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We propose an efficient numerical algorithm to solve Bogoliubov de Gennesequations self-consistently for inhomogeneous superconducting systems with areformulated polynomial expansion scheme. This proposed method is applied totypical issues such as a vortex under randomly distributed impurities and anormal conducting junction sandwiched between superconductors. With varioustechnical remarks, we show that its efficiency becomes remarkable inlarge-scale parallel performance.

Efficient Numerical Self-consistent Mean-field Approach for Fermionic Many-body Systems by Polynomial Expansion on Spectral Density