Theory of Superconductivity in Polar Semiconductors and Its Application to N-Type Semiconducting SrTiO₃

By solving the gap equation numtaerically from the first principles, we have investigated the mechanism of superconductivity in n -type seumiconducting SrTiO 3 . The observed transition temperature as a function of the carrier density and the applied stress is reproduced quite well, when we take account of the plasmon and the polar optic phonon which relates to the stress-induced ferroelectric transition. In the calculation, the conduction band of SrTiO 3 is assumed to be the single-valley model proposed by Mattheiss and all the physical quantities such as the effective mass, the dielectric constant and the phonon dispersion relation are taken to be the values measured by experiments, so that there are no adjustable parameters in the theory. The effect of other phonons like the acoustic one is also evaluated and found to be small.