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 SrTiO3. We examine solutions of Bogoliubov-de Gennes equation in two limiting confinement potential cases of 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 multiple gap structure of sub-band dependent surface superconductivity. These determine the depth-dependence of local superconductivity.