Monopoles and fractional vortices in chiral superconductors

TL;DR

This paper explores exotic topological objects in chiral superconductors, such as fractional vortices and monopoles, highlighting their properties, interactions, and potential experimental identification, with connections to relativistic theories and grand unified theories.

Contribution

It introduces the concept of nexus in chiral superconductors, linking fractional vortices and monopoles, and analyzes their topological interactions and properties.

Findings

Fractional vortices carry half or quarter quantum flux.

Nexus objects connect vortices and monopoles topologically.

Fermion zero modes are associated with these topological defects.

Abstract

We discuss two exotic objects, which must be experimentally identified in chiral superfluids and superconductors. These are (i) the vortex with fractional quantum number (N=1/2 in chiral superfluids, and N=1/2 and N=1/4 in chiral superconductors), which plays the part ofthe Alice string in relativistic theories; and (ii) the hedgehog in the l-field, which is the counterpart of the Dirac magnetic monopole. These objects of different dimensions are topologically connected. They form the combined object which is called nexus in relativistic theories. In chiral superconductors the nexus has magnetic charge emanating radially from the hedgehog, while the half-quantum vortices play the part of the Dirac string. Each of them supplies the fractional magnetic flux to the hedgehog, representing 1/4 of the "conventional" Dirac string. We discuss the topological interaction of the superconductor's nexus with the `t Hooft-Polyakov magnetic monopole, which can exist in GUT. The `t Hooft-Polyakov magnetic monopole and the hedgehog with the same magnetic charge are topologically confined by a piece of the Abrikosov vortex. Other properties of half-quantum vortices and monopoles are discussed as well, including fermion zero modes.