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# Chemical potential and compressibility of quantum Hall bilayer excitons

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### 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.

### Author and article information

###### Journal
2015-11-10
2016-03-02
10.1103/PhysRevB.93.085436
1511.03287