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Multiband superconductivity due to the electron - LO-phonon interaction in strontium titanate and on a SrTiO3/LaAlO3 interface

In strontium titanate, the Froehlich electron - LO-phonon interaction dominates the electron response and can also provide superconductivity. Because of high LO-phonon frequencies in SrTiO3, the superconducting system is non-adiabatic. We demonstrate that the dielectric function approach is an adequate theoretical method for superconductivity in SrTiO3 and on the SrTiO3-LaAlO3 interface. The critical temperatures are calculated using realistic material parameters. The obtained critical temperatures are in line with experimental data both for bulk and interface superconductivity. The present method explains the observed multi-dome shape of the critical temperature in SrTiO3 as a function of the electron concentration due to multiband superconductivity.