Exciton condensate modulation in electron-hole bilayers: A real-space visualization

We study the texture of the exciton condensate at low temperatures in an independently gated electron-hole bilayer system. A model Hamiltonian is solved in real space within a mean-field approximation. It is found that, with increased electron-hole density polarization, the system experiences phase transformations from the zero center-of-mass momentum superfluid state, through one- and two-dimensional exciton pair modulated states, into the normal state. At weak density polarization, the modulating state resembles the Larkin-Ovchinnikov state in superconductors in the presence of an exchange field in the weak-coupling BCS limit and becomes stripe-like in the strong-coupling BEC limit. In the one-dimensional modulated phase, the density of states exhibits low-energy intragap resonance quasiparticle states, which are localized in the nodal region.