Local density of states at polygonal boundaries of d-wave superconductors

TL;DR

This paper investigates how boundary geometry, including wedge and polygonal shapes, affects the zero-energy local density of states in d-wave superconductors, revealing oscillations and vortex interactions.

Contribution

It provides new insights into the impact of complex boundary geometries and vortex proximity on the local density of states in d-wave superconductors.

Findings

Zero-energy density of states oscillates with wedge opening angle.

Boundary roughness influences the local density of states.

Vortex proximity alters the boundary state characteristics.

Abstract

Besides the well-known existence of Andreev bound states, the zero-energy local density of states at the boundary of a d-wave superconductor strongly depends on the boundary geometry itself. In this work, we examine the influence of both a simple wedge-shaped boundary geometry and a more complicated polygonal or faceted boundary structure on the local density of states. For a wedge-shaped boundary geometry, we find oscillations of the zero-energy density of states in the corner of the wedge, depending on the opening angle of the wedge. Furthermore, we study the influence of a single Abrikosov vortex situated near a boundary, which is of either macroscopic or microscopic roughness.