1
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Lotrič T, Simon SH. Chern-Simons Modified RPA-Eliashberg Theory of the ν=1/2+1/2 Quantum Hall Bilayer. PHYSICAL REVIEW LETTERS 2024; 132:176502. [PMID: 38728712 DOI: 10.1103/physrevlett.132.176502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Revised: 01/31/2024] [Accepted: 04/04/2024] [Indexed: 05/12/2024]
Abstract
The ν=1/2+1/2 quantum Hall bilayer has been previsously modeled using Chern-Simons-RPA-Eliashberg (CSRPAE) theory to describe pairing between the two layers. However, these approaches are troubled by a number of divergences and ambiguities. By using a "modified" RPA approximation to account for mass renormalization, we can work in a limit where the cyclotron frequency is taken to infinity, effectively projecting to a single Landau level. This, surprisingly, controls the important divergences and removes ambiguities found in prior attempts at CSRPAE. Examining BCS pairing of composite fermions we find that the angular momentum channel l=+1 dominates for all distances d between layers and at all frequency scales. Examining BCS pairing of composite fermion electrons in one layer with composite fermion holes in the opposite layer, we find the l=0 pairing channel dominates for all d and all frequencies. The strength of the pairing in these two different descriptions of the same phase of matter is found to be almost identical. This agrees well with our understanding that these are two different but dual descriptions of the same phase of matter.
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Affiliation(s)
- Tevž Lotrič
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford, OX1 3PU, United Kingdom
| | - Steven H Simon
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford, OX1 3PU, United Kingdom
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2
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Liang J, Liu Z, Yang Z, Huang Y, Wurstbauer U, Dean CR, West KW, Pfeiffer LN, Du L, Pinczuk A. Evidence for chiral graviton modes in fractional quantum Hall liquids. Nature 2024; 628:78-83. [PMID: 38538799 DOI: 10.1038/s41586-024-07201-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2023] [Accepted: 02/16/2024] [Indexed: 04/01/2024]
Abstract
Exotic physics could emerge from interplay between geometry and correlation. In fractional quantum Hall (FQH) states1, novel collective excitations called chiral graviton modes (CGMs) are proposed as quanta of fluctuations of an internal quantum metric under a quantum geometry description2-5. Such modes are condensed-matter analogues of gravitons that are hypothetical spin-2 bosons. They are characterized by polarized states with chirality6-8 of +2 or -2, and energy gaps coinciding with the fundamental neutral collective excitations (namely, magnetorotons9,10) in the long-wavelength limit. However, CGMs remain experimentally inaccessible. Here we observe chiral spin-2 long-wavelength magnetorotons using inelastic scattering of circularly polarized lights, providing strong evidence for CGMs in FQH liquids. At filling factor v = 1/3, a gapped mode identified as the long-wavelength magnetoroton emerges under a specific polarization scheme corresponding to angular momentum S = -2, which persists at extremely long wavelength. Remarkably, the mode chirality remains -2 at v = 2/5 but becomes the opposite at v = 2/3 and 3/5. The modes have characteristic energies and sharp peaks with marked temperature and filling-factor dependence, corroborating the assignment of long-wavelength magnetorotons. The observations capture the essentials of CGMs and support the FQH geometrical description, paving the way to unveil rich physics of quantum metric effects in topological correlated systems.
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Affiliation(s)
- Jiehui Liang
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China
| | - Ziyu Liu
- Department of Physics, Columbia University, New York, NY, USA
| | - Zihao Yang
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China
| | - Yuelei Huang
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China
| | | | - Cory R Dean
- Department of Physics, Columbia University, New York, NY, USA
| | - Ken W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - Loren N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - Lingjie Du
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China.
- Shishan Laboratory, Suzhou Campus of Nanjing University, Suzhou, China.
| | - Aron Pinczuk
- Department of Physics, Columbia University, New York, NY, USA
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA
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3
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Tsui YC, He M, Hu Y, Lake E, Wang T, Watanabe K, Taniguchi T, Zaletel MP, Yazdani A. Direct observation of a magnetic-field-induced Wigner crystal. Nature 2024; 628:287-292. [PMID: 38600267 DOI: 10.1038/s41586-024-07212-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Accepted: 02/20/2024] [Indexed: 04/12/2024]
Abstract
Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of two-dimensional systems have shown evidence for Wigner crystals2-11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.
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Affiliation(s)
- Yen-Chen Tsui
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Minhao He
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Yuwen Hu
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Ethan Lake
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA
| | - Taige Wang
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Michael P Zaletel
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA.
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4
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Lu Z, Han T, Yao Y, Reddy AP, Yang J, Seo J, Watanabe K, Taniguchi T, Fu L, Ju L. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 2024; 626:759-764. [PMID: 38383622 DOI: 10.1038/s41586-023-07010-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Accepted: 12/21/2023] [Indexed: 02/23/2024]
Abstract
The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2-6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7-9. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2 (refs. 10-13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene-hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance [Formula: see text] at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals [Formula: see text] at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14-16. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7-9,17-19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20-22.
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Affiliation(s)
- Zhengguang Lu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Tonghang Han
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Yuxuan Yao
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Aidan P Reddy
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Jixiang Yang
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Junseok Seo
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Long Ju
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
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5
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Petrescu M, Berkson-Korenberg Z, Vijayakrishnan S, West KW, Pfeiffer LN, Gervais G. Large composite fermion effective mass at filling factor 5/2. Nat Commun 2023; 14:7250. [PMID: 37945585 PMCID: PMC10636205 DOI: 10.1038/s41467-023-42986-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Accepted: 10/25/2023] [Indexed: 11/12/2023] Open
Abstract
The 5/2 fractional quantum Hall effect in the second Landau level of extremely clean two-dimensional electron gases has attracted much attention due to its topological order predicted to host quasiparticles that obey non-Abelian quantum statistics and could serve as a basis for fault-tolerant quantum computations. While previous works have establish the Fermi liquid (FL) nature of its putative composite fermion (CF) normal phase, little is known regarding its thermodynamics properties and as a result its effective mass is entirely unknown. Here, we report on time-resolved specific heat measurements at filling factor 5/2, and we examine the ratio of specific heat to temperature as a function of temperature. Combining these specific heat data with existing longitudinal thermopower data measuring the entropy in the clean limit we find that, unless a phase transition/crossover gives rise to large specific heat anomaly, both datasets point towards a large effective mass in the FL phase of CFs at 5/2. We estimate the effective-to-bare mass ratio m*/me to be ranging from ~ 2 to 4, which is two to three times larger than previously measured values in the first Landau level.
