Fermions at a half-quantum vortex

Abstract

The spectrum of the fermion zero modes in the vicinity of a vortex with fractional winding number is discussed. This is inspired by the observation of the 1/2-vortex in high-temperature superconductors made by [J.R. Kirtley, C.C. Tsuei, M. Rupp et al., Phys. Rev. Lett. 76, 1336 (1996)]. The fractional value of the winding number leads to a frac-tional 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 fermion condensation is discussed.