# Enhancement of penetration field in vortex nanocrystals due to Andreev bound states

## TL;DR

This study demonstrates that surface Andreev bound states in d-wave superconductors increase the vortex penetration field in nanocrystals, especially when edges are aligned with nodal directions, revealing surface effects on vortex dynamics.

## Contribution

It provides experimental evidence that surface Andreev bound states enhance the vortex penetration field in vortex nanocrystals with edges along nodal directions.

## Key findings

- Penetration field is ~72% higher in nodal direction edges at low temperatures.
- Surface Andreev bound states increase the Bean-Livingston barrier.
- Vortex nanocrystals with high surface-to-volume ratio reveal surface effects.

## Abstract

We study the penetration field $H_{\rm P}$ for vortex nanocrystals nucleated in micron-sized samples with edges aligned along the nodal and anti-nodal directions of the d-wave superconducting parameter of Bi$_2$Sr$_2$CaCu$_2$O$_{8 - \delta}$. Here we present evidence that the $H_{\rm P}$ for nanocrystals nucleated in samples with edges parallel to the nodal direction is larger than for the antinodal case, $\sim 72$\,\% at low temperatures. This finding supports the theoretical proposal that surface Andreev bound states appearing in a sample with edges parallel to the nodal direction would produce an anomalous Meissner current that increases the Bean-Livingston barrier for vortex penetration.This has been detected thanks to the nucleation of vortex nanocrystals with a significant surface-to-volume ratio.