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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-Ovchinikov 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 intra-gap resonance quasiparticle states, which are localized in the nodal region.