Abstract
Local superconducting gap structure is studied as a function of nanoscale depth in electric-field-induced surface superconductivity such as in $\mathrm{SrT}\phantom{\rule{0.5pt}{0ex}}{\mathrm{iO}}_{3}$. 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.
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