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Affiliation(s)
- M Petrescu
- Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada
| | | | | | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - G Gervais
- Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada.
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6
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Park H, Cai J, Anderson E, Zhang Y, Zhu J, Liu X, Wang C, Holtzmann W, Hu C, Liu Z, Taniguchi T, Watanabe K, Chu JH, Cao T, Fu L, Yao W, Chang CZ, Cobden D, Xiao D, Xu X. Observation of fractionally quantized anomalous Hall effect. Nature 2023; 622:74-79. [PMID: 37591304 DOI: 10.1038/s41586-023-06536-0] [Citation(s) in RCA: 39] [Impact Index Per Article: 39.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 08/11/2023] [Indexed: 09/29/2023]
Abstract
The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field1-3. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe2. At zero magnetic field, near filling factor ν = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance Rxy quantized to h/e2 ± 0.1%, whereas the longitudinal resistance Rxx vanishes. Remarkably, at ν = -2/3 and -3/5, we see plateau features in Rxy at [Formula: see text] and [Formula: see text], respectively, whereas Rxx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, Rxy is approximately 2h/e2 near half-filling (ν = -1/2) and varies linearly as ν is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field8-14. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field.
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Affiliation(s)
- Heonjoon Park
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Jiaqi Cai
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Eric Anderson
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Yinong Zhang
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Jiayi Zhu
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Xiaoyu Liu
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Chong Wang
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | | | - Chaowei Hu
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Zhaoyu Liu
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Jiun-Haw Chu
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Ting Cao
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Wang Yao
- Department of Physics, University of Hong Kong, Hong Kong, China
- HKU-UCAS Joint Institute of Theoretical and Computational Physics, University of Hong Kong, Hong Kong, China
| | - Cui-Zu Chang
- Department of Physics, The Pennsylvania State University, University Park, PA, USA
| | - David Cobden
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Di Xiao
- Department of Physics, University of Washington, Seattle, WA, USA
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Xiaodong Xu
- Department of Physics, University of Washington, Seattle, WA, USA.
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA.
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7
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Goldman H, Reddy AP, Paul N, Fu L. Zero-Field Composite Fermi Liquid in Twisted Semiconductor Bilayers. PHYSICAL REVIEW LETTERS 2023; 131:136501. [PMID: 37832018 DOI: 10.1103/physrevlett.131.136501] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 07/19/2023] [Indexed: 10/15/2023]
Abstract
Recent experiments have produced evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in the semiconductor moiré superlattice system tMoTe_{2}. Here, we argue that a composite fermion description, already a unifying framework for the phenomenology of 2D electron gases at high magnetic fields, provides a similarly powerful perspective in this new context. To this end, we present exact diagonalization evidence for composite Fermi liquid states at zero magnetic field in tMoTe_{2} at fillings n=1/2 and n=3/4. We dub these non-Fermi liquid metals anomalous composite Fermi liquids (ACFLs), and we argue that they play a central organizing role in the FQAH phase diagram. We proceed to develop a long wavelength theory for this ACFL state that offers concrete experimental predictions upon doping the composite Fermi sea, including a Jain sequence of FQAH states and a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system.
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Affiliation(s)
- Hart Goldman
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Aidan P Reddy
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Nisarga Paul
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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8
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Dong J, Wang J, Ledwith PJ, Vishwanath A, Parker DE. Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe_{2}. PHYSICAL REVIEW LETTERS 2023; 131:136502. [PMID: 37832017 DOI: 10.1103/physrevlett.131.136502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 08/25/2023] [Indexed: 10/15/2023]
Abstract
The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing magnetic field is a long-standing quest of solid state physics. Recent experiments have observed spontaneous valley polarization and fractional Chern insulators in zero magnetic field in twisted bilayers of MoTe_{2}, at partial filling of the topological valence band (ν=-2/3 and -3/5). We study the topological valence band at half filling, using exact diagonalization and density matrix renormalization group calculations. We discover a composite Fermi liquid (CFL) phase even at zero magnetic field that covers a large portion of the phase diagram near twist angle ∼3.6°. The CFL is a non-Fermi liquid phase with metallic behavior despite the absence of Landau quasiparticles. We discuss experimental implications including the competition between the CFL and a Fermi liquid, which can be tuned with a displacement field. The topological valence band has excellent quantum geometry over a wide range of twist angles and a small bandwidth that is, remarkably, reduced by interactions. These key properties stabilize the exotic zero field quantum Hall phases. Finally, we present an optical signature involving "extinguished" optical responses that detects Chern bands with ideal quantum geometry.
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Affiliation(s)
- Junkai Dong
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Jie Wang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Patrick J Ledwith
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ashvin Vishwanath
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Daniel E Parker
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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9
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Patel AA, Guo H, Esterlis I, Sachdev S. Universal theory of strange metals from spatially random interactions. Science 2023; 381:790-793. [PMID: 37590350 DOI: 10.1126/science.abq6011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 07/17/2023] [Indexed: 08/19/2023]
Abstract
Strange metals-ubiquitous in correlated quantum materials-transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures (T), such metals generically exhibit strange metal behavior with a T-linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/T) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.
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Affiliation(s)
- Aavishkar A Patel
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA
- Department of Physics, University of California Berkeley, Berkeley, CA 94720, USA
| | - Haoyu Guo
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA
| | - Ilya Esterlis
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
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10
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Lake E, Senthil T. Non-Fermi Liquids from Kinetic Constraints in Tilted Optical Lattices. PHYSICAL REVIEW LETTERS 2023; 131:043403. [PMID: 37566868 DOI: 10.1103/physrevlett.131.043403] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 07/03/2023] [Indexed: 08/13/2023]
Abstract
We study Fermi-Hubbard models with kinetically constrained dynamics that conserves both total particle number and total center of mass, a situation that arises when interacting fermions are placed in strongly tilted optical lattices. Through a combination of analytics and numerics, we show how the kinetic constraints stabilize an exotic non-Fermi liquid phase described by fermions coupled to a gapless bosonic field, which in several respects mimics a dynamical gauge field. This offers a novel route towards the study of non-Fermi liquid phases in the precision environments afforded by ultracold atom platforms.
