Deformation of the Fermi surface of a spinless two-dimensional electron gas in presence of an anisotropic Coulomb interaction potential

Orion Ciftja

doi:10.1038/s41598-021-82564-y

Abstract

We consider the stability of the circular Fermi surface of a two-dimensional electron gas system against an elliptical deformation induced by an anisotropic Coulomb interaction potential. We use the jellium approximation for the neutralizing background and treat the electrons as fully spin-polarized (spinless) particles with a constant isotropic (effective) mass. The anisotropic Coulomb interaction potential considered in this work is inspired from studies of two-dimensional electron gas systems in the quantum Hall regime. We use a Hartree–Fock procedure to obtain analytical results for two special Fermi liquid quantum electronic phases. The first one corresponds to a system with circular Fermi surface while the second one corresponds to a liquid anisotropic phase with a specific elliptical deformation of the Fermi surface that gives rise to the lowest possible potential energy of the system. The results obtained suggest that, for the most general situations, neither of these two Fermi liquid phases represent the lowest energy state of the system within the framework of the family of states considered in this work. The lowest energy phase is one with an optimal elliptical deformation whose specific value is determined by a complex interplay of many factors including the density of the system.

Highlights

We consider the stability of the circular Fermi surface of a two-dimensional electron gas system against an elliptical deformation induced by an anisotropic Coulomb interaction potential
While an anisotropic m ass[11] is a trivial source that may cause a deformation of the Fermi surface, in this work we assume that the mass of the electrons is constant and, our principal concern is to study the effects of a specific anisotropic interaction potential in the overall stability of the system
We focus our attention on a 2DEG model in the jellium approximation and consider the possibility of an elliptical deformation of the Fermi surface in 2D reciprocal space induced by an internal anisotropy of the interaction potential

Summary

Introduction

We consider the stability of the circular Fermi surface of a two-dimensional electron gas system against an elliptical deformation induced by an anisotropic Coulomb interaction potential. We use the jellium approximation for the neutralizing background and treat the electrons as fully spin-polarized (spinless) particles with a constant isotropic (effective) mass. The general expectation is that the Fermi surface of an electron gas should be circular or spherical, respectively, in 2D or 3D if the electrons have a constant isotropic (effective) mass and they do not interact with each other. We focus our attention on a 2DEG model in the jellium approximation and consider the possibility of an elliptical deformation of the Fermi surface in 2D reciprocal space induced by an internal anisotropy of the interaction potential. We assume a fully spin-polarized (spinless) system of electrons described by a family of wave functions written as anti-symmetrized Slater determinant wave functions of plane waves[12] with quantum states that belong to an elliptical domain in 2D reciprocal space

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