Frustrated order on extrinsic geometries

TL;DR

This paper investigates how extrinsic curvature influences nematic defects on curved surfaces, revealing that extrinsic effects can expel defects from regions of high curvature, especially on negatively curved surfaces like catenoids.

Contribution

It provides an analytical and theoretical study of extrinsic curvature effects on nematic defects, highlighting their role in defect expulsion and complex ground state behavior.

Findings

Extrinsic curvature can expel disclinations from high curvature regions.

On catenoids, defects are completely expelled due to extrinsic effects.

Extrinsic effects lead to complex thermodynamics in negatively curved surfaces.

Abstract

We study, analytically and theoretically, defects in a nematically-ordered surface that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the nematic in the local direction of maximum or minimum bending. This additional frustration is unavoidable and most important on surfaces of negative Gaussian curvature, where it leads to a complex ground state thermodynamics. We show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic curvature expels disclinations from the region of maximum curvature above a critical coupling threshold. On catenoids lacking an "inside-outside" symmetry, defects are expelled altogether.