Topologically-Protected Remnant Vortices in Confined Superfluid $^3$He

TL;DR

This study investigates the formation of topologically protected remnant vortices in confined superfluid helium-3, revealing that vortex density depends on channel size rather than quench rate, challenging traditional Kibble-Zurek predictions.

Contribution

The paper introduces a modified defect formation model accounting for wall effects, explaining high vortex densities in confined superfluid helium-3.

Findings

Vortex density correlates with channel size, not quench time.

Remnant vortices form after the phase transition in confined geometries.

Walls prevent vortex reconnection, leading to higher defect densities.

Abstract

Symmetry breaking phase transitions from less to more ordered phases will typically produce topological defects in the ordered phase. Kibble-Zurek theory predicts that for any second-order phase transition, such as the early universe, the density of defects that form should be determined by the scaling law for the system coherence time and the phase transition quench time. We have performed measurements of fourth sound dissipation due to vortex mutual friction in thin channels of superfluid $^3$He where one spatial dimension is smaller than a characteristic length scale predicted by the Kibble-Zurek theory. Our measurements suggest that remnant vortices form after the normal to superfluid second-order phase transition, and that the density of vortices is correlated with the size of the channel, but crucially, is independent of quench time. We propose a modified picture of defect formation, where closely spaced walls prevent the ends of vortex lines from reconnecting into loops. This leads to a mean vortex separation set by the wall spacing, which can result in much higher defect densities than in bulk systems.