSICAL REVIEW LETTERS 2022; 129:036601. [PMID: 35905352 DOI: 10.1103/physrevlett.129.036601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2021] [Accepted: 06/07/2022] [Indexed: 06/15/2023]
Abstract
The interplay between the Fermi sea anisotropy, electron-electron interaction, and localization phenomena can give rise to exotic many-body phases. An exciting example is an anisotropic two-dimensional (2D) Wigner solid (WS), where electrons form an ordered array with an anisotropic lattice structure. Such a state has eluded experiments up to now as its realization is extremely demanding: First, a WS entails very low densities where the Coulomb interaction dominates over the kinetic (Fermi) energy. Attaining such low densities while keeping the disorder low is very challenging. Second, the low-density requirement has to be fulfilled in a material that hosts an anisotropic Fermi sea. Here, we report transport measurements in a clean (low-disorder) 2D electron system with anisotropic effective mass and Fermi sea. The data reveal that at extremely low electron densities, when the r_{s} parameter, the ratio of the Coulomb to the Fermi energy, exceeds ≃38, the current-voltage characteristics become strongly nonlinear at small dc biases. Several key features of the nonlinear characteristics, including their anisotropic voltage thresholds, are consistent with the formation of a disordered, anisotropic WS pinned by the ubiquitous disorder potential.
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Affiliation(s)
- Md S Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas-Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, 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
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Zhao L, Lin W, Fan X, Song Y, Lu H, Liu Y. High precision, low excitation capacitance measurement methods from 10 mK to room temperature. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:053910. [PMID: 35649778 DOI: 10.1063/5.0087772] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2022] [Accepted: 04/30/2022] [Indexed: 06/15/2023]
Abstract
Capacitance measurement is a useful technique in studying quantum devices, as it directly probes the local particle charging properties, i.e., the system compressibility. Here, we report one approach that can measure capacitance from mK to room temperature with excellent accuracy. Our experiments show that such a high-precision technique is able to reveal delicate and essential properties of high-mobility two-dimensional electron systems.
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Affiliation(s)
- Lili Zhao
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Wenlu Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xing Fan
- College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Yuanjun Song
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Hong Lu
- College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Yang Liu
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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7
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Ma MK, Villegas Rosales KA, Deng H, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Winkler R, Shayegan M. Thermal and Quantum Melting Phase Diagrams for a Magnetic-Field-Induced Wigner Solid. PHYSICAL REVIEW LETTERS 2020; 125:036601. [PMID: 32745416 DOI: 10.1103/physrevlett.125.036601] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 06/12/2020] [Indexed: 06/11/2023]
Abstract
A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors (ν≃1/5). In dilute GaAs 2D hole systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings (ν≃1/3). Here we report our measurements of the fundamental temperature vs filling phase diagram for the 2D holes' WS-liquid thermal melting. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs filling WS-liquid quantum melting phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.
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Affiliation(s)
- Meng K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - H Deng
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, 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
| | - K W Baldwin
- Department of Electrical 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 Engineering, Princeton University, Princeton, New Jersey 08544, USA
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