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This paper considers a system of two parallel quantum Hall layers with totalfilling factor $0$ or $1$. When the distance between the layers is smallenough, electrons and holes in opposite layers form inter-layer excitons, whichhave a finite effective mass and interact via a dipole-dipole potential.Results are presented for the chemical potential $\mu$ of the resulting bosonicsystem as a function of the exciton concentration $n$ and the interlayerseparation $d$. Both $\mu$ and the interlayer capacitance have an unusualnonmonotonic dependence on $d$, owing to the interplay between an increasingdipole moment and an increasing effective mass with increasing $d$. A phasetransition 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 numericcalculations.

Chemical potential and compressibility of quantum Hall bilayer excitons