Variational Monte-Carlo calculation of the nematic state of the two-dimensional electron gas in a magnetic field

TL;DR

This study employs variational Monte Carlo methods with a Jastrow-Slater wave function to evaluate the energetic favorability of the nematic phase in a two-dimensional electron gas under magnetic fields, comparing it with stripe and isotropic states.

Contribution

It introduces a Monte Carlo approach with an elliptical Fermi sea to analyze the nematic state, confirming previous results and providing more accurate energy bounds.

Findings

Nematic state is energetically favored over stripe-ordered phases in certain conditions.

The critical layer thickness for nematic stability closely matches experimental values.

Monte Carlo results support earlier hypernetted chain approximation conclusions.

Abstract

We use a Jastrow-Slater wave function with an elliptical Fermi sea to describe the nematic state of the two-dimensional electron gas in a magnetic field and the Monte Carlo method to calculate a variational energy upper bound. These energy upper bounds are compared with other upper bounds describing stripe-ordered ground states which are obtained from optimized Hartree-Fock calculations and with those which correspond to an isotropic ground state. Our findings support the conclusions drawn in our previous study where the Fermi-hypernetted chain approximation was used instead of the Monte Carlo method. Namely, the nematic state becomes energetically favorable relative to the stripe-ordered Wigner crystal phase for the second excited Landau level and below a critical value of the layer ``thickness'' parameter which is very close to its value in the actual materials.