Emergence of liquid crystalline order in the lowest Landau level of a quantum Hall system with internal anisotropy

Orion Ciftja

doi:10.1063/1.5004988

Abstract

It has now become evident that interplay between internal anisotropy parameters (such as electron mass anisotropy and/or anisotropic coupling of electrons to the substrate) and electron-electron correlation effects can create a rich variety of possibilities especially in quantum Hall systems. The electron mass anisotropy or material substrate effects (for example, the piezoelectric effect in GaAs) can lead to an effective anisotropic interaction potential between electrons. For lack of knowledge of realistic ab-initio potentials that may describe such effects, we adopt a phenomenological approach and assume that an anisotropic Coulomb interaction potential mimics the internal anisotropy of the system. In this work we investigate the emergence of liquid crystalline order at filling factor ν = 1/6 of the lowest Landau level, a state very close to the point where a transition from the liquid to the Wigner solid happens. We consider small finite systems of electrons interacting with an anisotropic Coulomb interaction potential and study the energy stability of an anisotropic liquid crystalline state relative to its isotropic Fermi-liquid counterpart. Quantum Monte Carlo simulation results in disk geometry show stabilization of liquid crystalline order driven by an anisotropic Coulomb interaction potential at all values of the interaction anisotropy parameter studied.

Highlights

A two-dimensional electron system (2DES) in a perpendicular magnetic field has been a fertile ground for discoveries of novel quantum phases of electrons such as incompressible quantum Hall liquid states (Laughlin states) at filling factors ν = 1/3 and 1/5 of the lowest Landau level (LLL),[1] compressible Fermi liquid states at even-denominator filling factors ν = 1/2, 1/4 and 1/6,2–5 Wigner solid states for very small filling factors,[6,7,8] etc
This means that in a realistic quantum system with some form of internal anisotropy the electrons may stabilize into novel anisotropic phases of matter because of an effective anisotropic interaction potential between themselves
The main objective of the calculations is to verify whether the system undergoes an anisotropic phase transition in presence of relatively small values of the interaction anisotropy parameter, γ, or whether the original isotropic phase is robust enough to survive the breakdown of rotational invariance

Summary

Introduction

This means that in a realistic quantum system with some form of internal anisotropy (in which the electrons have an anisotropic band mass, as the case of AlAs or in isotropic systems like GaAs in presence of piezoelectric effect and/or a tilted magnetic field) the electrons may stabilize into novel anisotropic phases of matter because of an effective anisotropic interaction potential between themselves. This anisotropic interaction potential may drive transitions from “ordinary” isotropic Hall liquids to other anisotropic phases.[20,21,22,23,24,25,26]

Results

Conclusion