Chebyshev-BdG: an efficient numerical approach to inhomogeneous superconductivity

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.

References in corpus (14)

• The Kernel Polynomial Method
• Self-consistent electronic structure of a $d_{x^2-y^2}$ and a $d_{x^2-y^2}+i{d}_{xy}$ vortex
• Low-lying Quasiparticle Excitations around a Vortex Core in Quantum Limit
• Dopant-modulated pair interaction in cuprate superconductors
• Proximity effects at ferromagnet-superconductor interfaces
• Self-consistent solution for proximity effect and Josephson current in ballistic graphene SNS Josephson junctions
• Proximity effect, quasiparticle transport, and local magnetic moment in ferromagnet-d-wave superconductor junctions
• Proximity effect in clean strong/weak/strong superconducting tri-layers
• Self-consistent interface properties of d and s-wave superconductors
• Chebyshev approach to quantum systems coupled to a bath
• Local density of states of a d-wave superconductor with inhomogeneous antiferromagnetic correlations
• Single-Particle Density of States of a Superconductor with a Spatially Varying Gap and Phase Fluctuations
• S-wave superconductivity near a surface
• Effect of CuO chains on the local density of states in the vortex phase of YBa_2Cu_3O_7

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