Roles of paramagnetic and diamagnetic pair-breaking effects in superconductivity in electric-field-induced surface metallic state are studied by Bogoliubov-de Gennes equation, when magnetic fields are applied parallel to the surface. The multi-gap states of sub-bands are related to the depth dependence and the magnetic field dependence of superconductivity. In the Fermi-energy density of states and the spin density, sub-band contributions successively appear from higher-level sub-bands with increasing magnetic fields. The characteristic magnetic field dependence may be a key feature to identify the multi-gap structure of the surface superconductivity.
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