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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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2
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Liu Z, Balram AC, Papić Z, Gromov A. Quench Dynamics of Collective Modes in Fractional Quantum Hall Bilayers. PHYSICAL REVIEW LETTERS 2021; 126:076604. [PMID: 33666472 DOI: 10.1103/physrevlett.126.076604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Accepted: 01/22/2021] [Indexed: 05/06/2023]
Abstract
We introduce different types of quenches to probe the nonequilibrium dynamics and multiple collective modes of bilayer fractional quantum Hall states. We show that applying an electric field in one layer induces oscillations of a spin-1 degree of freedom, whose frequency matches the long-wavelength limit of the dipole mode. On the other hand, oscillations of the long-wavelength limit of the quadrupole mode, i.e., the spin-2 graviton, as well as the combination of two spin-1 states, can be activated by a sudden change of band mass anisotropy. We construct an effective field theory to describe the quench dynamics of these collective modes. In particular, we derive the dynamics for both the spin-2 and the spin-1 states and demonstrate their excellent agreement with numerics.
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Affiliation(s)
- Zhao Liu
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China
| | - Ajit C Balram
- Institute of Mathematical Sciences, HBNI, CIT Campus, Chennai 600113, India
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Andrey Gromov
- Brown Theoretical Physics Center and Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
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3
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Hossain MS, Mueed MA, Ma MK, Villegas Rosales KA, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System. PHYSICAL REVIEW LETTERS 2020; 125:046601. [PMID: 32794794 DOI: 10.1103/physrevlett.125.046601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 06/24/2020] [Indexed: 06/11/2023]
Abstract
A fundamental concept in physics is the Fermi surface, the constant-energy surface in momentum space encompassing all the occupied quantum states at absolute zero temperature. In 1960, Luttinger postulated that the area enclosed by the Fermi surface should remain unaffected even when electron-electron interaction is turned on, so long as the interaction does not cause a phase transition. Understanding what determines the Fermi surface size is a crucial and yet unsolved problem in strongly interacting systems such as high-T_{c} superconductors. Here we present a precise test of the Luttinger theorem for a two-dimensional Fermi liquid system where the exotic quasiparticles themselves emerge from the strong interaction, namely, for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs' Fermi wave vector down to very low electron densities, we show that the Luttinger theorem is obeyed over a significant range of interaction strengths, in the sense that the Fermi sea area is determined by the density of the minority carriers in the lowest Landau level. Our data also address the ongoing debates on whether or not CFs obey particle-hole symmetry, and if they are Dirac particles. We find that particle-hole symmetry is obeyed, but the measured Fermi sea area differs quantitatively from that predicted by the Dirac model for CFs.
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Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M A Mueed
- 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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4
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Sun J, Zhong X, Cui W, Shi J, Hao J, Xu M, Li Y. The intrinsic magnetism, quantum anomalous Hall effect and Curie temperature in 2D transition metal trihalides. Phys Chem Chem Phys 2020; 22:2429-2436. [DOI: 10.1039/c9cp05084a] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
It has been theoretically demonstrated that 2D transition metal trihalides can host the QAH effect.
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Affiliation(s)
- Jiaxiang Sun
- School of Physics and Electronic Engineering
- Jiangsu Normal University
- Xuzhou 221116
- China
- Department of Informationization Construction and Management
| | - Xin Zhong
- Center for High Pressure Science and Technology Advanced Research
- Changchun 130012
- China
| | - Wenwen Cui
- School of Physics and Electronic Engineering
- Jiangsu Normal University
- Xuzhou 221116
- China
| | - Jingming Shi
- School of Physics and Electronic Engineering
- Jiangsu Normal University
- Xuzhou 221116
- China
| | - Jian Hao
- School of Physics and Electronic Engineering
- Jiangsu Normal University
- Xuzhou 221116
- China
| | - Meiling Xu
- School of Physics and Electronic Engineering
- Jiangsu Normal University
- Xuzhou 221116
- China
| | - Yinwei Li
- Center for High Pressure Science and Technology Advanced Research
- Changchun 130012
- China
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5
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Wang J. Dirac Fermion Hierarchy of Composite Fermi Liquids. PHYSICAL REVIEW LETTERS 2019; 122:257203. [PMID: 31347889 DOI: 10.1103/physrevlett.122.257203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2018] [Revised: 04/13/2019] [Indexed: 06/10/2023]
Abstract
Composite Fermi liquids (CFLs) are compressible states that can occur for 2D interacting fermions confined in the lowest Landau level at certain Landau level fillings. They have been understood as Fermi seas formed by composite fermions which are bound states of electromagnetic fluxes and electrons as reported by Halperin, Lee, and Read [Phys. Rev. B 47, 7312 (1993)PRBMDO0163-182910.1103/PhysRevB.47.7312]. At half filling, an explicitly particle-hole symmetric theory based on Dirac fermions was proposed by Son [Phys. Rev. X 5, 031027 (2015)PRXHAE2160-330810.1103/PhysRevX.5.031027] as an alternative low energy description. In this work, we investigate the Berry curvature of CFL model wave functions at a filling fraction of one-quarter, and observe that it is uniformly distributed over the Fermi sea except at the center where an additional π phase was found. Motivated by this, we propose an effective theory which generalizes Son's half filling theory, by internal gauge flux attachment, to all filling fractions in which fermionic CFLs can occur. The numerical results support the idea of internal gauge flux attachment.
