1
|
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.
Collapse
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
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
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.
Collapse
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.
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
Liu Z, Wurstbauer U, Du L, West KW, Pfeiffer LN, Manfra MJ, Pinczuk A. Domain Textures in the Fractional Quantum Hall Effect. PHYSICAL REVIEW LETTERS 2022; 128:017401. [PMID: 35061454 DOI: 10.1103/physrevlett.128.017401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Revised: 10/18/2021] [Accepted: 12/12/2021] [Indexed: 06/14/2023]
Abstract
Impacts of domain textures on low-lying neutral excitations in the bulk of fractional quantum Hall effect (FQHE) systems are probed by resonant inelastic light scattering. We demonstrate that large domains of quantum fluids support long-wavelength neutral collective excitations with well-defined wave vector (momentum) dispersion that could be interpreted by theories for uniform phases. Access to dispersive low-lying neutral collective modes in large domains of FQHE fluids such as long wavelength magnetorotons at filling factor v=1/3 offer significant experimental access to strong electron correlation physics in the FQHE.
Collapse
Affiliation(s)
- Ziyu Liu
- Department of Physics, Columbia University, New York, New York 10027, USA
| | - Ursula Wurstbauer
- Institute of Physics, University of Münster, Wilhelm-Klemm-Straße 10, 48149 Münster, Germany
| | - Lingjie Du
- School of Physics, and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
| | - Ken W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Loren N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Michael J Manfra
- Department of Physics and Astronomy, School of Materials Engineering, and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, Indiana 47907, USA
| | - Aron Pinczuk
- Department of Physics, Columbia University, New York, New York 10027, USA
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
| |
Collapse
|
6
|
Dickmann S. Spin-rotation mode in a quantum Hall ferromagnet. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:015603. [PMID: 31491770 DOI: 10.1088/1361-648x/ab4230] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
A spin-rotation mode emerging in a quantum Hall ferromagnet due to laser pulse excitation is studied. This state, macroscopically representing a rotation of the entire electron spin-system to a certain angle, is not microscopically equivalent to a coherent turn of all spins as a single-whole and is presented in the form of a combination of eigen quantum states corresponding to all possible S z spin numbers. The motion of the macroscopic quantum state is studied microscopically by solving a non-stationary Schrödinger equation and by means of a kinetic approach where damping of the spin-rotation mode is related to an elementary process, namely, transformation of a 'Goldstone spin exciton' to a 'spin-wave exciton'. The system exhibits a spin stochastization mechanism (determined by spatial fluctuations of the Landé factor) ensuring damping, transverse spin relaxation, but irrelevant to decay of spin-wave excitons and thus not involving longitudinal relaxation, i.e. recovery of the S z number to its equilibrium value.
Collapse
Affiliation(s)
- S Dickmann
- Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, 142432, Russia
| |
Collapse
|
7
|
Du L, Wurstbauer U, West KW, Pfeiffer LN, Fallahi S, Gardner GC, Manfra MJ, Pinczuk A. Observation of new plasmons in the fractional quantum Hall effect: Interplay of topological and nematic orders. SCIENCE ADVANCES 2019; 5:eaav3407. [PMID: 30915397 PMCID: PMC6430622 DOI: 10.1126/sciadv.aav3407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/06/2018] [Accepted: 02/04/2019] [Indexed: 06/09/2023]
Abstract
Collective modes of exotic quantum fluids reveal underlying physical mechanisms responsible for emergent quantum states. We observe unexpected new collective modes in the fractional quantum Hall (FQH) regime: intra-Landau-level plasmons measured by resonant inelastic light scattering. The plasmons herald rotational-symmetry-breaking (nematic) phases in the second Landau level and uncover the nature of long-range translational invariance in these phases. The intricate dependence of plasmon features on filling factor provides insights on interplays between topological quantum Hall order and nematic electronic liquid crystal phases. A marked intensity minimum in the plasmon spectrum at Landau level filling factor v = 5/2 strongly suggests that this paired state, which may support non-Abelian excitations, overwhelms competing nematic phases, unveiling the robustness of the 5/2 superfluid state for small tilt angles. At v = 7/3, a sharp and strong plasmon peak that links to emerging macroscopic coherence supports the proposed model of a FQH nematic state.
Collapse
Affiliation(s)
- Lingjie Du
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
| | - Ursula Wurstbauer
- Walter Schottky Institut and Physik-Department, Technische Universität München, Am Coulombwall 4a, 85748 Garching, Germany
- Institute of Physics, University of Münster, Wilhelm-Klemm-Str.10, 48149 Münster, Germany
| | - Ken W. West
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Loren N. Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Saeed Fallahi
- Department of Physics and Astronomy, Purdue University, IN 47907, USA
- Birck Nanotechnology Center, Purdue University, IN 47907, USA
| | - Geoff C. Gardner
- Birck Nanotechnology Center, Purdue University, IN 47907, USA
- Microsoft Station Q Purdue, Purdue University, IN 47907, USA
| | - Michael J. Manfra
- Department of Physics and Astronomy, Purdue University, IN 47907, USA
- Birck Nanotechnology Center, Purdue University, IN 47907, USA
- Microsoft Station Q Purdue, Purdue University, IN 47907, USA
- School of Materials Engineering and School of Electrical and Computer Engineering, IN 47907, USA
| | - Aron Pinczuk
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
- Department of Physics, Columbia University, New York, NY 10027, USA
| |
Collapse
|
8
|
Hossain MS, Ma MK, Mueed MA, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Erratum: Direct observation of composite fermions and their fully-spin-polarized Fermi sea near ν=5/2 [Phys. Rev. Lett. 120, 256601 (2018)]. PHYSICAL REVIEW LETTERS 2018; 121:209901. [PMID: 30500222 DOI: 10.1103/physrevlett.121.209901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2018] [Indexed: 06/09/2023]
Abstract
This corrects the article DOI: 10.1103/PhysRevLett.120.256601.
