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PHYS. REV. LETT.

We study excitonic condensation in an electron-hole bilayer system with unequal layer densities at zero temperature. Using mean-field theory we solve the Bardeen-Cooper-Schrieffer (BCS) gap equations numerically and investigate the effects of intralayer interactions. The electron-hole system evolves from BCS in the weak coupling limit to Bose-Einstein condensation (BEC) in the strong coupling limit. We analyze the stability of the Sarma phase with k,-k pairing by calculating the superfluid mass density and also by checking the compressibility matrix. We find that with bare Coulomb interactions the superfluid density is always positive in the Sarma phase, due to a peculiar momentum structure of the gap function originating from the singular behavior of the Coulomb potential at zero momentum and the presence of a sharp Fermi surface. Introducing a simple model for screening, we find that the superfluid density becomes negative in some regions of the phase diagram, corresponding to an instability toward a Fulde-Ferrel-Larkin-Ovchinnikov-type superfluid phase. Thus, intralayer interaction and screening together can lead to a rich phase diagram in the BCS-BEC crossover regime in electron-hole bilayer systems.

The nonlinear response of an arbitrary electronic system to a time-dependent perturbation is treated within the density-functional formalism. Expressions for quadratic and cubic responses for a system of independent electrons are obtained in a form suitable for numerical calculations. The frequency dependence of the linear and cubic electric susceptibilities of rare-gas atoms are computed and compared with experiment.