The behaviour of classical superconductors is well described by the BCS theory which is a mean-field variational approach with electrons forming pairs and causing a gap in the energy spectrum of single electrons. High temperature superconductors as copper oxides have many features that are not understood in the framework of BCS theory. One of the most important problems is the presence of a region in the normal regime above the critical temperature Tc and below a temperature T* where observable quantities deviate from the free electron gas behaviour. This region is called pseudogap region because it contains effects similar to superconductivity like a partial suppression of electronic density of states. In the underdoped regime especially, the averaged amplitude of the pairing field is of the order of the zero temperature gap up to room temperature. Above some crossover temperature T_phi larger than the critical temperature Tc, the pseudogap region is mainly determined by the amplitude whereas phase fluctuations are only important near Tc up to T_phi. Figure To is the mean-field pairing temperature.
Vo is the phase stiffness and is proportionnal to the charge carrier density.
T_phi is the temperature where correlations disappear.
The hatched region is where the pseudogap starts, i.e. where T* is located. Note the agreement with To.
Inset: Eg is the energy scale of the pseudogap, here defined as the average pairing amplitude <|psi|> at 200K. | 
