Curvature-Induced Defect Unbinding in Toroidal Geometries

TL;DR

This paper investigates how the geometry of a torus influences defect formation in materials with hexatic, tilt, or nematic order, revealing that certain defect configurations are energetically favored in specific toroidal shapes.

Contribution

It provides explicit energy calculations for disclination defects in toroidal geometries, highlighting conditions where defect unbinding is energetically preferred.

Findings

Defects are energetically favored in fat torii or moderate vesicle sizes.

Explicit energy expressions for disclinations in toroidal geometries.

Implications for experimental observations of defects in toroidal materials.

Abstract

Toroidal templates such as vesicles with hexatic bond orientational order are discussed. The total energy including disclination charges is explicitly computed for hexatic order embedded in a toroidal geometry. Related results apply for tilt or nematic order on the torus in the one Frank constant approximation. