Disclination classes, fractional excitations, and the melting of quantum liquid crystals

TL;DR

This paper explores how fractional excitations associated with dislocations in quantum liquid crystals depend on the dislocation's disclination structure, influencing the nature of phase transitions in these systems.

Contribution

It reveals that the presence of multiple inequivalent disclination classes determines the existence of fractional excitations and the melting behavior of quantum liquid crystals.

Findings

Fractional excitations depend on disclination structure.

Multiple disclination classes influence melting transitions.

Superfluidity and orientational order can vanish simultaneously.

Abstract

We consider how fractional excitations bound to a dislocation evolve as the dislocation is separated into a pair of disclinations. We show that some dislocation-bound excitations (such as Majorana modes and half-quantum vortices) are possible only if the elementary dislocation consists of two inequivalent disclinations, as is the case for stripes or square lattices but not for triangular lattices. The existence of multiple inequivalent disclination classes governs the two-dimensional melting of quantum liquid crystals (i.e., nematics and hexatics), determining whether superfluidity and orientational order can simultaneously vanish at a continuous transition.