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Affiliation(s)
- Ethan Lake
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - T Senthil
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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11
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Wang R, Sedrakyan TA, Wang B, Du L, Du RR. Excitonic topological order in imbalanced electron-hole bilayers. Nature 2023:10.1038/s41586-023-06065-w. [PMID: 37316659 DOI: 10.1038/s41586-023-06065-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 04/11/2023] [Indexed: 06/16/2023]
Abstract
Correlation and frustration play essential roles in physics, giving rise to novel quantum phases1-6. A typical frustrated system is correlated bosons on moat bands, which could host topological orders with long-range quantum entanglement4. However, the realization of moat-band physics is still challenging. Here, we explore moat-band phenomena in shallowly inverted InAs/GaSb quantum wells, where we observe an unconventional time-reversal-symmetry breaking excitonic ground state under imbalanced electron and hole densities. We find that a large bulk gap exists, encompassing a broad range of density imbalances at zero magnetic field (B), accompanied by edge channels that resemble helical transport. Under an increasing perpendicular B, the bulk gap persists, and an anomalous plateau of Hall signals appears, which demonstrates an evolution from helical-like to chiral-like edge transport with a Hall conductance approximately equal to e2/h at 35 tesla, where e is the elementary charge and h is Planck's constant. Theoretically, we show that strong frustration from density imbalance leads to a moat band for excitons, resulting in a time-reversal-symmetry breaking excitonic topological order, which explains all our experimental observations. Our work opens up a new direction for research on topological and correlated bosonic systems in solid states beyond the framework of symmetry-protected topological phases, including but not limited to the bosonic fractional quantum Hall effect.
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Affiliation(s)
- Rui Wang
- School of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing, China
| | - Tigran A Sedrakyan
- Department of Physics, University of Massachusetts Amherst, Amherst, MA, USA
| | - Baigeng Wang
- School of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, China.
- Collaborative Innovation Center for Advanced Microstructures, Nanjing, China.
| | - Lingjie Du
- School of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, China.
- Collaborative Innovation Center for Advanced Microstructures, Nanjing, China.
- Shishan Laboratory, Suzhou Campus of Nanjing University, Suzhou, China.
| | - Rui-Rui Du
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, China.
- Collaborative Innovation Center of Quantum Matter, Beijing, China.
- CAS Center for Excellence, University of Chinese Academy of Sciences, Beijing, China.
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12
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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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13
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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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14
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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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15
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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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16
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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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17
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Nakamura J, Liang S, Gardner GC, Manfra MJ. Half-Integer Conductance Plateau at the ν=2/3 Fractional Quantum Hall State in a Quantum Point Contact. PHYSICAL REVIEW LETTERS 2023; 130:076205. [PMID: 36867801 DOI: 10.1103/physrevlett.130.076205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2022] [Accepted: 01/17/2023] [Indexed: 06/18/2023]
Abstract
The ν=2/3 fractional quantum Hall state is the hole-conjugate state to the primary Laughlin ν=1/3 state. We investigate transmission of edge states through quantum point contacts fabricated on a GaAs/AlGaAs heterostructure designed to have a sharp confining potential. When a small but finite bias is applied, we observe an intermediate conductance plateau with G=0.5(e^{2}/h). This plateau is observed in multiple QPCs, and persists over a significant range of magnetic field, gate voltage, and source-drain bias, making it a robust feature. Using a simple model that considers scattering and equilibration between counterflowing charged edge modes, we find this half-integer quantized plateau to be consistent with full reflection of an inner counterpropagating -1/3 edge mode while the outer integer mode is fully transmitted. In a QPC fabricated on a different heterostructure which has a softer confining potential, we instead observe an intermediate conductance plateau at G=(1/3)(e^{2}/h). These results provide support for a model at ν=2/3 in which the edge transitions from a structure having an inner upstream -1/3 charge mode and outer downstream integer mode to a structure with two downstream 1/3 charge modes when the confining potential is tuned from sharp to soft and disorder prevails.
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Affiliation(s)
- J Nakamura
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - S Liang
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - G C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Lab West Lafayette, West Lafayette, Indiana 47907, USA
| | - M J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Lab West Lafayette, West Lafayette, Indiana 47907, USA
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
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18
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Asymptotic Pomeranchuk instability of Fermi liquids in half-filled Landau levels. Sci Rep 2023; 13:1400. [PMID: 36697504 PMCID: PMC9877013 DOI: 10.1038/s41598-023-28614-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 01/20/2023] [Indexed: 01/26/2023] Open
Abstract
We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form [Formula: see text]). We assume the half-filled level to be in a compressible, Fermi liquid state with a circular Fermi surface. The Landau level projection is incorporated via a modified effective electron-electron interaction and the resulting band structure is described within the Hartree-Fock approximation. We regulate the infrared divergences in the theory and probe the intrinsic tendency of the Fermi surface to deform through Pomeranchuk instabilities. We find that the corresponding susceptibility never diverges, though the system is asymptotically unstable in the [Formula: see text] limit.
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19
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Wijewardena UK, Nanayakkara TR, Kriisa A, Reichl C, Wegscheider W, Mani RG. Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields. Sci Rep 2022; 12:19204. [PMID: 36357438 PMCID: PMC9649807 DOI: 10.1038/s41598-022-22812-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2022] [Accepted: 10/19/2022] [Indexed: 11/12/2022] Open
Abstract
Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting, \documentclass[12pt]{minimal}
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\begin{document}$$g \mu _B B$$\end{document}gμBB, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in \documentclass[12pt]{minimal}
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\begin{document}$$\nu = 8/5$$\end{document}ν=8/5, and a corresponding change in the \documentclass[12pt]{minimal}
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\begin{document}$$R_{xy}/R_{K} = (11/7)^{-1}$$\end{document}Rxy/RK=(11/7)-1 to \documentclass[12pt]{minimal}
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\begin{document}$$R_{xy}/R_{K} = (8/5)^{-1}$$\end{document}Rxy/RK=(8/5)-1, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the \documentclass[12pt]{minimal}
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\begin{document}$$\nu = 7/5$$\end{document}ν=7/5 resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of \documentclass[12pt]{minimal}
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\begin{document}$$\nu = 4/3, 7/5$$\end{document}ν=4/3,7/5 and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same \documentclass[12pt]{minimal}
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\begin{document}$$R_{xy}$$\end{document}Rxy, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.
