1
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Freeman ML, Madathil PT, Pfeiffer LN, Baldwin KW, Chung YJ, Winkler R, Shayegan M, Engel LW. Origin of Pinning Disorder in Magnetic-Field-Induced Wigner Solids. PHYSICAL REVIEW LETTERS 2024; 132:176301. [PMID: 38728701 DOI: 10.1103/physrevlett.132.176301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Revised: 02/28/2024] [Accepted: 03/29/2024] [Indexed: 05/12/2024]
Abstract
At low Landau level filling factors (ν), Wigner solid phases of two-dimensional electron systems in GaAs are pinned by disorder and exhibit a pinning mode, whose frequency is a measure of the disorder that pins the Wigner solid. Despite numerous studies spanning the past three decades, the origin of the disorder that causes the pinning and determines the pinning mode frequency remains unknown. Here, we present a study of the pinning mode resonance in the low-ν Wigner solid phases of a series of ultralow-disorder GaAs quantum wells which are similar except for their varying well widths d. The pinning mode frequencies f_{p} decrease strongly as d increases, with the widest well exhibiting f_{p} as low as ≃35 MHz. The amount of reduction of f_{p} with increasing d can be explained remarkably well by tails of the wave function impinging into the alloy-disordered Al_{x}Ga_{1-x}As barriers that contain the electrons. However, it is imperative that the model for the confinement and wave function includes the Coulomb repulsion in the growth direction between the electrons as they occupy the quantum well.
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Affiliation(s)
- Matthew L Freeman
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
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2
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Madathil PT, Wang C, Singh SK, Gupta A, Rosales KAV, Chung YJ, West KW, Baldwin KW, Pfeiffer LN, Engel LW, Shayegan M. Signatures of Correlated Defects in an Ultraclean Wigner Crystal in the Extreme Quantum Limit. PHYSICAL REVIEW LETTERS 2024; 132:096502. [PMID: 38489610 DOI: 10.1103/physrevlett.132.096502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Revised: 01/04/2024] [Accepted: 02/05/2024] [Indexed: 03/17/2024]
Abstract
Low-disorder two-dimensional electron systems in the presence of a strong, perpendicular magnetic field terminate at very small Landau level filling factors in a Wigner crystal (WC), where the electrons form an ordered array to minimize the Coulomb repulsion. The nature of this exotic, many-body, quantum phase is yet to be fully understood and experimentally revealed. Here we probe one of WC's most fundamental parameters, namely, the energy gap that determines its low-temperature conductivity, in record mobility, ultrahigh-purity, two-dimensional electrons confined to GaAs quantum wells. The WC domains in these samples contain ≃1000 electrons. The measured gaps are a factor of three larger than previously reported for lower quality samples, and agree remarkably well with values predicted for the lowest-energy, intrinsic, hypercorrelated bubble defects in a WC made of flux-electron composite fermions, rather than bare electrons. The agreement is particularly noteworthy, given that the calculations are done for disorder-free composite fermion WCs, and there are no adjustable parameters. The results reflect the exceptionally high quality of the samples, and suggest that composite fermion WCs are indeed more stable compared to their electron counterparts.
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Affiliation(s)
- P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - C Wang
- 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 A Villegas Rosales
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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3
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Huang H, Hussain W, Myers SA, Pfeiffer LN, West KW, Baldwin KW, Csáthy GA. Evidence for Topological Protection Derived from Six-Flux Composite Fermions. Nat Commun 2024; 15:1461. [PMID: 38368413 PMCID: PMC10874392 DOI: 10.1038/s41467-024-45860-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 02/05/2024] [Indexed: 02/19/2024] Open
Abstract
The composite fermion theory opened a new chapter in understanding many-body correlations through the formation of emergent particles. The formation of two-flux and four-flux composite fermions is well established. While there are limited data linked to the formation of six-flux composite fermions, topological protection associated with them is conspicuously lacking. Here we report evidence for the formation of a quantized and gapped fractional quantum Hall state at the filling factor ν = 9/11, which we associate with the formation of six-flux composite fermions. Our result provides evidence for the most intricate composite fermion with six fluxes and expands the already diverse family of highly correlated topological phases with a new member that cannot be characterized by correlations present in other known members. Our observations pave the way towards the study of higher order correlations in the fractional quantum Hall regime.
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Affiliation(s)
- Haoyun Huang
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - Waseem Hussain
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - S A Myers
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - G A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA.
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4
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Wang C, Gupta A, Madathil PT, Singh SK, Chung YJ, Pfeiffer LN, Baldwin KW, Shayegan M. Next-generation even-denominator fractional quantum Hall states of interacting composite fermions. Proc Natl Acad Sci U S A 2023; 120:e2314212120. [PMID: 38113254 PMCID: PMC10756197 DOI: 10.1073/pnas.2314212120] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Accepted: 10/10/2023] [Indexed: 12/21/2023] Open
Abstract
The discovery of the fractional quantum Hall state (FQHS) in 1982 ushered a new era of research in many-body condensed matter physics. Among the numerous FQHSs, those observed at even-denominator Landau level filling factors are of particular interest as they may host quasiparticles obeying non-Abelian statistics and be of potential use in topological quantum computing. The even-denominator FQHSs, however, are scarce and have been observed predominantly in low-disorder two-dimensional (2D) systems when an excited electron Landau level is half filled. An example is the well-studied FQHS at filling factor [Formula: see text] 5/2 which is believed to be a Bardeen-Cooper-Schrieffer-type, paired state of flux-particle composite fermions (CFs). Here, we report the observation of even-denominator FQHSs at [Formula: see text] 3/10, 3/8, and 3/4 in the lowest Landau level of an ultrahigh-quality GaAs 2D hole system, evinced by deep minima in longitudinal resistance and developing quantized Hall plateaus. Quite remarkably, these states can be interpreted as even-denominator FQHSs of CFs, emerging from pairing of higher-order CFs when a CF Landau level, rather than an electron or a hole Landau level, is half-filled. Our results affirm enhanced interaction between CFs in a hole system with significant Landau level mixing and, more generally, the pairing of CFs as a valid mechanism for even-denominator FQHSs, and suggest the realization of FQHSs with non-Abelian anyons.
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Affiliation(s)
- Chengyu Wang
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ08544
| | - Adbhut Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ08544
| | - Pranav T. Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ08544
| | - Siddharth K. Singh
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ08544
| | - Yoon Jang Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ08544
| | - Loren N. Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ08544
| | - Kirk W. Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ08544
| | - Mansour Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ08544
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5
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Zhao L, Lin W, Chung YJ, Gupta A, Baldwin KW, Pfeiffer LN, Liu Y. Dynamic Response of Wigner Crystals. PHYSICAL REVIEW LETTERS 2023; 130:246401. [PMID: 37390428 DOI: 10.1103/physrevlett.130.246401] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Accepted: 05/26/2023] [Indexed: 07/02/2023]
Abstract
The Wigner crystal, an ordered array of electrons, is one of the very first proposed many-body phases stabilized by the electron-electron interaction. We examine this quantum phase with simultaneous capacitance and conductance measurements, and observe a large capacitive response while the conductance vanishes. We study one sample with four devices whose length scale is comparable with the crystal's correlation length, and deduce the crystal's elastic modulus, permittivity, pinning strength, etc. Such a systematic quantitative investigation of all properties on a single sample has a great promise to advance the study of Wigner crystals.
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Affiliation(s)
- Lili Zhao
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
| | - Wenlu Lin
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
| | - Yoon Jang Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Adbhut Gupta
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Kirk W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Loren N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Yang Liu
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
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6
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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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7
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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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8
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Chung YJ, Graf D, Engel LW, Rosales KAV, Madathil PT, Baldwin KW, West KW, Pfeiffer LN, Shayegan M. Correlated States of 2D Electrons near the Landau Level Filling ν=1/7. PHYSICAL REVIEW LETTERS 2022; 128:026802. [PMID: 35089735 DOI: 10.1103/physrevlett.128.026802] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2021] [Revised: 10/27/2021] [Accepted: 12/08/2021] [Indexed: 06/14/2023]
Abstract
The ground state of two-dimensional electron systems (2DESs) at low Landau level filling factors (ν≲1/6) has long been a topic of interest and controversy in condensed matter. Following the recent breakthrough in the quality of ultrahigh-mobility GaAs 2DESs, we revisit this problem experimentally and investigate the impact of reduced disorder. In a GaAs 2DES sample with density n=6.1×10^{10}/cm^{2} and mobility μ=25×10^{6} cm^{2}/V s, we find a deep minimum in the longitudinal magnetoresistance (R_{xx}) at ν=1/7 when T≃104 mK. There is also a clear sign of a developing minimum in R_{xx} at ν=2/13. While insulating phases are still predominant when ν≲1/6, these minima strongly suggest the existence of fractional quantum Hall states at filling factors that comply with the Jain sequence ν=p/(2mp±1) even in the very low Landau level filling limit. The magnetic-field-dependent activation energies deduced from the relation R_{xx}∝e^{E_{A}/2kT} corroborate this view and imply the presence of pinned Wigner solid states when ν≠p/(2mp±1). Similar results are seen in another sample with a lower density, further generalizing our observations.
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Affiliation(s)
- Yoon Jang Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D Graf
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - K A Villegas Rosales
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- 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
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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9
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Ma MK, Villegas Rosales KA, Deng H, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Winkler R, Shayegan M. Thermal and Quantum Melting Phase Diagrams for a Magnetic-Field-Induced Wigner Solid. PHYSICAL REVIEW LETTERS 2020; 125:036601. [PMID: 32745416 DOI: 10.1103/physrevlett.125.036601] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 06/12/2020] [Indexed: 06/11/2023]
Abstract
A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors (ν≃1/5). In dilute GaAs 2D hole systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings (ν≃1/3). Here we report our measurements of the fundamental temperature vs filling phase diagram for the 2D holes' WS-liquid thermal melting. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs filling WS-liquid quantum melting phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.
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Affiliation(s)
- Meng K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - H Deng
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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10
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Fremling M, Slingerland JK. An investigation of pre-crystalline order, ruling out Pauli crystals and introducing Pauli anti-crystals. Sci Rep 2020; 10:3710. [PMID: 32111894 PMCID: PMC7048835 DOI: 10.1038/s41598-020-60556-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2019] [Accepted: 02/11/2020] [Indexed: 11/22/2022] Open
Abstract
Fluid states of matter can locally exhibit characteristics of the onset of crystalline order. Traditionally this has been theoretically investigated using multipoint correlation functions. However new measurement techniques now allow multiparticle configurations of cold atomic systems to be observed directly. This has led to a search for new techniques to characterize the configurations that are likely to be observed. One of these techniques is the configuration density (CD), which has been used to argue for the formation of “Pauli crystals” by non-interacting electrons in e.g. a harmonic trap. We show here that such Pauli crystals do not exist, but that other other interesting spatial structures can occur in the form of an “anti-Crystal”, where the fermions preferentially avoid a lattice of positions surrounding any given fermion. Further, we show that configuration densities must be treated with great care as naive application can lead to the identification of crystalline structures which are artifacts of the method and of no physical significance. We analyze the failure of the CD and suggest methods that might be more suitable for characterizing multiparticle correlations which may signal the onset of crystalline order. In particular, we introduce neighbour counting statistics (NCS), which is the full counting statistics of the particle number in a neighborhood of a given particle. We test this on two dimensional systems with emerging triangular and square crystal structures.
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Affiliation(s)
- Mikael Fremling
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands. .,Department of Theoretical Physics, Maynooth University, Maynooth, co. Kildare, Ireland.
| | - J K Slingerland
- Department of Theoretical Physics, Maynooth University, Maynooth, co. Kildare, Ireland.,Dublin Institute for Advanced Studies, School of Theoretical Physics, 10 Burlington Rd, Dublin, Ireland
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11
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Deng H, Pfeiffer LN, West KW, Baldwin KW, Engel LW, Shayegan M. Probing the Melting of a Two-Dimensional Quantum Wigner Crystal via its Screening Efficiency. PHYSICAL REVIEW LETTERS 2019; 122:116601. [PMID: 30951347 DOI: 10.1103/physrevlett.122.116601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Indexed: 06/09/2023]
Abstract
One of the most fundamental and yet elusive collective phases of an interacting electron system is the quantum Wigner crystal (WC), an ordered array of electrons expected to form when the electrons' Coulomb repulsion energy eclipses their kinetic (Fermi) energy. In low-disorder, two-dimensional (2D) electron systems, the quantum WC is known to be favored at very low temperatures (T) and small Landau level filling factors (ν), near the termination of the fractional quantum Hall states. This WC phase exhibits an insulating behavior, reflecting its pinning by the small but finite disorder potential. An experimental determination of a T vs ν phase diagram for the melting of the WC, however, has proved to be challenging. Here we use capacitance measurements to probe the 2D WC through its effective screening as a function of T and ν. We find that, as expected, the screening efficiency of the pinned WC is very poor at very low T and improves at higher T once the WC melts. Surprisingly, however, rather than monotonically changing with increasing T, the screening efficiency shows a well-defined maximum at a T that is close to the previously reported melting temperature of the WC. Our experimental results suggest a new method to map out a T vs ν phase diagram of the magnetic-field-induced WC precisely.
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Affiliation(s)
- H Deng
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
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12
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Zhao J, Zhang Y, Jain JK. Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing. PHYSICAL REVIEW LETTERS 2018; 121:116802. [PMID: 30265120 DOI: 10.1103/physrevlett.121.116802] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2018] [Indexed: 06/08/2023]
Abstract
The interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the nonperturbative fixed-phase diffusion Monte Carlo method, we determine the phase diagram of the Wigner crystal in the ν-κ plane, where ν is the filling factor and κ is the strength of Landau-level (LL) mixing. The phase boundary is seen to exhibit a striking ν dependence, with the states away from the magic filling factors ν=n/(2pn+1) being much more susceptible to crystallization due to Landau-level mixing than those at ν=n/(2pn+1). Our results explain the qualitative difference between the experimental behaviors observed in n- and p-doped gallium arsenide quantum wells and, in particular, the existence of an insulating state for ν<1/3 and also for 1/3<ν<2/5 in low-density p-doped systems. We predict that, in the vicinity of ν=1/5 and ν=2/9, increasing LL mixing causes a transition not into an ordinary electron Wigner crystal, but rather into a strongly correlated crystal of composite fermions carrying two vortices.
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Affiliation(s)
- Jianyun Zhao
- Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Yuhe Zhang
- Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - J K Jain
- Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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13
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Kumar M, Laitinen A, Hakonen P. Unconventional fractional quantum Hall states and Wigner crystallization in suspended Corbino graphene. Nat Commun 2018; 9:2776. [PMID: 30018365 PMCID: PMC6050265 DOI: 10.1038/s41467-018-05094-8] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Accepted: 06/11/2018] [Indexed: 11/08/2022] Open
Abstract
Competition between liquid and solid states in two-dimensional electron systems is an intriguing problem in condensed matter physics. We have investigated competing Wigner crystal and fractional quantum Hall (FQH) liquid phases in atomically thin suspended graphene devices in Corbino geometry. Low-temperature magnetoconductance and transconductance measurements along with IV characteristics all indicate strong charge density dependent modulation of electron transport. Our results show unconventional FQH phases which do not fit the standard Jain's series for conventional FQH states, instead they appear to originate from residual interactions of composite fermions in partially filled Landau levels. Also at very low charge density with filling factors [Formula: see text], electrons crystallize into an ordered Wigner solid which eventually transforms into an incompressible Hall liquid at filling factors around ν ≤ 1/7. Building on the unique Corbino sample structure, our experiments pave the way for enhanced understanding of the ordered phases of interacting electrons.
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Affiliation(s)
- Manohar Kumar
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland
- Laboratoire Pierre Aigrain, Département de Physique de l'École Normale Supérieure -PSL Research University, CNRS Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, Paris, France
| | - Antti Laitinen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland
| | - Pertti Hakonen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland.
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14
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Bennaceur K, Lupien C, Reulet B, Gervais G, Pfeiffer LN, West KW. Competing Charge Density Waves Probed by Nonlinear Transport and Noise in the Second and Third Landau Levels. PHYSICAL REVIEW LETTERS 2018; 120:136801. [PMID: 29694212 DOI: 10.1103/physrevlett.120.136801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2017] [Indexed: 06/08/2023]
Abstract
Charge density waves (CDWs) in the second and third Landau levels (LLs) are investigated by both nonlinear electronic transport and noise. The use of a Corbino geometry ensures that only bulk properties are probed, with no contribution from edge states. Sliding transport of CDWs is revealed by narrow band noise in reentrant quantum Hall states R2a and R2c of the second LL, as well as in pinned CDWs of the third LL. Competition between various phases-stripe, pinned CDW, or fractional quantum Hall liquid-in both LLs are clearly revealed by combining noise data with maps of conductivity versus magnetic field and bias voltage.
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Affiliation(s)
- K Bennaceur
- Département de Physique et Institut Quantique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
- Department of Physics, Amrita Vishwa Vidyapeetham, Amritapuri 690525, India
- Department of Physics, McGill University, Montréal, Québec H3A 2T8, Canada
| | - C Lupien
- Département de Physique et Institut Quantique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - B Reulet
- Département de Physique et Institut Quantique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - G Gervais
- Department of Physics, McGill University, Montréal, Québec H3A 2T8, Canada
| | - 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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15
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Santos LH, Hughes TL. Parafermionic Wires at the Interface of Chiral Topological States. PHYSICAL REVIEW LETTERS 2017; 118:136801. [PMID: 28409966 DOI: 10.1103/physrevlett.118.136801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Indexed: 06/07/2023]
Abstract
We explore a scenario where local interactions form one-dimensional gapped interfaces between a pair of distinct chiral two-dimensional topological states-referred to as phases 1 and 2-such that each gapped region terminates at a domain wall separating the chiral gapless edge states of these phases. We show that this type of T junction supports pointlike fractionalized excitations obeying parafermion statistics, thus implying that the one-dimensional gapped interface forms an effective topological parafermionic wire possessing a nontrivial ground state degeneracy. The physical properties of the anyon condensate that gives rise to the gapped interface are investigated. Remarkably, this condensate causes the gapped interface to behave as a type of anyon "Andreev reflector" in the bulk, whereby anyons from one phase, upon hitting the interface, can be transformed into a combination of reflected anyons and outgoing anyons from the other phase. Thus, we conclude that while different topological orders can be connected via gapped interfaces, the interfaces are themselves topological.
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Affiliation(s)
- Luiz H Santos
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
| | - Taylor L Hughes
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
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16
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Kleinbaum E, Kumar A, Pfeiffer LN, West KW, Csáthy GA. Gap reversal at filling factors 3+1/3 and 3+1/5: towards novel topological order in the fractional quantum Hall regime. PHYSICAL REVIEW LETTERS 2015; 114:076801. [PMID: 25763967 DOI: 10.1103/physrevlett.114.076801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Indexed: 06/04/2023]
Abstract
In the region of the second Landau level several theories predict fractional quantum Hall states with novel topological order. We report the opening of an energy gap at the filling factor ν=3+1/3, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the ν=3+1/3 and 3+1/5 states from the upper spin branch are reversed when compared to the ν=2+1/3 and 2+1/5 counterpart states in the lower spin branch. Our findings raise the possibility that at least one of the former states is of an unusual topological order.
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Affiliation(s)
- Ethan Kleinbaum
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Ashwani Kumar
- Department of Physics, Monmouth College, Monmouth, Illinois 61462, 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
| | - G A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
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17
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Wilson RM, Peden BM, Clark CW, Rittenhouse ST. Spin waves and dielectric softening of polar molecule condensates. PHYSICAL REVIEW LETTERS 2014; 112:135301. [PMID: 24745433 DOI: 10.1103/physrevlett.112.135301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2013] [Indexed: 06/03/2023]
Abstract
We consider an oblate Bose-Einstein condensate of heteronuclear polar molecules in a weak applied electric field. This system supports a rich quasiparticle spectrum that plays a critical role in determining its bulk dielectric properties. In particular, in sufficiently weak fields the system undergoes a polarization wave rotonization, leading to the development of textured electronic structure and a dielectric instability that is characteristic of the onset of a negative static dielectric function.
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Affiliation(s)
- Ryan M Wilson
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
| | - Brandon M Peden
- Department of Physics and Astronomy, Western Washington University, Bellingham, Washington 98225, USA
| | - Charles W Clark
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
| | - Seth T Rittenhouse
- Department of Physics and Astronomy, Western Washington University, Bellingham, Washington 98225, USA and ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
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18
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Archer AC, Park K, Jain JK. Competing crystal phases in the lowest Landau level. PHYSICAL REVIEW LETTERS 2013; 111:146804. [PMID: 24138264 DOI: 10.1103/physrevlett.111.146804] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Indexed: 06/02/2023]
Abstract
We show that the solid phase between the 1/5 and 2/9 fractional quantum Hall states arises from an extremely delicate interplay between type-1 and type-2 composite fermion crystals, clearly demonstrating its nontrivial, strongly correlated character. We also compute the phase diagram of various crystals occurring over a wide range of filling factors and demonstrate that the elastic constants exhibit nonmonotonic behavior as a function of the filling factor, possibly leading to distinctive experimental signatures that can help mark the phase boundaries separating different kinds of crystals.
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Affiliation(s)
- Alexander C Archer
- Department of Physics, 104 Davey Lab, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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19
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Samkharadze N, Kumar A, Manfra MJ, Pfeiffer LN, West KW, Csáthy GA. Integrated electronic transport and thermometry at milliKelvin temperatures and in strong magnetic fields. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2011; 82:053902. [PMID: 21639513 DOI: 10.1063/1.3586766] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We fabricated a He-3 immersion cell for transport measurements of semiconductor nanostructures at ultra low temperatures and in strong magnetic fields. We have a new scheme of field-independent thermometry based on quartz tuning fork Helium-3 viscometry which monitors the local temperature of the sample's environment in real time. The operation and measurement circuitry of the quartz viscometer is described in detail. We provide evidence that the temperature of two-dimensional electron gas confined to a GaAs quantum well follows the temperature of the quartz viscometer down to 4 mK.
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Affiliation(s)
- N Samkharadze
- Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA
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20
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Tunneling Effect in Quantum Hall Device. E-JOURNAL OF SURFACE SCIENCE AND NANOTECHNOLOGY 2010. [DOI: 10.1380/ejssnt.2010.121] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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21
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Kopelevich Y, Raquet B, Goiran M, Escoffier W, da Silva RR, Pantoja JCM, Luk'yanchuk IA, Sinchenko A, Monceau P. Searching for the fractional quantum Hall effect in graphite. PHYSICAL REVIEW LETTERS 2009; 103:116802. [PMID: 19792390 DOI: 10.1103/physrevlett.103.116802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2009] [Indexed: 05/28/2023]
Abstract
Measurements of basal plane longitudinal rho(b)(B) and Hall rho(H)(B) resistivities were performed on highly oriented pyrolytic graphite samples in a pulsed magnetic field up to B=50 T applied perpendicular to graphene planes, and temperatures 1.5 K<or=T<or=4.2 K. At B>30 T and for all studied samples, we observed a sign change in rho(H)(B) from electron- to holelike. For our best quality sample, the measurements revealed the enhancement in rho(b)(B) for B>34 T (T=1.8 K), presumably associated with the field-driven charge density wave or Wigner crystallization transition. In addition, well-defined plateaus in rho(H)(B) were detected in the ultraquantum limit revealing possible signatures of the fractional quantum Hall effect in graphite.
