Nematic metal in a multi-valley electron gas: Variational Monte Carlo analysis and application to AlAs

TL;DR

This paper uses variational Monte Carlo to study a two-valley electron gas with anisotropic masses, revealing a valley-polarized metallic state relevant to AlAs quantum wells and identifying a transition at a specific density.

Contribution

It introduces a minimal model with $C_4$ symmetry and applies variational Monte Carlo to uncover a valley-polarized metallic phase in a two-valley electron gas.

Findings

Discovery of a valley-polarized metallic phase at intermediate densities.

Identification of a transition from anisotropic to valley-polarized metal at $r_s \\approx 12$.

Relevance to the nematic state observed in AlAs quantum wells.

Abstract

The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with $C_4$ (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized ground-state. Our results are of direct relevance to the recently discovered ``nematic'' state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, $m_x/m_y\approx 5.2$, we obtain a transition from an anisotropic metal to a valley-polarized metal at $r_s \approx 12$ (where $r_s$ is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy.