Topological exciton condensate of imbalanced electrons and holes

I study the effects of particle-hole imbalance on the exciton superfluid formed in a topological insulator thin-film and obtain the mean-field phase diagram. At finite imbalance a spatially modulated condensate is formed, akin to the Fulde-Ferrel-Larkin-Ovchinikov state in a superconductor, which preempts a first-order transition from the uniform condensate to the normal state at low temperatures. The imbalance can be tuned by changing the chemical potential at the two surfaces separately or, alternatively, by an asymmetric application of Zeeman fields at constant chemical potential. A vortex in the condensate carries a precisely fractional charge half of that of an electron. Possible experimental signatures for realistic parameters are discussed.