Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid $^3$He

TL;DR

This paper explores the existence and properties of half-quantum vortices in superfluid $^3$He under nanoconfinement, revealing their potential for hosting Majorana modes and forming walls bounded by strings, with implications for topological quantum computing and cosmology.

Contribution

It demonstrates the survival of half-quantum vortices across phase transitions in nanoconfined superfluid $^3$He and identifies their complex structures and potential for hosting non-Abelian Majorana modes.

Findings

Half-quantum vortices persist through phase transitions.

HQV cores in 2D host Majorana modes.

HQVs form walls bounded by strings in certain phases.

Abstract

Symmetries of the physical world have guided formulation of fundamental laws, including relativistic quantum field theory and understanding of possible states of matter. Topological defects (TDs) often control the universal behavior of macroscopic quantum systems, while topology and broken symmetries determine allowed TDs. Taking advantage of the symmetry-breaking patterns in the phase diagram of nanoconfined superfluid $^3$He, we show that half-quantum vortices (HQVs) -- linear topological defects carrying half quantum of circulation -- survive transitions from the polar phase to other superfluid phases with polar distortion. In the polar-distorted A phase, HQV cores in 2D systems should harbor non-Abelian Majorana modes. In the polar-distorted B phase, HQVs form composite defects -- walls bounded by strings hypothesized decades ago in cosmology. Our experiments establish the superfluid phases of $^3$He in nanostructured confinement as a promising topological media for further investigations ranging from topological quantum computing to cosmology and grand unification scenarios.