Multiple-gap structure in electric-field-induced surface superconductivity

Local superconducting gap structure is studied as a function of nanoscale depth in electric-field-induced surface superconductivity such as in SrTiO ₃. We examine solutions of the Bogoliubov-de Gennes equation in two limiting confinement potential cases of an electric field with and without screening effects. As unique properties different from bulk superconductivity, there appear in-gap states even for isotropic s-wave pairing, due to the multiple-gap structure of sub-band-dependent surface superconductivity. These determine the depth dependence of local superconductivity.