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Title: Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects

Abstract

The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wave function and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wave function of the strongly correlated solid. Exchange, correlation, and magnetic-field effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin orderings are observed in the ground state of the electron crystal in various two-dimensional lattices. In particular, two-dimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground state. In the quantum Hall effect regime, a strong magnetic field introduces energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wave function when the system is in a uniform magnetic field. We have examined the exchange, intra-Landau-level correlation as well as Landau-level-mixing effects with various variational wave functions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulation-doped semiconductor heterojunction. Our results, when combined with some recent calculationsmore » for the energy of the fractional quantum Hall liquid including Landau-level-mixing, show quantitatively that in going from {ital n} doping to {ital p} doping in GaAs/Al{sub {ital x}}Ga{sub 1{minus}{ital x}}As heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor {nu}{similar_to}1/5 to {nu}{similar_to}1/3.« less

Authors:
 [1];  [2]
  1. Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855 (United States)
  2. Department of Physics, University of California, Berkeley, California 94720 (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory
OSTI Identifier:
122268
DOE Contract Number:  
AC03-76SF00098
Resource Type:
Journal Article
Journal Name:
Physical Review, B: Condensed Matter
Additional Journal Information:
Journal Volume: 52; Journal Issue: 8; Other Information: PBD: 15 Aug 1995
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; CRYSTAL MODELS; GROUND STATES; COLLECTIVE EXCITATIONS; CORRELATED-PARTICLE MODELS; MONTE CARLO METHOD; TWO-DIMENSIONAL CALCULATIONS; TRANSPORT THEORY; WIGNER THEORY; QUANTIZATION; MAGNETORESISTANCE; LANDAU FLUCTUATIONS; EXCHANGE INTERACTIONS

Citation Formats

Zhu, X, Department of Physics, University of California, Berkeley, California 94720, Materials Science DIvision, Lawrence Livermore Laboratory, Berkeley, California 94720, Louie, S G, and Materials Science Division, Lawrence Livermore Laboratory, Berkeley, California 94720. Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects. United States: N. p., 1995. Web. doi:10.1103/PhysRevB.52.5863.
Zhu, X, Department of Physics, University of California, Berkeley, California 94720, Materials Science DIvision, Lawrence Livermore Laboratory, Berkeley, California 94720, Louie, S G, & Materials Science Division, Lawrence Livermore Laboratory, Berkeley, California 94720. Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects. United States. doi:10.1103/PhysRevB.52.5863.
Zhu, X, Department of Physics, University of California, Berkeley, California 94720, Materials Science DIvision, Lawrence Livermore Laboratory, Berkeley, California 94720, Louie, S G, and Materials Science Division, Lawrence Livermore Laboratory, Berkeley, California 94720. Tue . "Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects". United States. doi:10.1103/PhysRevB.52.5863.
@article{osti_122268,
title = {Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects},
author = {Zhu, X and Department of Physics, University of California, Berkeley, California 94720 and Materials Science DIvision, Lawrence Livermore Laboratory, Berkeley, California 94720 and Louie, S G and Materials Science Division, Lawrence Livermore Laboratory, Berkeley, California 94720},
abstractNote = {The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wave function and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wave function of the strongly correlated solid. Exchange, correlation, and magnetic-field effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin orderings are observed in the ground state of the electron crystal in various two-dimensional lattices. In particular, two-dimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground state. In the quantum Hall effect regime, a strong magnetic field introduces energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wave function when the system is in a uniform magnetic field. We have examined the exchange, intra-Landau-level correlation as well as Landau-level-mixing effects with various variational wave functions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulation-doped semiconductor heterojunction. Our results, when combined with some recent calculations for the energy of the fractional quantum Hall liquid including Landau-level-mixing, show quantitatively that in going from {ital n} doping to {ital p} doping in GaAs/Al{sub {ital x}}Ga{sub 1{minus}{ital x}}As heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor {nu}{similar_to}1/5 to {nu}{similar_to}1/3.},
doi = {10.1103/PhysRevB.52.5863},
journal = {Physical Review, B: Condensed Matter},
number = 8,
volume = 52,
place = {United States},
year = {1995},
month = {8}
}