Vortex core near planar defects in a clean layered superconductor

TL;DR

This paper studies how planar defects in a layered superconductor affect vortex core states, revealing that even highly transparent defects open a minigap and influence localized subgap states, with effects depending on defect configuration and vortex position.

Contribution

It provides a detailed analysis of vortex core quasiparticle states near planar defects, highlighting the formation and behavior of minigaps and subgap states in various defect configurations.

Findings

A highly transparent defect opens a minigap at the Fermi energy.

The minigap magnitude depends on defect transparency and vortex position.

Complex defect arrangements exhibit strong commensurability effects on the minigap.

Abstract

We investigate the structure of quasiparticle states localized in a core of an Abrikosov vortex in a clean layered superconductor in the presence of planar defects. It is shown that even a highly transparent defect opens a minigap at the Fermi energy. Its magnitude, $E_g\sim\Delta\sqrt{R}$, exceeds the mean level spacing for the chiral branch, $\omega_0\sim\Delta^2/E_F$, already for very small values of the reflection coefficient off the defect, $R\ll1$ ($\Delta$ is the bulk gap). For $R\gtrsim\sqrt{\Delta/E_F}$, formation of the minigap is accompanied by the appearance of subgap states localized along the defect, in accordance with [A. V. Samokhvalov \emph{et al.}, Phys.\ Rev.\ B \textbf{102}, 174501 (2020)]. The minigap takes its maximal value for the vortex located right at the defect, decreases with increasing the distance $b$ from the defect, and closes when $k_Fb\sim (\Delta/\omega_0)\sqrt{R}$. We also study various configurations of several planar defects (few crossing planes, stars, periodic structures). Although the minigap remains, a strong commensurability effect is observed. For two crossing planar defects, the magnitude of the minigap strongly depends on how close the intersection angle is to a rational fraction of $\pi$.