Theory of Coulomb driven nematicity in a multi-valley two-dimensional electron gas

TL;DR

This paper investigates how Coulomb interactions induce nematic phases in a multi-valley 2DEG, revealing a first-order transition to a valley-polarized nematic state consistent with experiments.

Contribution

It demonstrates that correlation effects favor valley polarization and induce a nematic phase transition, providing a theoretical explanation aligned with experimental observations.

Findings

Correlation effects enhance valley susceptibility over spin susceptibility.

A first-order transition from unpolarized to valley-polarized nematic phase is predicted.

Results qualitatively agree with experiments on AlAs heterostructures.

Abstract

The properties of a two-dimensional electron gas (2DEG) in a semiconductor host with two valleys related by an underlying $C_4$ rotational symmetry are studied using Hartree-Fock (HF) and various other many-body approaches. A familiar artifact of the HF approach is a degeneracy between the valley polarized - ``Ising nematic'' - and spin polarized - ferromagnetic - phases, which is inconsistent with recent variational Monte Carlo (VMC) results. Correlation effects, computed either within the random phase approximation (RPA) or the T-matrix approximation, enhance the valley susceptibility relative to the spin susceptibility. Extrapolating the results to finite interaction strength, we find a direct first-order transition from a symmetry-unbroken state to a spin unpolarized Ising nematic fluid with full valley polarization, in qualitative agreement with VMC. The RPA results are also reminiscent of experiments on the corresponding 2DEG in AlAs heterostructures.