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20
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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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21
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Nguyen DX, Haldane FDM, Rezayi EH, Son DT, Yang K. Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems. PHYSICAL REVIEW LETTERS 2022; 128:246402. [PMID: 35776452 DOI: 10.1103/physrevlett.128.246402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 05/12/2022] [Indexed: 05/06/2023]
Abstract
We study, numerically, the charge neutral excitations (magnetorotons) in fractional quantum Hall systems, concentrating on the two Jain states near quarter filling, ν=2/7 and ν=2/9, and the ν=1/4 Fermi-liquid state itself. In contrast to the ν=1/3 states and the Jain states near half filling, on each of the two Jain states ν=2/7 and ν=2/9 the graviton spectral densities show two, instead of one, magnetoroton peaks. The magnetorotons have spin 2 and have opposite chiralities in the ν=2/7 state and the same chirality in the ν=2/9 state. We also provide a numerical verification of a sum rule relating the guiding center spin s[over ¯] with the spectral densities of the stress tensor.
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Affiliation(s)
- Dung Xuan Nguyen
- Brown Theoretical Physics Center and Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
| | - F D M Haldane
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - E H Rezayi
- Physics Department, California State University Los Angeles, Los Angeles, California 90032, USA
| | - Dam Thanh Son
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Kun Yang
- NHMFL and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
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22
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Ye W, Lee SS, Zou L. Ultraviolet-Infrared Mixing in Marginal Fermi Liquids. PHYSICAL REVIEW LETTERS 2022; 128:106402. [PMID: 35333078 DOI: 10.1103/physrevlett.128.106402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Accepted: 02/16/2022] [Indexed: 06/14/2023]
Abstract
When Fermi surfaces (FSs) are subject to long-range interactions that are marginal in the renormalization-group sense, Landau Fermi liquids are destroyed, but only barely. With the interaction further screened by particle-hole excitations through one-loop quantum corrections, it has been believed that these marginal Fermi liquids (MFLs) are described by weakly coupled field theories at low energies. In this Letter, we point out a possibility in which higher-loop processes qualitatively change the picture through UV-IR mixing, in which the size of the FS enters as a relevant scale. The UV-IR mixing effect enhances the coupling at low energies, such that the basin of attraction for the weakly coupled fixed point of a (2+1)-dimensional MFL shrinks to a measure-zero set in the low-energy limit. This UV-IR mixing is caused by gapless virtual Cooper pairs that spread over the entire FS through marginal long-range interactions. Our finding signals a possible breakdown of the patch description for the MFL and questions the validity of using the MFL as the base theory in a controlled scheme for non-Fermi liquids that arise from relevant long-range interactions.
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Affiliation(s)
- Weicheng Ye
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Sung-Sik Lee
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Liujun Zou
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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23
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Berman OL, Kezerashvili RY, Lozovik YE, Ziegler KG. Strain-induced quantum Hall phenomena of excitons in graphene. Sci Rep 2022; 12:2950. [PMID: 35194045 PMCID: PMC8863812 DOI: 10.1038/s41598-022-06486-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Accepted: 01/24/2022] [Indexed: 11/28/2022] Open
Abstract
We study direct and indirect pseudomagnetoexcitons, formed by an electron and a hole in the layers of gapped graphene under strain-induced gauge pseudomagnetic field. Since the strain-induced pseudomagnetic field acts on electrons and holes the same way, it occurs that the properties of single pseudomagnetoexcitons, their collective effects and phase diagram are cardinally different from those of magnetoexcitons in a real magnetic field. We have derived wave functions and energy spectrum of direct in a monolayer and indirect pseudomagnetoexcitons in a double layer of gapped graphene. The quantum Hall effect for direct and indirect excitons was predicted in the monolayers and double layers of gapped graphene under strain-induced gauge pseudomagnetic field, correspondingly.
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Affiliation(s)
- Oleg L Berman
- Physics Department, New York City College of Technology, The City University of New York, Brooklyn, NY, 11201, USA.,The Graduate School and University Center, The City University of New York, New York, NY, 10016, USA
| | - Roman Ya Kezerashvili
- Physics Department, New York City College of Technology, The City University of New York, Brooklyn, NY, 11201, USA. .,The Graduate School and University Center, The City University of New York, New York, NY, 10016, USA.
| | - Yurii E Lozovik
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, Russia, 142190.,Research University Higher School of Economics, Moscow, Russia, 101000
| | - Klaus G Ziegler
- Institut für Physik, Universität Augsburg, 86135, Augsburg, Germany
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24
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Two-dimensional finite quantum Hall clusters of electrons with anisotropic features. Sci Rep 2022; 12:2383. [PMID: 35149720 PMCID: PMC8837620 DOI: 10.1038/s41598-022-06093-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Accepted: 01/21/2022] [Indexed: 11/08/2022] Open
Abstract
Low-dimensional nano and two-dimensional materials are of great interest to many disciplines and may have a lot of applications in fields such as electronics, optoelectronics, and photonics. One can create quantum Hall phases by applying a strong magnetic field perpendicular to a two-dimensional electron system. One characterizes the nature of the system by looking at magneto-transport data. There have been a few quantum phases seen in past experiments on GaAs/AlGaAs heterostructures that manifest anisotropic magnetoresistance, typically, in high Landau levels. In this work, we model the source of anisotropy as originating from an internal anisotropic interaction between electrons. We use this framework to study the possible anisotropic behavior of finite clusters of electrons at filling factor 1/6 of the lowest Landau level.
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25
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Liu X, Li JIA, Watanabe K, Taniguchi T, Hone J, Halperin BI, Kim P, Dean CR. Crossover between strongly coupled and weakly coupled exciton superfluids. Science 2022; 375:205-209. [PMID: 35025642 DOI: 10.1126/science.abg1110] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
In fermionic systems, superconductivity and superfluidity occur through the condensation of fermion pairs. The nature of this condensate can be tuned by varying the pairing strength, which is challenging in electronic systems. We studied graphene double layers separated by an atomically thin insulator. Under applied magnetic field, electrons and holes couple across the barrier to form bound magneto-excitons whose pairing strength can be continuously tuned by varying the effective layer separation. Using temperature-dependent Coulomb drag and counterflow current measurements, we were able to tune the magneto-exciton condensate through the entire phase diagram from weak to strong coupling. Our results establish magneto-exciton condensates in graphene as a model platform to study the crossover between two bosonic quantum condensate phases in a solid-state system.
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Affiliation(s)
- Xiaomeng Liu
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - J I A Li
- Department of Physics, Brown University, Providence, RI 02912, USA
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - James Hone
- Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA
| | | | - Philip Kim
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Cory R Dean
- Department of Physics, Columbia University, New York, NY 10027, USA
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26
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Abstract
Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations in a subregion of the full system, focusing on geometries with sharp corners. We report that the angle dependence is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We exemplify our findings with fractional quantum Hall states, topological insulators, scale invariant quantum critical theories, and metals. We suggest experimental tests, and anticipate that our findings can be generalized to other spatial dimensions or geometries. In addition, we highlight the similarities of the fluctuation shape dependence with findings relating to quantum entanglement measures. Fluctuations, both quantum and classical, contain important information about the underlying system. Here, the authors show that for measurements on a subregion with a sharp corner, fluctuations have the same shape dependence for a large variety of systems.
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27
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Wagner G, Nguyen DX, Simon SH, Halperin BI. s-Wave Paired Electron and Hole Composite Fermion Trial State for Quantum Hall Bilayers with ν=1. PHYSICAL REVIEW LETTERS 2021; 127:246803. [PMID: 34951796 DOI: 10.1103/physrevlett.127.246803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 11/12/2021] [Indexed: 06/14/2023]
Abstract
We introduce a new variational wave function for a quantum Hall bilayer at total filling ν_{T}=1, which is based on s-wave BCS pairing between electron composite fermions in one layer and hole composite fermions in the other. In addition, we reexamine a trial wave function based on p-wave BCS pairing between electron composite fermions in both layers. We compute the overlap of the optimized trial functions with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length. The s-wave trial wave function naturally allows for charge imbalance between the layers and provides important insights into how the physics at large interlayer separations crosses over to that at small separations in a fashion analogous to the BEC-BCS crossover.
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Affiliation(s)
- Glenn Wagner
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Dung X Nguyen
- Brown Theoretical Physics Center, Brown University, Providence, Rhode Island 02912, USA
| | - Steven H Simon
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Bertrand I Halperin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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28
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Yang B. Statistical Interactions and Boson-Anyon Duality in Fractional Quantum Hall Fluids. PHYSICAL REVIEW LETTERS 2021; 127:126406. [PMID: 34597114 DOI: 10.1103/physrevlett.127.126406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2021] [Accepted: 08/26/2021] [Indexed: 06/13/2023]
Abstract
We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For interacting electrons, the statistical transmutation from anyons to bosons allows us to explicitly derive the microscopic statistical interaction between the anyons, in the form of the effective two-body and few-body interactions. This also leads to a number of unexpected topological phases of the single component bosonic fractional quantum Hall effect that may be experimentally accessible. Numerical analysis of the energy spectrum and ground state entanglement properties are carried out for simple examples.
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Affiliation(s)
- Bo Yang
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371and Institute of High Performance Computing, A *STAR, Singapore 138632
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29
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Villegas Rosales KA, Madathil PT, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Fractional Quantum Hall Effect Energy Gaps: Role of Electron Layer Thickness. PHYSICAL REVIEW LETTERS 2021; 127:056801. [PMID: 34397247 DOI: 10.1103/physrevlett.127.056801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
The fractional quantum Hall effect stands as a quintessential manifestation of an interacting two-dimensional electron system. One of the fractional quantum Hall effect's most fundamental characteristics is the energy gap separating the incompressible ground state from its excitations. Yet, despite nearly four decades of investigations, a quantitative agreement between the theoretically calculated and experimentally measured energy gaps is lacking. Here we report a systematic experimental study that incorporates very high-quality two-dimensional electron systems confined to GaAs quantum wells with fixed density and varying well widths. The results demonstrate a clear decrease of the energy gap as the electron layer is made thicker and the short-range component of the Coulomb interaction is weakened. We also provide a quantitative comparison between the measured energy gaps and the available theoretical calculations that takes into account the role of finite layer thickness and Landau level mixing. All the measured energy gaps fall below the calculations, but as the electron layer thickness increases, the results of experiments and calculations come closer. Accounting for the role of disorder in a phenomenological manner, we find better overall agreement between the measured and calculated energy gaps, although some puzzling discrepancies remain.
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Affiliation(s)
- K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - P T Madathil
- 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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30
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Mani RG, Wijewardena UK, Nanayakkara TR, Kriisa A, Reichl C, Wegscheider W. Marginal metallic state at a fractional filling of '8/5' and '4/3' of Landau levels in the GaAs/AlGaAs 2D electron system. Sci Rep 2021; 11:15003. [PMID: 34294839 PMCID: PMC8298480 DOI: 10.1038/s41598-021-94563-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 07/08/2021] [Indexed: 11/09/2022] Open
Abstract
A metallic state with a vanishing activation gap, at a filling factor [Formula: see text] in the untilted specimen with [Formula: see text], and at [Formula: see text] at [Formula: see text] under a [Formula: see text] tilted magnetic field, is examined through a microwave photo-excited transport study of the GaAs/AlGaAs 2 dimensional electron system (2DES). The results presented here suggest, remarkably, that at the possible degeneracy point of states with different spin polarization, where the 8/5 or 4/3 FQHE vanish, there occurs a peculiar marginal metallic state that differs qualitatively from a quantum Hall insulating state and the usual quantum Hall metallic state. Such a marginal metallic state occurs most prominently at [Formula: see text], and at [Formula: see text] under tilt as mentioned above, over the interval [Formula: see text], that also includes the [Formula: see text] state, which appears perceptibly gapped in the first instance.
