Chemical potential and compressibility of quantum Hall bilayer excitons

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.