Three-dimensional simulation of quasi-particle structures in nano-scaled superconductors

We have developed numerical simulation method for quasi-particle structures in the three-dimensional nano-sized superconductors, using the three-dimensional finite element method and the Bogoliubov-de Gennes equation. Using this method, we analyzed the superconducting state in the nano-sized cubic superconductors. We found the spatial oscillations of order parameter because of the confinement of superconducting electrons, and also we found the quasi-particle bound states at the corners of the cubic superconductors because of suppression of superconductivity at the corners.

Research highlights
► We develop a numerical method for nano-sized superconductors.
► We use finite element method and Bogoliubov-de Gennes equation.
► We examine quasi-particle structures in cubic superconductor.
► Oscillation of order parameter appears because of quantum size effect.
► Bound states appear at corners because of spatial distribution of order parameter.