Self-consistent interface properties of d and s-wave superconductors

TL;DR

This paper introduces a self-consistent method using the recursion technique to analyze interface properties of s-wave and d-wave superconductors, revealing complex local density of states and order parameter behaviors at various interfaces.

Contribution

A novel recursive approach for self-consistent solutions of the Bogoliubov de Gennes equations applicable to both local and non-local pairing interactions in superconductors.

Findings

Density of states shows complex structures at interfaces.

Surface effects cause mixing of order parameter symmetries.

Substantial local filling of the gap in d-wave superconductors.

Abstract

We develop a method to solve the Bogoliubov de Gennes equation for superconductors self-consistently, using the recursion method. The method allows the pairing interaction to be either local or non-local corresponding to s and d-wave superconductivity, respectively. Using this method we examine the properties of various S-N and S-S interfaces. In particular we calculate the spatially varying density of states and order parameter for the following geometries (i) s-wave superconductor to normal metal, (ii) d-wave superconductor to normal metal, (iii) d-wave superconductor to s-wave superconductor. We show that the density of states at the interface has a complex structure including the effects of normal surface Friedel oscillations, the spatially varying gap and Andeev states within the gap, and the subtle effects associated with the interplay of the gap and the normal van Hove peaks in the density of states. In the case of bulk d-wave superconductors the surface leads to mixing of different order parameter symmetries near the interface and substantial local filling in of the gap.