From semiconductors to superconductors: a simple model for pseudogaps

We consider a two-dimensional semiconductor with a local attraction among t he carriers. We study the ground state of this system as a function of the semiconductor gap. We find a direct transition from a superconducting to an insulating phase for no doping at a critical value; the single particle ex citations being always gapped. For finite doping we find a smooth crossover . We calculate the critical temperature due to both the particle excitation s and the Berezinkii-Kosterlitz-Thouless transition.