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 wavefunction and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wavefunction 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 new 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 wavefunction 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 wavefunctions. 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 $n$-doping to $p$-doping in $GaAS/AlGaAS$ heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor $\nu \sim 1/5$ to $\nu \sim 1/3$. This lends strong support to the claim that the

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References in corpus (4)

• Topological Defects, Orientational Order, and Depinning of the Electron Solid in a Random Potential
• Laughlin liquid - Wigner solid transition at high density in wide quantum wells
• Sliding motion of a two-dimensional Wigner crystal in a strong magnetic field
• Freezing of the quantum Hall liquid at $\nu =$ 1/7 and 1/9

Cited by in corpus (35)

• Transition from an electron solid to the sequence of fractional quantum Hall states at very low Landau level filling factor
• Correlation lengths of Wigner crystal order in two dimensional electron system at high magnetic field
• Wigner Glass, Spin-liquids, and the Metal-Insulator Transition
• Microwave Resonance of 2D Wigner Crystal around integer Landau fillings
• Exchange Frequencies in the 2d Wigner crystal
• Evidence for Two Different Solid Phases of Two Dimensional Electrons in High Magnetic Fields
• Ground-state energy of the electron liquid in ultrathin wires
• Monte Carlo study of Bose Laughlin wave function for filling factors 1/2, 1/4 and 1/6
• Tilt Induced Localization and Delocalization in the Second Landau Level
• Mach-Zehnder interferometry of fractional quantum Hall edge states
• Skyrme and Wigner crystals in graphene
• Connecting the Reentrant Insulating Phase and the Zero Field Metal-Insulator Transition in a 2D Hole System
• Two-dimensional electron system in high magnetic fields: Wigner crystal vs. composite-fermion liquid
• Magnetic Field Induced Insulating Phases at Large $r_s$
• The Magnetic Ordering of the 3d Wigner Crystal
• Single and Paired Point Defects in a 2D Wigner Crystal
• Anisotropic magnetoresistance and piezoelectric effect in GaAs Hall samples
• Correlated states of 2D electrons near the Landau level filling $\nu =1/7$
• Probing magnetism in moiré heterostructures with quantum twisting microscopes
• Functional-renormalization-group aided density-functional analysis for the correlation energy of the two-dimensional homogeneous electron gas
• Vertical Confinement and Evolution of Reentrant Insulating Transition in the Fractional Quantum Hall Regime
• Structural and insulator-metal quantum phase transitions on a lattice
• Replica study of pinned bubble crystals
• Tuning of the Gap in a Laughlin-Bychkov-Rashba Incompressible Liquid
• Interaction between Surface Acoustic Wave and Quantum Hall Effects
• Ground-state energy and Wigner crystallization in thick 2D-electron systems
• Discovery of an insulating ferromagnetic phase of electrons in two dimensions
• Dynamical matrix of two-dimensional electron crystals
• Evidence for Topological Protection Derived from Six-Flux Composite Fermions
• Developing fractional quantum Hall states at $\nu$ = $\frac{1}{7}$ and $\frac{2}{11}$ in the presence of significant Landau level mixing
• Driven Tunneling: Chaos and Decoherence
• Wigner Crystallization of a two dimensional electron gas in a magnetic field: single electrons versus electron pairs at the lattice sites
• Absence of diagonal force constants in cubic Coulomb crystals
• Disorder-induced strong-field strong-localization in 2D systems
• Quantum melting a Wigner crystal into Hall liquids