Half - Quantum Vortices

TL;DR

This paper explores the existence and properties of half-quantum vortices in superfluid $^3$He phases, their challenges, and recent discoveries in related materials like Sr$_2$RuO$_4$ and exciton-polariton condensates.

Contribution

It discusses the theoretical and experimental aspects of half-quantum vortices in superfluid $^3$He and related systems, highlighting recent discoveries and the conditions enabling their existence.

Findings

Half-quantum vortices exist in superfluid $^3$He-A and polar phases.

Magnetic dipole interactions influence vortex stability and domain wall formation.

Recent observations confirm half-quantum vortices in Sr$_2$RuO$_4$ and exciton-polariton condensates.

Abstract

Unlike to superfluid $^4$He the superfluid $^3$He-A support the existence of vortices with half quantum of circulation as well as single quantum vortices. The singular single quanta vortices as well as nonsingular vortices with 2 quanta of circulation have been revealed in rotating $^3$He-A. However, the half quantum vortices in open geometry always possess an extra energy due to spin-orbit coupling leading to formation of domain wall at distances larger than dipole length $\sim 10^{-3}cm$ from the vortex axis. Fortunately the same magnetic dipole-dipole interaction does not prevent the existence of half-quantum vortices in the polar phase of superfluid $^3$He recently discovered in peculiar porous media "nematically ordered" aerogel. Here we discuss this exotic possibility. The discoveries of half-quantum vortices in triplet pairing superconductor Sr$_2$RuO$_4$ as well in the exciton-polariton condensates are the other parts of the story about half-quantum vortices also described in the paper.