Braiding and exchange statistics of liquid crystalline Majorana quasiparticles

TL;DR

This paper explores liquid crystalline defects as analogues of Majorana quasiparticles, demonstrating their non-Abelian braiding properties and potential for topological quantum computation.

Contribution

It reveals that nematic liquid crystalline defects can exhibit non-Abelian anyon-like braiding behavior, extending the physical analogy beyond mathematical mapping.

Findings

Defect profiles behave as classical non-Abelian anyons during braiding.

Defect bivectors can be described on a Bloch-like hemisphere.

Elastic interactions and dynamics increase gate complexity.

Abstract

Liquid crystalline defects in 3D can be viewed as geometric spinors, whose emergent properties are reminiscent of those of topological excitations in quantum condensed matter, such as Majorana quasiparticles. However, it is unclear how deep this analogy is, and whether this is a purely mathematical mapping, or it extends to key physical features, such as the exchange statistics or braiding behaviour. To address this question, here we consider a simple pattern made up of four nematic Majorana-like defect profiles, and ask how the defect profiles change as we braid them repeatedly around each other. Surprisingly, we find that in a large range of parameter space the defect profiles behave as classical analogues of non-Abelian anyons, which can be described in our case by defect bivectors moving on a Bloch-like hemisphere. Elastic interactions and dynamical effects enhance the complexity of the gates which can be performed by braiding these quasiparticles, making these liquid crystalline spinors promising candidates as components of topological computers.