Temperature-doping phase diagram of layered superconductors

The superconducting properties of a layered system are analyzed for the cases of zero and nonzero angular momenta of the pairs. The effective thermodynamic potential for the quasi-two-dimensional XY model for the gradients of the phase of the order parameter is derived from the microscopic superconducting Hamiltonian. The dependence of the superconducting critical temperature T-c on doping, or carrier density, is studied at different values of coupling and interlayer hopping. It is shown that the critical temperature T-c of the layered system can be lower than the critical temperature of the two-dimensional Berezinskii-Kosterlitz-Thouless transition T-BKT at some values of the model parameters, contrary to the case in which the parameters of the XY model do not depend on the microscopic Hamiltonian parameters.