The importance of self-consistency in determining interface properties of S-I-N and D-I-N structures

TL;DR

This paper presents a self-consistent method using the recursion approach to solve the Bogoliubov de Gennes equations for superconductor interfaces, revealing the critical role of self-consistency especially in d-wave superconductors.

Contribution

The paper introduces a recursive self-consistent method for solving Bogoliubov de Gennes equations applicable to both s-wave and d-wave superconductors at interfaces.

Findings

Changing barrier strength has little effect on s-wave local density of states.

D-wave interfaces show significant changes in local density of states with barrier modifications.

Self-consistent calculations are crucial for accurate conductance predictions 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 $S-I-N$ and $D-I-N$ interfaces. In particular we self-consistently calculate the spatially varying density of states and the superconducting order parameter. We see that changing the strength of the insulating barrier, at the interface, does not, in the case of an $s$--wave superconductor, dramatically, change the low energy local density of states, in the superconducting region near the interface. This is in stark contrast to what we see in the case of a $D-I-N$ interface where the local particle density of states is changed dramatically. Hence we deduce that in calculating such properties as the conductance of $S-I-N$ and $D-I-N$ structures it is far more important to carry out a self-consistent calculations in the $d$--wave case.