Critical gate distance for Wigner crystallization in the two-dimensional electron gas

Abstract

We report on the properties of the two-dimensional electron gas in a dual-gate geometry, using quantum Monte Carlo methods to obtain aspects of the phase diagram as a function of electron density and gate distance. We identify the critical gate distance below which the Wigner crystal phase disappears. For larger gate distances, the system undergoes a re-entrant transition from crystal to liquid at sufficiently low density. We also present preliminary evidence for a fully polarized ferromagnetic liquid state at low electron density and intermediate gate distances. The quantum Monte Carlo results are compared with simpler approximate methods, which are shown to be semi-quantitatively reliable for determining key features of the phase diagram. These methods are then used to obtain the phase boundary between the Wigner crystal and liquid in the single-gate geometry.

4+4 pages

References in corpus (31)

• Correlation energy and spin polarization in the 2D electron gas
• QMCPACK : An open source ab initio Quantum Monte Carlo package for the electronic structure of atoms, molecules, and solids
• Signatures of bilayer Wigner crystals in a transition metal dichalcogenide heterostructure
• Observation of Wigner crystal of electrons in a monolayer semiconductor
• The Finite Size Error in Many-body Simulations with long-Ranged Interactions
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo
• Universal Aspects of Coulomb Frustrated Phase Separation
• Theory of Finite Size Effects for Electronic Quantum Monte Carlo Calculations of Liquids and Solids
• Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
• Direct observation of a magnetic field-induced Wigner crystal
• Competing correlated states around the zero field Wigner crystallization transition of electrons in two-dimensions
• Anomalously large capacitance of a plane capacitor with a two-dimensional electron gas
• Theory of volumetric capacitance of an electric double-layer supercapacitor
• Liquid and crystal phase of dipolar fermions in two dimensions
• Fermions on bilayer graphene: symmetry breaking for B=0 and nu=0
• Observation of Spontaneous Ferromagnetism in a Two-Dimensional Electron System
• Pair-distribution functions of the two-dimensional electron gas
• Hybrid phase at the quantum melting of the Wigner crystal
• Observation of spontaneous valley polarization of itinerant electrons
• Anatomy of the quantum melting of the two dimensional Wigner crystal
• Anisotropic, two-dimensional, disordered Wigner solid
• Ground state phases of the two-dimension electron gas with a unified variational approach
• Observation of an electronic microemulsion phase emerging from a quantum crystal-to-liquid transition
• Interstitial-induced ferromagnetism in a two-dimensional Wigner crystal
• Universal behavior of repulsive two-dimensional fermions in the vicinity of the quantum freezing point
• A simple variational method for calculating energy and quantum capacitance of an electron gas with screened interactions
• Superconductivity in Engineered Two-Dimensional Electron Gases
• Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid
• Wigner Crystallization in Two Dimensions: Evolution from Long- to Short-Ranged Forces
• The two-dimensional homogeneous electron gas with symmetric dual-gate screening: exchange-correlation functional and other ground-state properties

Cited by in corpus (4)

• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
• Spin-triplet paired Wigner crystal stabilized by quantum geometry
• Engineering Hubbard models with gated two-dimensional moiré systems
• Elementary Excitations, Melting Temperature, and Correlation Energy in Wigner Crystals