Chemical potential and compressibility of quantum Hall bilayer excitons

TL;DR

This paper investigates the chemical potential and compressibility of quantum Hall bilayer excitons, revealing nonmonotonic behaviors and a phase transition between superfluid and Wigner crystal phases as interlayer distance varies.

Contribution

It provides a detailed analysis of exciton interactions in quantum Hall bilayers, introducing new insights into phase transitions and nonmonotonic properties related to interlayer separation.

Findings

Chemical potential and capacitance show nonmonotonic dependence on layer separation.

A phase transition from superfluid to Wigner crystal occurs at a specific interlayer distance.

Results are validated through analytic and numerical methods.

Abstract

This paper considers a system of two parallel quantum Hall layers with total filling factor $0$ or $1$. When the distance between the layers is small enough, electrons and holes in opposite layers form inter-layer excitons, which have a finite effective mass and interact via a dipole-dipole potential. Results are presented for the chemical potential $\mu$ of the resulting bosonic system as a function of the exciton concentration $n$ and the interlayer separation $d$. Both $\mu$ and the interlayer capacitance have an unusual nonmonotonic dependence on $d$, owing to the interplay between an increasing dipole moment and an increasing effective mass with increasing $d$. A phase transition between superfluid and Wigner crystal phases is shown to occur at $d \propto n^{-1/10}$. Results are derived first via simple intuitive arguments, and then verified with more careful analytic derivations and numeric calculations.