Topology of chiral superfluid: skyrmions, Weyl fermions and chiral anomaly

TL;DR

This paper explores the complex topological phenomena in chiral superfluid $^3$He-A, including skyrmions, Weyl fermions, and chiral anomaly, emphasizing the interplay of real and momentum space topologies.

Contribution

It introduces a comprehensive topological framework for understanding the chiral anomaly in superfluid $^3$He-A, extending beyond relativistic systems.

Findings

Identification of topological charges in extended ({f k},{f r})-space

Connection between real space and momentum space topologies

Insights into the nature of chiral anomaly in superfluid systems

Abstract

Chiral anomaly observed in the chiral superfluid $^3$He-A is the result of the combined effect of the real space and momentum space topologies. This effect incorporates several topological charges in the extended $({\bf k},{\bf r})$-space, which is beyond the conventional chiral anomaly in the relativistic systems.