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Affiliation(s)
- R G Mani
- Dept. of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA.
| | - U K Wijewardena
- Dept. of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA
| | - T R Nanayakkara
- Dept. of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA
| | - Annika Kriisa
- Dept. of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA
| | - C Reichl
- Department of Physics, ETH Zurich, 8093, Zurich, Switzerland
| | - W Wegscheider
- Department of Physics, ETH Zurich, 8093, Zurich, Switzerland
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31
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Grossman O, Hofmann JS, Holder T, Berg E. Specific Heat of a Quantum Critical Metal. PHYSICAL REVIEW LETTERS 2021; 127:017601. [PMID: 34270320 DOI: 10.1103/physrevlett.127.017601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 05/30/2021] [Indexed: 06/13/2023]
Abstract
We investigate the specific heat c, near an Ising nematic quantum critical point (QCP), using sign problem-free quantum Monte Carlo simulations. Cooling towards the QCP, we find a broad regime of temperature where c/T is close to the value expected from the noninteracting band structure, even for a moderately large coupling strength. At lower temperature, we observe a rapid rise of c/T, followed by a drop to zero as the system becomes superconducting. The spin susceptibility begins to drop at roughly the same temperature where the enhancement of c/T onsets, most likely due to the opening of a gap associated with superconducting fluctuations. These findings suggest that superconductivity and non-Fermi liquid behavior (manifested in an enhancement of the effective mass) onset at comparable energy scales. We support these conclusions with an analytical perturbative calculation.
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Affiliation(s)
- Ori Grossman
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Johannes S Hofmann
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Tobias Holder
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Erez Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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32
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Anand A, Jain JK, Sreejith GJ. Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field. PHYSICAL REVIEW LETTERS 2021; 126:136601. [PMID: 33861091 DOI: 10.1103/physrevlett.126.136601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 03/03/2021] [Indexed: 06/12/2023]
Abstract
States of strongly interacting particles are of fundamental interest in physics and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the standard practice of restricting to the lowest LL, introduce a model short-range interaction that is infinitely strong compared to the cyclotron energy. We demonstrate that this model lends itself to an exact solution for the ground as well as excited states at arbitrary filling factors ν<1/2p and produces a fractional quantum Hall effect at fractions of the form ν=n/(2pn+1), where n and p are integers. The fractional quantum Hall states of our model share many topological properties with the corresponding Coulomb ground states in the lowest Landau level, such as the edge physics and the fractional charge of the excitations.
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Affiliation(s)
- Abhishek Anand
- Indian Institute of Science Education and Research, Pune 411008, India
| | - J K Jain
- The Pennsylvania State University, 104 Davey Laboratory, University Park, Pennsylvania 16802, USA
| | - G J Sreejith
- Indian Institute of Science Education and Research, Pune 411008, India
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33
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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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34
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Huang KS, Raghu S, Kumar P. Numerical Study of a Dual Representation of the Integer Quantum Hall Transition. PHYSICAL REVIEW LETTERS 2021; 126:056802. [PMID: 33605754 DOI: 10.1103/physrevlett.126.056802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
We study the critical properties of the noninteracting integer quantum Hall to insulator transition (IQHIT) in a "dual" composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at criticality CF states are delocalized at all energies. The CF approach thus enables us to study the transition from a new vantage point. Using a lattice representation of CF mean-field theory, we compute the critical and multifractal exponents of the IQHIT. We obtain ν=2.56±0.02 and η=0.51±0.01, both of which are consistent with the predictions of the Chalker-Coddington network model formulated in the electron representation.
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Affiliation(s)
- Kevin S Huang
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
| | - S Raghu
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Prashant Kumar
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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35
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Wang J, Santos LH. Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices. PHYSICAL REVIEW LETTERS 2020; 125:236805. [PMID: 33337183 DOI: 10.1103/physrevlett.125.236805] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Accepted: 10/21/2020] [Indexed: 06/12/2023]
Abstract
We study quantum phase transitions in graphene superlattices in external magnetic fields, where a framework is presented to classify multiflavor Dirac fermion critical points describing hopping-tuned topological phase transitions of integer and fractional Hofstadter-Chern insulators. We argue and provide numerical support for the existence of transitions that can be explained by a nontrivial interplay of Chern bands and van Hove singularities near charge neutrality. This work provides a route to critical phenomena beyond conventional quantum Hall plateau transitions.
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Affiliation(s)
- Jian Wang
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Luiz H Santos
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
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36
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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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37
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Pan W, Kang W, Lilly MP, Reno JL, Baldwin KW, West KW, Pfeiffer LN, Tsui DC. Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level. PHYSICAL REVIEW LETTERS 2020; 124:156801. [PMID: 32357056 DOI: 10.1103/physrevlett.124.156801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2019] [Revised: 12/14/2019] [Accepted: 03/19/2020] [Indexed: 06/11/2023]
Abstract
We report on detailed experimental studies of a high-quality heterojunction insulated-gate field-effect transistor (HIGFET) to probe the particle-hole symmetry of the fractional quantum Hall effect (FQHE) states about half-filling in the lowest Landau level. The HIGFET is specially designed to vary the density of a two-dimensional electronic system under constant magnetic fields. We find in our constant magnetic field, variable density measurements that the sequence of FQHE states at filling factors ν=1/3,2/5,3/7… and its particle-hole conjugate states at filling factors 1-ν=2/3,3/5,4/7… have a very similar energy gap. Moreover, a reflection symmetry can be established in the magnetoconductivities between the ν and 1-ν states about half-filling. Our results demonstrate that the FQHE states in the lowest Landau level are manifestly particle-hole symmetric.
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Affiliation(s)
- W Pan
- Materials Physics Department, Sandia National Laboratories, Livermore, California 94551, USA
- Quantum Phenomena Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - W Kang
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - M P Lilly
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - J L Reno
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - K W Baldwin
- 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
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D C Tsui
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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38
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Zhu Z, Sheng DN, Sodemann I. Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2020; 124:097604. [PMID: 32202902 DOI: 10.1103/physrevlett.124.097604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2019] [Accepted: 02/11/2020] [Indexed: 06/10/2023]
Abstract
We develop a proposal to realize a widely tunable and clean quantum phase transition in bilayer graphene between two paradigmatic fractionalized phases of matter: the Moore-Read fractional quantum Hall state and the composite Fermi liquid metal. This transition can be realized at total fillings ν=±3+1/2 and the critical point can be controllably accessed by tuning either the interlayer electric bias or the perpendicular magnetic field values over a wide range of parameters. We study the transition numerically within a model that contains all leading single particle corrections to the band structure of bilayer graphene and includes the fluctuations between the n=0 and n=1 cyclotron orbitals of its zeroth Landau level to delineate the most favorable region of parameters to experimentally access this unconventional critical point. We also find evidence for a new anisotropic gapless phase stabilized near the level crossing of n=0/1 orbits.
