On the pseudogap phase in high-T_c superconductors

We describe the approach of the superconducting state as a sequence of cross-over phenomena. As the temperature is decreased, uncorrelated pairing of the electrons leads to the opening of a pseudogap at T_F^*. Upon further lowering the temperature those electron pairs acquire well behaved itinerant features at T_B^*, leading to partial Meissner screening and Drude type behavior of the optical conductivity. Further decrease of the temperature leads to their condensation and superconductivity at T_c. The analysis is done on the basis of the Boson-Fermion model in the cross-over regime between 2D and 3D.