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

Superconductors in nano-sized shape are 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 $$T_c$$ becomes higher than that of a bulk superconductor. In the extremely dirty nano-sized superconductor, the critical temperature becomes much higher than that of a clean nano-sized superconductor. This is because a part of superconducting electrons concentrates in a localized state and has a high density of states. However, if the superconducting state remains localized below $$T_c$$ , resistivity may not be zero just below $$T_c$$ . Therefore we investigate how this localized state of superconductivity develops with decreasing temperature below $$T_c$$ . We show this localized state extends to whole superconductor just below $$T_c$$ .