  We investigate the possibility of excitonic superfluidity in electron-hole
bilayers. We calculate the phase diagram of the system for the whole range of
electron-hole density imbalance and for different degrees of electrostatic
screening, using mean-field theory and a Ginzburg-Landau expansion. We are able
to resolve differences on previous work in the literature which concentrated on
restricted regions of the parameter space. We also give detailed descriptions
of the pairing wavefunction in the Fulde-Ferrell-Larkin-Ovchinnikov paired
state. The Ginzburg-Landau treatment allows us to investigate the energy scales
involved in the pairing state and discuss the possible spontaneous breaking of
two-dimensional translation symmetry in the ground state.