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Affiliation(s)
- Zheng Zhu
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - D N Sheng
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Inti Sodemann
- Max-Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany
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39
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Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions. Proc Natl Acad Sci U S A 2019; 116:26431-26434. [PMID: 31818954 DOI: 10.1073/pnas.1913096116] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Recent experimental [I. Jo et al, Phys. Rev. Lett. 119, 016402 (2017)] and numerical [M. Ippoliti, S. D. Geraedts, R. N. Bhatt, Phys. Rev. B 95, 201104 (2017)] evidence suggests an intriguing universal relationship between the Fermi surface anisotropy of the noninteracting parent 2-dimensional (2D) electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filling. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed [H. -K. Tang et al, Science 361, 570 (2018)] nonperturbative and numerically exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac fermions with long-range Coulomb interactions do we find a universal square-root decrease of the Fermi-surface anisotropy. For the [Formula: see text] composite Fermi liquid, this result is surprising since a Dirac fermion ground state was only recently proposed as an alternative to the usual Halperin-Lee-Read state. Our proposed universality can be tested in several anisotropic Dirac materials including graphene, topological insulators, organic conductors, and magic-angle twisted bilayer graphene.
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40
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Han Z, Li T, Zhang L, Sullivan G, Du RR. Anomalous Conductance Oscillations in the Hybridization Gap of InAs/GaSb Quantum Wells. PHYSICAL REVIEW LETTERS 2019; 123:126803. [PMID: 31633941 DOI: 10.1103/physrevlett.123.126803] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Revised: 05/09/2019] [Indexed: 06/10/2023]
Abstract
We observe the magnetic oscillation of electric conductance in the two-dimensional InAs/GaSb quantum spin Hall insulator. Its insulating bulk origin is unambiguously demonstrated by the antiphase oscillations of the conductance and the resistance. Characteristically, the in-gap oscillation frequency is higher than the Shubnikov-de Haas oscillation close to the conduction band edge in the metallic regime. The temperature dependence shows both thermal activation and smearing effects, which cannot be described by the Lifshitz-Kosevich theory. A two-band Bernevig-Hughes-Zhang model with a large quasiparticle self-energy in the insulating regime is proposed to capture the main properties of the in-gap oscillations.
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Affiliation(s)
- Zhongdong Han
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Tingxin Li
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Long Zhang
- Kavli Institute for Theoretical Sciences and CAS Center for Excellence, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Gerard Sullivan
- Teledyne Scientific and Imaging, Thousand Oaks, California 91603, USA
| | - Rui-Rui Du
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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41
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Eisenstein JP, Pfeiffer LN, West KW. Precursors to Exciton Condensation in Quantum Hall Bilayers. PHYSICAL REVIEW LETTERS 2019; 123:066802. [PMID: 31491172 DOI: 10.1103/physrevlett.123.066802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2019] [Indexed: 06/10/2023]
Abstract
Tunneling spectroscopy reveals evidence for interlayer electron-hole correlations in quantum Hall bilayer two-dimensional electron systems at layer separations near, but above, the transition to the incompressible exciton condensate at total Landau level filling ν_{T}=1. These correlations are manifested by a nonlinear suppression of the Coulomb pseudogap which inhibits low energy interlayer tunneling in weakly coupled bilayers. The pseudogap suppression is strongest at ν_{T}=1 and grows rapidly as the critical layer separation for exciton condensation is approached from above.
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Affiliation(s)
- J P Eisenstein
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, California 91125, 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
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42
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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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43
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Parameswaran SA, Feldman BE. Quantum Hall valley nematics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:273001. [PMID: 30743251 DOI: 10.1088/1361-648x/ab0636] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states: quantum Hall valley nematics. These phases of matter emerge when the formation of a topologically insulating quantum Hall state is accompanied by the spontaneous breaking of a point-group symmetry that combines a spatial rotation with a permutation of valley indices. The resulting orientational order is particularly sensitive to quenched disorder, while quantum Hall physics links charge conduction to topological defects. We discuss how these combine to yield a rich phase structure, and their implications for transport and spectroscopy measurements. In parallel, we discuss relevant experimental systems. We close with an outlook on future directions.
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Affiliation(s)
- S A Parameswaran
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom
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44
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Faugno WN, Balram AC, Barkeshli M, Jain JK. Prediction of a Non-Abelian Fractional Quantum Hall State with f-Wave Pairing of Composite Fermions in Wide Quantum Wells. PHYSICAL REVIEW LETTERS 2019; 123:016802. [PMID: 31386406 DOI: 10.1103/physrevlett.123.016802] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2019] [Indexed: 05/06/2023]
Abstract
We theoretically investigate the nature of the state at the quarter filled lowest Landau level and predict that, as the quantum well width is increased, a transition occurs from the composite fermion Fermi sea into a novel non-Abelian fractional quantum Hall state that is topologically equivalent to f-wave pairing of composite fermions. This state is topologically distinct from the familiar p-wave paired Pfaffian state. We compare our calculated phase diagram with experiments and make predictions for many observable quantities.
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Affiliation(s)
- W N Faugno
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Ajit C Balram
- Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Maissam Barkeshli
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20472 USA
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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45
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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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46
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Zeng Y, Li JIA, Dietrich SA, Ghosh OM, Watanabe K, Taniguchi T, Hone J, Dean CR. High-Quality Magnetotransport in Graphene Using the Edge-Free Corbino Geometry. PHYSICAL REVIEW LETTERS 2019; 122:137701. [PMID: 31012609 DOI: 10.1103/physrevlett.122.137701] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2018] [Indexed: 06/09/2023]
Abstract
We report fabrication of graphene devices in a Corbino geometry consisting of concentric circular electrodes with no physical edge connecting the inner and outer electrodes. High device mobility is realized using boron nitride encapsulation together with a dual-graphite gate structure. Bulk conductance measurement in the quantum Hall effect (QHE) regime outperforms previously reported Hall bar measurements, with improved resolution observed for both the integer and fractional QHE states. We identify apparent phase transitions in the fractional sequence in both the lowest and first excited Landau levels (LLs) and observe features consistent with electron solid phases in higher LLs.
