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Title: Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing

Abstract

Here, 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 non-perturbative 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 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-doped and p-doped GaAs 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.

Authors:
 [1];  [1];  [1]
  1. The Pennsylvania State Univ., University Park, PA (United States)
Publication Date:
Research Org.:
Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1489112
Alternate Identifier(s):
OSTI ID: 1469437
Grant/Contract Number:  
SC0005042
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 121; Journal Issue: 11; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; composite fermions; Wigner crystal; fractional quantum Hall effect; Landau level mixing

Citation Formats

Zhao, Jianyun, Zhang, Yuhe, and Jain, J. K. Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing. United States: N. p., 2018. Web. doi:10.1103/PhysRevLett.121.116802.
Zhao, Jianyun, Zhang, Yuhe, & Jain, J. K. Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing. United States. doi:10.1103/PhysRevLett.121.116802.
Zhao, Jianyun, Zhang, Yuhe, and Jain, J. K. Tue . "Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing". United States. doi:10.1103/PhysRevLett.121.116802. https://www.osti.gov/servlets/purl/1489112.
@article{osti_1489112,
title = {Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing},
author = {Zhao, Jianyun and Zhang, Yuhe and Jain, J. K.},
abstractNote = {Here, 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 non-perturbative 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 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-doped and p-doped GaAs 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.},
doi = {10.1103/PhysRevLett.121.116802},
journal = {Physical Review Letters},
number = 11,
volume = 121,
place = {United States},
year = {2018},
month = {9}
}

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Works referenced in this record:

New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field
journal, October 1993


Microscopic Verification of Topological Electron-Vortex Binding in the Lowest Landau-Level Crystal State
journal, January 2005


Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States
journal, August 1983


Competing Crystal Phases in the Lowest Landau Level
journal, October 2013


Quantum Monte Carlo simulations of solids
journal, January 2001


Evidence for two-dimentional quantum Wigner crystal
journal, October 1990


Fractional quantum Hall liquid, Wigner solid phase boundary at finite density and magnetic field
journal, January 1993


Wigner crystallization in the fractional quantum Hall regime: A variational quantum Monte Carlo study
journal, January 1993


Defect motifs for spherical topologies
journal, June 2009


Fixed‐node quantum Monte Carlo for molecules a) b)
journal, December 1982

  • Reynolds, Peter J.; Ceperley, David M.; Alder, Berni J.
  • The Journal of Chemical Physics, Vol. 77, Issue 11
  • DOI: 10.1063/1.443766

Electrical conductivity and Wigner crystallization
journal, June 1992


Theory of the half-filled Landau level
journal, March 1993


Hamiltonian theory of the composite-fermion Wigner crystal
journal, December 2001


Evidence for a Bilayer Quantum Wigner Solid
journal, August 1996


Quantum Monte Carlo with variable spins: Fixed-phase and fixed-node approximations
journal, October 2017


Fractional quantum Hall effect and Chern-Simons gauge theories
journal, September 1991


Microwave resonances in low-filling insulating phases of two-dimensional electron and hole systems
journal, January 1997

  • Engel, L. W.; Li, C. -C; Shahar, D.
  • Physica E: Low-dimensional Systems and Nanostructures, Vol. 1, Issue 1-4
  • DOI: 10.1016/S1386-9477(97)00025-8

Wigner crystal versus Hall insulator
journal, December 1994


Pinning mode resonances of new phases of 2D electron systems in high magnetic fields
journal, October 2006

  • Sambandamurthy, G.; Wang, Zhihai; Lewis, R. M.
  • Solid State Communications, Vol. 140, Issue 2
  • DOI: 10.1016/j.ssc.2006.05.053

Transition from a fractional quantum Hall liquid to an electron solid at Landau level filling ν = 1 3 in tilted magnetic fields
journal, January 2005


Quantitative study of large composite-fermion systems
journal, February 1997


Landau level mixing and the fractional quantum Hall effect
journal, June 2013


Two-Dimensional Magnetotransport in the Extreme Quantum Limit
journal, May 1982


Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
journal, May 1983


Liquid-solid transition and the fractional quantum-Hall effect
journal, July 1984


Transition from an Electron Solid to the Sequence of Fractional Quantum Hall States at Very Low Landau Level Filling Factor
journal, April 2002


Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study
journal, December 1997


Correlation Lengths of the Wigner-Crystal Order in a Two-Dimensional Electron System at High Magnetic Fields
journal, October 2002


Observation of a reentrant insulating phase near the 1/3 fractional quantum Hall liquid in a two-dimensional hole system
journal, February 1992


Melting of a 2D quantum electron solid in high magnetic field
journal, June 2006

  • Chen, Yong P.; Sambandamurthy, G.; Wang, Z. H.
  • Nature Physics, Vol. 2, Issue 7
  • DOI: 10.1038/nphys322

Crystallization of the incompressible quantum-fluid state of a two-dimensional electron gas in a strong magnetic field
journal, July 1984


Sharp tunnelling resonance from the vibrations of an electronic Wigner crystal
journal, December 2016

  • Jang, Joonho; Hunt, Benjamin M.; Pfeiffer, Loren N.
  • Nature Physics, Vol. 13, Issue 4
  • DOI: 10.1038/nphys3979

Maximum-density droplet to lower-density droplet transition in quantum dots
journal, July 2005


Commensurability Oscillations of Composite Fermions Induced by the Periodic Potential of a Wigner Crystal
journal, August 2016


Transport of a sliding Wigner crystal in the four flux composite fermion regime
journal, August 2015


Magnetic-Field-Induced Insulating Phases at Large r s
journal, June 2005


Effect of Landau-level mixing on quantum-liquid and solid states of two-dimensional hole systems
journal, November 1992


On the Interaction of Electrons in Metals
journal, December 1934


Microwave resonance and weak pinning in two-dimensional hole systems at high magnetic fields
journal, April 2000


Tunnel transport and interlayer excitons in bilayer fractional quantum Hall systems
journal, May 2017


Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
journal, September 1997


Quantum liquid versus electron solid around ν=1/5 Landau-level filling
journal, July 1990


Structure and dynamics of spherical crystals characterized for the Thomson problem
journal, December 2006


Static and dynamic properties of a two-dimensional Wigner crystal in a strong magnetic field
journal, October 1983


Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field
journal, August 1998


Quantum freezing of the fractional quantum Hall liquid
journal, May 1993


Composite-fermion approach for the fractional quantum Hall effect
journal, July 1989


Fractional Quantum Hall Effect and Wigner Crystal of Interacting Composite Fermions
journal, December 2014


Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect
journal, September 2016


Evidence for Two Different Solid Phases of Two-Dimensional Electrons in High Magnetic Fields
journal, November 2004