Collapse
|
9
|
Hossain MS, Ma MK, Mueed MA, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Direct Observation of Composite Fermions and Their Fully-Spin-Polarized Fermi Sea near ν=5/2. PHYSICAL REVIEW LETTERS 2018; 120:256601. [PMID: 29979050 DOI: 10.1103/physrevlett.120.256601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2018] [Indexed: 06/08/2023]
Abstract
The enigmatic even-denominator fractional quantum Hall state at Landau level filling factor ν=5/2 is arguably the most promising candidate for harboring Majorana quasiparticles with non-Abelian statistics and, thus, of potential use for topological quantum computing. The theoretical description of the ν=5/2 state is generally believed to involve a topological p-wave pairing of fully-spin-polarized composite fermions through their condensation into a non-Abelian Moore-Read Pfaffian state. There is, however, no direct and conclusive experimental evidence for the existence of composite fermions near ν=5/2 or for an underlying fully-spin-polarized Fermi sea. Here, we report the observation of composite fermions very near ν=5/2 through geometric resonance measurements and find that the measured Fermi wave vector provides direct demonstration of a Fermi sea with full spin polarization. This lends crucial credence to the model of 5/2 fractional quantum Hall effect as a topological p-wave paired state of composite fermions.
Collapse
Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Meng K Ma
- 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
| | - 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
| |
Collapse
|
10
|
Competing ν = 5/2 fractional quantum Hall states in confined geometry. Proc Natl Acad Sci U S A 2016; 113:12386-12390. [PMID: 27791162 DOI: 10.1073/pnas.1614543113] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.
Collapse
|
11
|
Levy AL, Wurstbauer U, Kuznetsova YY, Pinczuk A, Pfeiffer LN, West KW, Manfra MJ, Gardner GC, Watson JD. Optical Emission Spectroscopy Study of Competing Phases of Electrons in the Second Landau Level. PHYSICAL REVIEW LETTERS 2016; 116:016801. [PMID: 26799037 DOI: 10.1103/physrevlett.116.016801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2015] [Indexed: 06/05/2023]
Abstract
Quantum phases of electrons in the filling factor range 2≤ν≤3 are probed by the weak optical emission from the partially populated second Landau level and spin wave measurements. Observations of optical emission include a multiplet of sharp peaks that exhibit a strong filling factor dependence. Spin wave measurements by resonant inelastic light scattering probe breaking of spin rotational invariance and are used to link this optical emission with collective phases of electrons. A remarkably rapid interplay between emission peak intensities manifests phase competition in the second Landau level.
Collapse
Affiliation(s)
- A L Levy
- Department of Physics, Columbia University, New York, New York 10027, USA
| | - U Wurstbauer
- Walter Schottky Institut and Physik-Department, Technische Universität München, Am Coulombwall 4a, 85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Munich, Germany
| | - Y Y Kuznetsova
- Department of Physics, Columbia University, New York, New York 10027, USA
| | - A Pinczuk
- Department of Physics, Columbia University, New York, New York 10027, USA
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, 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
| | - M J Manfra
- Department of Physics and Astronomy, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - G C Gardner
- School of Materials Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - J D Watson
- Department of Physics and Astronomy, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| |
Collapse
|
12
|
Lin X, Du R, Xie X. Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene. Natl Sci Rev 2014. [DOI: 10.1093/nsr/nwu071] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Abstract
The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.
Collapse
Affiliation(s)
- Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ruirui Du
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xincheng Xie
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| |
Collapse
|
13
|
Deng N, Gardner GC, Mondal S, Kleinbaum E, Manfra MJ, Csáthy GA. ν=5/2 fractional quantum Hall state in the presence of alloy disorder. PHYSICAL REVIEW LETTERS 2014; 112:116804. [PMID: 24702403 DOI: 10.1103/physrevlett.112.116804] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2013] [Indexed: 06/03/2023]
Abstract
We report quantitative measurements of the impact of alloy disorder on the ν = 5/2 fractional quantum Hall state. Alloy disorder is controlled by the aluminum content x in the Al(x)Ga(1-x)As channel of a quantum well. We find that the ν = 5/2 state is suppressed with alloy scattering. To our surprise, in samples with alloy disorder the ν = 5/2 state appears at significantly reduced mobilities when compared to samples in which alloy disorder is not the dominant scattering mechanism. Our results highlight the distinct roles of the different types of disorder present in these samples, such as the short-range alloy and the long-range Coulomb disorder.
Collapse
Affiliation(s)
- Nianpei Deng
- Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA
| | - G C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA and School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - S Mondal
- Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - E Kleinbaum
- Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA
| | - M J Manfra
- Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA and School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - G A Csáthy
- Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| |
Collapse
|
14
|
Balram AC, Wu YH, Sreejith GJ, Wójs A, Jain JK. Role of exciton screening in the 7/3 fractional quantum Hall effect. PHYSICAL REVIEW LETTERS 2013; 110:186801. [PMID: 23683230 DOI: 10.1103/physrevlett.110.186801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2012] [Indexed: 06/02/2023]
Abstract
The excitations of the 7/3 fractional Hall state, one of the most prominent states in the second Landau level, are not understood. We study the effect of screening by composite fermion excitons and find that it causes a strong renormalization at 7/3, thanks to a relatively small exciton gap and a relatively large residual interaction between composite fermions. The excitations of the 7/3 state are to be viewed as composite fermions dressed by a large exciton cloud. Their wide extent has implications for experiments as well as for analysis of finite system exact diagonalization studies.
Collapse
Affiliation(s)
- Ajit C Balram
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | | | | | | | | |
Collapse
|