Andreev bound states in rounded corners of d-wave superconductors

TL;DR

This paper investigates how the geometry of boundaries, specifically rounded corners in wedge-shaped boundaries, affects the presence of zero-energy Andreev bound states in d-wave superconductors, revealing geometry-dependent spectral features.

Contribution

It provides a detailed analysis of the influence of boundary shape and orientation on Andreev bound states in d-wave superconductors, highlighting the role of rounded corners.

Findings

Zero-energy bound states depend on boundary orientation and shape.

Strong bound states occur when the wedge bisecting line aligns with the nodal direction.

Boundary geometry critically influences quasiparticle spectral weight.

Abstract

Andreev bound states at boundaries of d-wave superconductors are strongly influenced by the boundary geometry itself. In this work, the zero-energy spectral weight of the local quasiparticle density of states is presented for the case of wedge-shaped boundaries with rounded corners. Generally, both orientation of the d-wave and the specific local reflection properties of the rounded wedges determine, whether Andreev bound states exist or not. For the bisecting line of the wedge being parallel to the nodal direction of the d-wave gap function, strong zero-energy Andreev bound states are expected at the round part of the boundary.