Dependences of local density of state on temperature, size, and shape in two-dimensional nano-structured superconductors

Abstract

In this paper, we investigate a local density of state (LDOS) in a two-dimensional nano-structured superconductor. We solve the Bogoliubov-de Gennes equations self-consistently with the two-dimensional finite element method. In the nano-structured superconductor, the LDOS as a function of energy has many discrete peaks. Discretization of the LDOS comes from discretization of energy levels due to the quantum confinement effect in the nano-structured system. When temperature increases, a width of a peak in the LDOS is spread to a large energy range and neighbor peaks are overlapped. On the other hand, for the fixed temperature, the behavior of the LDOS is different between nano-scaled rectangular and square systems. In the nano-scaled rectangular system, when only a length of a long side increases, a contribution of the quantum confinement effect from the long side is suppressed, while the contribution from a length of a short side remains large. Then, some peaks are left in the LDOS even when the length of the long side is very large. These peaks form a periodic structure and can be regarded as gaps in a multi gap structure due to the quantum confinement effect. On the other hand, energy levels in the square system tend to arrange equally. Then, in the square system, peaks in the LDOS which exist in the rectangular system are small. Also, the period between peaks in the LDOS in the square system is smaller than that in the rectangular system.