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Affiliation(s)
- Y Kopelevich
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, UNICAMP 13083-970, Campinas, São Paulo, Brasil
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22
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Shabani J, Gokmen T, Shayegan M. Correlated states of electrons in wide quantum wells at low fillings: the role of charge distribution symmetry. PHYSICAL REVIEW LETTERS 2009; 103:046805. [PMID: 19659383 DOI: 10.1103/physrevlett.103.046805] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2009] [Indexed: 05/28/2023]
Abstract
Magnetotransport measurements on electrons confined to a 57-nm-wide, GaAs quantum well reveal that the correlated electron states at low Landau level fillings (nu) display a remarkable dependence on the symmetry of the electron charge distribution. At a density of 1.93 x 10;{11} cm;{-2}, a developing fractional quantum Hall state is observed at the even-denominator filling nu = 1/4 when the distribution is symmetric, but it quickly vanishes when the distribution is made asymmetric. At lower densities, as we make the charge distribution asymmetric, we observe a rapid strengthening of the insulating phases that surround the nu = 1/5 fractional quantum Hall state.
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Affiliation(s)
- J Shabani
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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23
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Luhman DR, Pan W, Tsui DC, Pfeiffer LN, Baldwin KW, West KW. Observation of a fractional quantum hall state at nu = 1/4 in a wide GaAs quantum well. PHYSICAL REVIEW LETTERS 2008; 101:266804. [PMID: 19437661 DOI: 10.1103/physrevlett.101.266804] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We report the observation of an even-denominator fractional quantum Hall state at nu = 1/4 in a high quality, wide GaAs quantum well. The sample has a quantum well width of 50 nm and an electron density of n(e) = 2.55 x 10(11) cm(-2). We have performed transport measurements at T - 35 mK in magnetic fields up to 45 T. When the sample is perpendicular to the applied magnetic field, the diagonal resistance displays a kink at nu = 1/4. Upon tilting the sample to an angle of theta = 20.3 degrees a clear fractional quantum Hall state emerges at nu = 1/4 with a plateau in the Hall resistance and a strong minimum in the diagonal resistance.
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Affiliation(s)
- D R Luhman
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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24
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Yannouleas C, Landman U. Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2007; 70:2067-2148. [PMID: 34996294 DOI: 10.1088/0034-4885/70/12/r02] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2007] [Indexed: 06/14/2023]
Abstract
Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations.Strongly-correlated phenomena emerging from symmetry breaking include the following.Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solid-state quantum-computing devices.Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit ro-vibrational excitation spectra, in analogy with natural molecules.At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit).Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the Gross-Pitaevskii solutions describing vortex formation.We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.
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Affiliation(s)
| | - Uzi Landman
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
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25
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Chang CC, Jeon GS, Jain JK. Microscopic verification of topological electron-vortex binding in the lowest Landau-level crystal state. PHYSICAL REVIEW LETTERS 2005; 94:016809. [PMID: 15698119 DOI: 10.1103/physrevlett.94.016809] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2004] [Indexed: 05/24/2023]
Abstract
When two-dimensional electrons are subjected to a very strong magnetic field, they are believed to form a triangular crystal. By a direct comparison with the exact wave function, we demonstrate that this crystal is not a simple Hartree-Fock crystal of electrons but an inherently quantum mechanical crystal characterized by a nonperturbative binding of quantized vortices to electrons. It is suggested that this has qualitative consequences for experiment.
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Affiliation(s)
- Chia-Chen Chang
- Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, PA 16802, USA
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26
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Gervais G, Engel LW, Stormer HL, Tsui DC, Baldwin KW, West KW, Pfeiffer LN. Competition between a fractional quantum hall liquid and bubble and Wigner crystal phases in the third Landau level. PHYSICAL REVIEW LETTERS 2004; 93:266804. [PMID: 15698005 DOI: 10.1103/physrevlett.93.266804] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2004] [Indexed: 05/24/2023]
Abstract
Magnetotransport measurements were performed in an ultrahigh mobility GaAs/AlGaAs quantum well of density approximately 3.0 x 10(11) cm(-2). The temperature dependence of the magnetoresistance Rxx was studied in detail in the vicinity of nu=9/2. In particular, we discovered new minima in Rxx at a filling factor nu approximately 41/5 and 44/5, but only at intermediate temperatures 80 approximately less than T approximately less than 120 mK. We interpret these as evidence for a fractional quantum Hall liquid forming in the N=2 Landau level and competing with bubble and Wigner crystal phases favored at lower temperatures. Our data suggest that a magnetically driven insulator-insulator quantum phase transition occurs between the bubble and Wigner crystal phases at T=0.
