Chemical potential and compressibility of quantum Hall bilayer excitons

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 interlayer excitons, which have a finite effective mass and interact via a dipole-dipole potential. I present results for the chemical potential μ of the resulting bosonic system as a function of the exciton concentration n and the interlayer separation d. Both μ 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 ∝ n[superscript −1/10]. Results are derived first via simple intuitive arguments, and then verified with more careful analytic derivations and numeric calculations.