Self-consistent interface properties of- and-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 nonlocal, corresponding to (Formula presented)- and (Formula presented)-wave superconductivity, respectively. Using this method we examine the properties of various (Formula presented) and (Formula presented) interfaces. In particular, we calculate the spatially varying density of states and order parameter for the following geometries: (i) (Formula presented)-wave superconductor to normal metal, (ii) (Formula presented)-wave superconductor to normal metal, (iii) (Formula presented)-wave superconductor to (Formula presented)-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 (Formula presented)-wave superconductors, the surface leads to mixing of different order-parameter symmetries near the interface and substantial local filling in of the gap. © 1998 The American Physical Society.