Anomalous coupling between topological defects and curvature

TL;DR

This paper explores how topological defects in thin curved layers of superfluids, superconductors, and liquid crystals interact with surface curvature, revealing a geometric potential that influences defect behavior based on the order parameter.

Contribution

It uncovers a universal geometric potential affecting defects on curved surfaces, with specific interactions depending on the type of material and defect charge.

Findings

Defects in superfluids and superconductors are repelled or attracted by curvature depending on charge squared.

Liquid crystal defects with charges between 0 and 4π are attracted to positive curvature regions.

The geometric potential is determined solely by surface shape and the order parameter's transformation properties.

Abstract

We investigate a counterintuitive geometric interaction between defects and curvature in thin layers of superfluids, superconductors and liquid crystals deposited on curved surfaces. Each defect feels a geometric potential whose functional form is determined only by the shape of the surface, but whose sign and strength depend on the transformation properties of the order parameter. For superfluids and superconductors, the strength of this interaction is proportional to the square of the charge and causes all defects to be repelled (attracted) by regions of positive (negative) Gaussian curvature. For liquid crystals in the one elastic constant approximation, charges between 0 and $4\pi$ are attracted by regions of positive curvature while all other charges are repelled.