Effect of Surface Andreev Bound States on the Bean-Livingston Barrier in d-Wave Superconductors

TL;DR

This paper investigates how surface Andreev bound states in d-wave superconductors modify the Bean-Livingston vortex entry barrier, revealing significant temperature-dependent effects influenced by surface orientation.

Contribution

The authors derive a generalized London theory incorporating surface Andreev bound states, providing an analytical expression for the modified vortex entry barrier in d-wave superconductors.

Findings

First vortex entry field is significantly increased.

Depinning field near the surface is renormalized.

Effects depend on temperature and surface orientation.

Abstract

We study the influence of surface Andreev bound states in d-wave superconductors on the Bean-Livingston surface barrier for entry of a vortex line into a strongly type-II superconductor. Starting from Eilenberger theory we derive a generalization of London theory to incorporate the anomalous surface currents arising from the Andreev bound states. This allows us to find an analytical expression for the modification of the Bean-Livingston barrier in terms of a single parameter describing the influence of the Andreev bound states. We find that the field of first vortex entry is significantly enhanced. Also, the depinning field for vortices near the surface is renormalized. Both effects are temperature dependent and depend on the orientation of the surface relative to the d-wave gap function.