Fermions on half-quantum vortex

TL;DR

This paper analyzes the zero-energy fermion modes near vortices with fractional winding numbers, revealing a unique 'half-crossing' phenomenon linked to topological invariants in high-temperature superconductors.

Contribution

It introduces the concept of fractional winding number vortices affecting fermion spectra and discusses the resulting half-crossing phenomenon in the context of topological energy states.

Findings

Fractional winding numbers lead to fractional topological invariants.

Fermion spectra exhibit a 'half-crossing' near zero energy.

The phenomenon relates to fermion condensation concepts.

Abstract

The spectrum of the fermion zero modes in the vicinity of the vortex with fractional winding number is discussed. This is inspired by the observation of the 1/2 vortex in high-temperature superconductors (Kirtley, et al, Phys. Rev. Lett. 76 (1996) 1336). The fractional value of the winding number leads to the fractional value of the invariant, which describes the topology of the energy spectrum of fermions. This results in the phenomenon of the "half-crossing": the spectrum approaches zero but does not cross it, being captured at the zero energy level. The similarity with the phenomenon of the fermion condensation is discussed.