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 Tc 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 Tc , resistivity may not be zero just below Tc . Therefore we investigate how this localized state of superconductivity develops with decreasing temperature below Tc . We show this localized state extends to whole superconductor just below Tc .