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

TL;DR

This study uses quantum Monte Carlo simulations to explore the phase diagram of a two-dimensional electron gas, identifying critical gate distances for Wigner crystallization and revealing complex phase transitions including re-entrant behavior and potential ferromagnetic states.

Contribution

It introduces a detailed phase diagram analysis of the 2D electron gas with dual gates, highlighting the critical gate distance for Wigner crystal disappearance and comparing quantum Monte Carlo with approximate methods.

Findings

Identified critical gate distance for Wigner crystal phase transition.

Observed re-entrant transition from crystal to liquid at low density.

Provided evidence for a ferromagnetic liquid state at certain conditions.

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.