Temperature Dependence of Superconducting State in a Nano-sized Dirty superconductor

Abstract Superconductor in nano-sized shape is investigated. Superconductor and also electrons which form superconductivity have quantum nature. This means when size of superconductor is small, there appear quantum effects.The critical temperature becomes higher than that of a bulk superconductor.In the extremely dirty nano-sized superconductor, the critical temperature becomes much higherthan that of a clean nano-sized superconductor. This is because a part of superconducting electrons concentrates in a localized state and has ahigh density of states.We show how this localized state of superconducting electrons developswith decreasing temperature just below the critical temperature.