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Affiliation(s)
- G Gervais
- Department of Physics and Department of Applied Physics, Columbia University, New York, New York 10027, USA
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27
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Chen YP, Lewis RM, Engel LW, Tsui DC, Ye PD, Wang ZH, Pfeiffer LN, West KW. Evidence for two different solid phases of two-dimensional electrons in high magnetic fields. PHYSICAL REVIEW LETTERS 2004; 93:206805. [PMID: 15600955 DOI: 10.1103/physrevlett.93.206805] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2004] [Indexed: 05/24/2023]
Abstract
We have observed two different rf resonances in the frequency dependent real diagonal conductivity of very high quality two-dimensional electron systems in the high magnetic field insulating phase and interpret them as coming from two different pinned electron solid phases (labeled as "A" and "B"). The "A" resonance is observable for Landau level filling nu<2/9 [reentrant around the nu=1/5 fractional quantum Hall effect (FQHE)] and then crosses over to the different "B" resonance which dominates at sufficiently low nu. Moreover, the "A" resonance is found to show dispersion with respect to the size of the transmission line, indicating that the "A" phase has a large correlation length. We suggest that quantum correlations such as those responsible for FQHE may play an important role in giving rise to such different solids.
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Affiliation(s)
- Yong P Chen
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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28
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Xia JS, Pan W, Vicente CL, Adams ED, Sullivan NS, Stormer HL, Tsui DC, Pfeiffer LN, Baldwin KW, West KW. Electron correlation in the second Landau level: a competition between many nearly degenerate quantum phases. PHYSICAL REVIEW LETTERS 2004; 93:176809. [PMID: 15525110 DOI: 10.1103/physrevlett.93.176809] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2004] [Indexed: 05/24/2023]
Abstract
At a very low-temperature of 9 mK, electrons in the second Landau level of an extremely high-mobility two-dimensional electron system exhibit a very complex electronic behavior. With a varying filling factor, quantum liquids of different origins compete with several insulating phases leading to an irregular pattern in the transport parameters. We observe a fully developed nu=2+2/5 state separated from the even-denominator nu=2+1/2 state by an insulating phase and a nu=2+2/7 and nu=2+1/5 state surrounded by such phases. A developing plateau at nu=2+3/8 points to the existence of other even-denominator states.
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Affiliation(s)
- J S Xia
- University of Florida, Gainesville, Florida 32611, USA
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29
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Mandal SS, Peterson MR, Jain JK. Two-dimensional electron system in high magnetic fields: Wigner crystal versus composite-fermion liquid. PHYSICAL REVIEW LETTERS 2003; 90:106403. [PMID: 12689018 DOI: 10.1103/physrevlett.90.106403] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2002] [Indexed: 05/24/2023]
Abstract
The two-dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a parameter range where theory and many experiments had previously suggested the Wigner crystal phase, thus calling into question our current understanding. This Letter shows how very small quantitative corrections (<1%) in the energy due to the weak interaction between composite fermions can cause a fundamental change in the nature of the ground state, thus providing insight into the puzzling experimental results.
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Affiliation(s)
- Sudhansu S Mandal
- Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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30
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Dujovne I, Pinczuk A, Kang M, Dennis BS, Pfeiffer LN, West KW. Evidence of Landau levels and interactions in low-lying excitations of composite fermions at 1/3<or= nu <or=2/5. PHYSICAL REVIEW LETTERS 2003; 90:036803. [PMID: 12570516 DOI: 10.1103/physrevlett.90.036803] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2002] [Indexed: 05/24/2023]
Abstract
Excitation modes in the range 2/5>or=nu>or=1/3 of the fractional quantum Hall regime are observed by resonant inelastic light scattering. Spectra of spin-reversed excitations suggest a structure of lowest spin-split Landau levels of composite fermions that is similar to that of electrons. Spin-flip energies determined from spectra reveal significant composite fermion interactions. The filling factor dependence of mode energies displays an abrupt change in the middle of the range when there is partial population of a composite fermion level.
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Affiliation(s)
- Irene Dujovne
- Department of Applied Physics and Applied Math, Columbia University, New York, New York 10027, USA
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