Paramagnetic and diamagnetic pair-breaking effect in electric-field-induced surface superconductivity under parallel magnetic fields

Electric-field-induced surface superconductivity is studied by Bogoliubov-de Gennes equation under magnetic fields parallel to the surface. We estimate the pair-breaking effects by the paramagnetic Zeeman shift and by diamagnetic screening current. We find that the depth dependences of pair potential, screening current, spin current, and paramagnetic moment under the magnetic fields reflect the multi-gap superconductivity in the sub-band structure.