Chebyshev-BdG: an efficient numerical approach to inhomogeneous superconductivity

TL;DR

This paper introduces Chebyshev-BdG, a highly efficient numerical method leveraging the kernel polynomial approach to study inhomogeneous superconductivity, capable of handling complex geometries and large systems.

Contribution

The paper presents a novel Chebyshev polynomial-based numerical method that efficiently computes Green's functions for inhomogeneous superconductors, surpassing previous size limitations.

Findings

Enables simulation of large, complex superconducting systems

Incorporates various types of translational symmetry breaking

Applicable to other inhomogeneous mean-field theories

Abstract

We propose a highly efficient numerical method to describe inhomogeneous superconductivity by using the kernel polynomial method in order to calculate the Green's functions of a superconductor. Broken translational invariance of any type (impurities, surfaces or magnetic fields) can be easily incorporated. We show that limitations due to system size can be easily circumvented and therefore this method opens the way for the study of scenarios and/or geometries that were unaccessible before. The proposed method is highly efficient and amenable to large scale parallel computation. Although we only use it in the context of superconductivity, it is applicable to other inhomogeneous mean-field theories.