Exciton Bose condensation: the ground state of an electron-hole gas. 2. Spin states, screening and band structure effects

We first generalize the approach of the previous paper by including spin degrees of freedom. We classify the various spin states and we discuss the effect of interband exchange interactions. We then introduce screening, in the framework of a generalized RPA which incorporates Bose condensation of bound electron-hole pairs. We discuss in detail the low density limit: screening corrections do not change the sign of the compressibility, which remains positive, in contrast to previous estimates. We show that such RPA corrections reduce to an approximate form of the Van der Waals attraction between excitons. Viewing this RPA approach as an interpolation procedure at intermediate densities, we propose several interpolation schemes that should account for the Mott transition, and we give some preliminary very rough numerical estimates. Finally, we discuss the effect of band degeneracy on the ground state: different degeneracies in the two bands should lead to a normal plasma at high density while at low densities bound excitons 'Bose condense'', with a breakdown of their internal symmetry; we expect a first order transition with a liquid-gas phase separation