# Quasiparticle Bound States around Fractional Vortices in s-wave Superconductor

## TL;DR

This paper investigates the local density of states around fractional vortices in s-wave superconductors, revealing unique bound state patterns that could be experimentally observed and are analogous to Josephson junctions.

## Contribution

It provides the first detailed theoretical analysis of LDOS patterns around fractional vortices in s-wave superconductors using quasiclassical theory.

## Key findings

- Distinct bow-tie-shaped bound states at high energy regions.
- LDOS patterns differ significantly from those around conventional vortices.
- Fractional vortices exhibit similarities to Josephson junctions.

## Abstract

Since the experimental formation of a vortex with a fractional quantized magnetic flux in a thin superconducting $s$-wave bi-layer was recently reported, we calculate the local density of states (LDOS) around two half quantum vortices in a $s$-wave superconductor on the basis of the quasiclassical Eilenberger theory to investigate the effect of the phase discontinuity. We show that the LDOS pattern around fractional vortices is qualitatively different from that around conventional vortex. We find that the novel bow-tie-shaped bound states appear in the high energy region, which can be an evidence for the fractional vortices through scanning tunneling microscopy/spectroscopy. We also show that the system with $n$ fractional vortices with the vorticity $1/n$ has a similarity to the Josephson junctions.