Possibility of an excitonic insulator at the semiconductor-semimetal transition

We calculate the critical temperature below which an excitonic insulator exists at the pressure-induced semiconductor-semimetal transition. Our approach is based on an effective-mass model for valence and conduction band electrons interacting via a statically screened Coulomb potential. Assuming pressure to control the energy gap, we derive, in the spirit of a crossover from a Bose-Einstein (BE) to a BCS condensate, a set of equations that determines, as a function of the energy gap (pressure), the chemical potentials for the two bands, the screening wave number, and the critical temperature. We (i) show that in leading order the chemical potentials are not affected by the exciton states, (ii) verify that on the strong-coupling (semiconductor) side the critical temperatures obtained from the linearized gap equation coincide with the transition temperatures for a BEC of noninteracting bosons, (iii) demonstrate that mass asymmetry strongly suppresses BCS-type pairing, (iv) investigate the composition of the environment of the excitonic insulator, and (v) discuss in the context of our theory recent experimental claims for exciton condensation in TmSe0.45Te0.55.