Temperature-carrier-concentration phase diagram of a two-dimensional doped d -wave superconductor

The finite-temperature properties of a two-dimensional d -wave superconductor with the Lifshitz disorder, introduced by dopants, are studied. The doping dependence of the mean-field critical temperature T c MF and of the superconducting critical temperature T c defined by the Berezinskii-Kosterlitz-Thouless transition are calculated at different values of coupling, dopant potential, and intermediate boson energy. It is shown that superconductivity tends to disappear with increasing doping when the dopant potential is large enough, though the metallic properties of the system are preserved.