Local superconducting gap structure is studied as a function of nanoscale depth in electric-field-induced surface superconductivity such as in $\mathrm{SrT}{\mathrm{iO}}_3$. 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.

• Received 9 November 2012

DOI:https://doi.org/10.1103/PhysRevB.87.014505