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Affiliation(s)
- Jie Wang
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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Jo I, Deng H, Liu Y, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Cyclotron Orbits of Composite Fermions in the Fractional Quantum Hall Regime. PHYSICAL REVIEW LETTERS 2018; 120:016802. [PMID: 29350938 DOI: 10.1103/physrevlett.120.016802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Indexed: 06/07/2023]
Abstract
We study a bilayer GaAs hole system that hosts two distinct many-body phases at low temperatures and high perpendicular magnetic fields. The higher-density (top) layer develops a Fermi sea of composite fermions (CFs) in its half-filled lowest Landau level, while the lower-density (bottom) layer forms a Wigner crystal (WC) as its filling becomes very small. Owing to the interlayer interaction, the CFs in the top layer feel the periodic Coulomb potential of the WC in the bottom layer. We measure the magnetoresistance of the top layer while changing the bottom-layer density. As the WC layer density increases, the resistance peaks separating the adjacent fractional quantum Hall states in the top layer change nonmonotonically and attain maximum values when the cyclotron orbit of the CFs encloses one WC lattice point. These features disappear at T=275 mK when the WC melts. The observation of such geometric resonance features is unprecedented and surprising as it implies that the CFs retain a well-defined cyclotron orbit and Fermi wave vector even deep in the fractional quantum Hall regime, far from half-filling.
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Affiliation(s)
- Insun Jo
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Hao Deng
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Yang Liu
- 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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Nguyen DX, Can T, Gromov A. Particle-Hole Duality in the Lowest Landau Level. PHYSICAL REVIEW LETTERS 2017; 118:206602. [PMID: 28581783 DOI: 10.1103/physrevlett.118.206602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2017] [Indexed: 06/07/2023]
Abstract
We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several nontrivial checks of the relations, including for the Jain states and their PH conjugates.
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Affiliation(s)
- Dung Xuan Nguyen
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Tankut Can
- Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, New York 11794, USA
| | - Andrey Gromov
- Kadanoff Center for Theoretical Physics and Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
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Mueed MA, Kamburov D, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States. PHYSICAL REVIEW LETTERS 2016; 117:246801. [PMID: 28009213 DOI: 10.1103/physrevlett.117.246801] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 06/06/2023]
Abstract
Via the application of a parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells and study the geometric resonance of composite fermions (CFs) with a periodic density modulation in our samples. The measurements reveal that CFs exist close to bilayer quantum Hall states, formed at Landau level filling factors ν=1 and 1/2. Near ν=1, the geometric resonance features are consistent with half the total electron density in the bilayer system, implying that CFs prefer to stay in separate layers and exhibit a two-component behavior. In contrast, close to ν=1/2, CFs appear single-layer-like (single component) as their resonance features correspond to the total density.
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Affiliation(s)
- M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D Kamburov
- 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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Geraedts SD, Zaletel MP, Mong RSK, Metlitski MA, Vishwanath A, Motrunich OI. The half-filled Landau level: The case for Dirac composite fermions. Science 2016; 352:197-201. [DOI: 10.1126/science.aad4302] [Citation(s) in RCA: 107] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2015] [Accepted: 02/16/2016] [Indexed: 11/03/2022]
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