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Affiliation(s)
- Y Zeng
- Department of Physics, Columbia University, New York, New York 10025, USA
| | - J I A Li
- Department of Physics, Columbia University, New York, New York 10025, USA
| | - S A Dietrich
- Department of Physics, Columbia University, New York, New York 10025, USA
| | - O M Ghosh
- Department of Physics, Columbia University, New York, New York 10025, USA
| | - K Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - T Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - J Hone
- Department of Mechanical Engineering, Columbia University, New York, New York 10025, USA
| | - C R Dean
- Department of Physics, Columbia University, New York, New York 10025, USA
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47
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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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48
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Maryenko D, McCollam A, Falson J, Kozuka Y, Bruin J, Zeitler U, Kawasaki M. Composite fermion liquid to Wigner solid transition in the lowest Landau level of zinc oxide. Nat Commun 2018; 9:4356. [PMID: 30341295 PMCID: PMC6195604 DOI: 10.1038/s41467-018-06834-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Accepted: 09/27/2018] [Indexed: 12/05/2022] Open
Abstract
Interactions between the constituents of a condensed matter system can drive it through a plethora of different phases due to many-body effects. A prominent platform for it is a dilute two-dimensional electron system in a magnetic field, which evolves intricately through various gaseous, liquid and solid phases governed by Coulomb interaction. Here we report on the experimental observation of a phase transition between the composite fermion liquid and adjacent magnetic field induced phase with a character of Wigner solid. The experiments are performed in the lowest Landau level of a MgZnO/ZnO two-dimensional electron system with attributes of both a liquid and a solid. An in-plane magnetic field component applied on top of the perpendicular magnetic field extends the Wigner-like phase further into the composite fermion liquid phase region. Our observations indicate the direct competition between a composite fermion liquid and a Wigner solid formed either by electrons or composite fermions. In two-dimensional electron systems, strong Coulomb interactions lead to the formation of new phases. Here the authors observe a transition between two of these correlated phases, a composite fermion liquid and Wigner solid, in a zinc oxide heterostructure.
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Affiliation(s)
- D Maryenko
- RIKEN Center for Emergent Matter Science (CEMS), Wako, 351-0198, Japan.
| | - A McCollam
- High Field Magnet Laboratory (HFML-EMFL) and Institute for Molecules and Materials, Radboud University, 6525 ED, Nijmegen, The Netherlands
| | - J Falson
- Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), The University of Tokyo, Tokyo, 113-8656, Japan.,Max Planck Institute for Solid State Research, Stuttgart, Germany
| | - Y Kozuka
- Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), The University of Tokyo, Tokyo, 113-8656, Japan.,National Institute for Materials Science, Tsukuba, Ibaraki, Japan
| | - J Bruin
- High Field Magnet Laboratory (HFML-EMFL) and Institute for Molecules and Materials, Radboud University, 6525 ED, Nijmegen, The Netherlands.,Max Planck Institute for Solid State Research, Stuttgart, Germany
| | - U Zeitler
- High Field Magnet Laboratory (HFML-EMFL) and Institute for Molecules and Materials, Radboud University, 6525 ED, Nijmegen, The Netherlands
| | - M Kawasaki
- RIKEN Center for Emergent Matter Science (CEMS), Wako, 351-0198, Japan.,Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), The University of Tokyo, Tokyo, 113-8656, Japan
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49
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Mandal SS. Generalization of Laughlin's theory for the fractional quantum Hall effect. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:405605. [PMID: 30152794 DOI: 10.1088/1361-648x/aadd37] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Motivated by the structure of the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor [Formula: see text] (m odd), I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin's quasiparticle operator, that reproduces quasiparticle wave function as predicted in the CF theory, without a priori assumption of the presence of CFs. I further consider the conjugate of this operator as quasihole operator for obtaining a novel quasihole wave function for 1/m state. Each of these wave functions is interpreted as expelling an electron into a different Hilbert subspace from the original Hilbert space of the Laughlin condensate while still maintaining its correlation (although changed) with the electrons in the condensate such that the expelled electron behaves as a CF with respect to the electrons in the condensate. With this interpretation, I show that the ground state wavefunctions for general states at filling fractions [Formula: see text], respectively, can be constructed as coherent superposition of n coupled Laughlin condensates and their 'conjugates', formed at different Hilbert subspaces. The corresponding wave functions, specially surprising for [Formula: see text] sequence of states, are identical with those proposed in the theory of noninteracting CFs. The states which were considered as fractional quantum Hall effect of interacting CFs, can also be treated in the same footing as for the prominent sequences of states describing as the coupled condensates among which one is a non-Laughlin condensate in a different Hilbert subspace. Further, I predict that the half filling of the lowest Landau level is a quantum critical point for phase transition between two topologically distinct phases each corresponding to a family of states: one consists of large number of coupled Laughlin condensates of filling factor 1/3 and the other corresponds to large number of coupled conjugate Laughlin condensates of filling factor 1, which may be distinguished, respectively, by the absence and presence of upstream edge modes.
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Affiliation(s)
- Sudhansu S Mandal
- Department of Physics and Centre for Theoretical Studies, Indian Institute of Technology Kharagpur, West Bengal 721302, India
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50
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Geraedts SD, Wang J, Rezayi EH, Haldane FDM. Berry Phase and Model Wave Function in the Half-Filled Landau Level. PHYSICAL REVIEW LETTERS 2018; 121:147202. [PMID: 30339436 DOI: 10.1103/physrevlett.121.147202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2017] [Indexed: 06/08/2023]
Abstract
We construct model wave functions for the half-filled Landau level parametrized by "composite fermion occupation-number configurations" in a two-dimensional momentum space, which correspond to a Fermi sea with particle-hole excitations. When these correspond to a weakly excited Fermi sea, they have a large overlap with wave functions obtained by the exact diagonalization of lowest-Landau-level electrons interacting with a Coulomb interaction, allowing exact states to be identified with quasiparticle configurations. We then formulate a many-body version of the single-particle Berry phase for adiabatic transport of a single quasiparticle around a path in momentum space, and evaluate it using a sequence of exact eigenstates in which a single quasiparticle moves incrementally. In this formulation the standard free-particle construction in terms of the overlap between "periodic parts of successive Bloch wave functions" is reinterpreted as the matrix element of a "momentum boost" operator between the full Bloch states, which becomes the matrix elements of a Girvin-MacDonald-Platzman density operator in the many-body context. This allows the computation of the Berry phase for the transport of a single composite fermion around the Fermi surface. In addition to a phase contributed by the density operator, we find a phase of exactly π for this process.
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Affiliation(s)
- Scott D Geraedts
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Jie Wang
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - E H Rezayi
- Department of Physics, California State University, Los Angeles, California 90032, USA
| | - F D M Haldane
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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