An overview of the phase diagram of cuprate superconductors is presented, focusing on the properties of the metallic state as a function of doping and temperature. The main features of the pseudogap state observed in cuprates at low doping are reported.
The various theoretical possibilities to explain the pseudogap phenomena in cuprates are summarized.
The crossover from BCS superconductivity (high doping) to Bose-Einstein condensation of local pairs (low doping) is a possible key to understand the complex phase diagram of cuprates and in particular in this view the pseudogap opening can be associated to the presence of pair fluctuations above Tc which couple with fermions.
A simple 3D attractive model is introduced to evaluate the selfenergy, the spectral function and the particle-particle propagator and to follow their evolution from weak to strong coupling.
A systematic comparison of theoretical results with experiments and ideas for further developments are discussed.
References and information on high-Tc superconductivity and BCS to BE crossover can be found in the web site http://www.htcs.org.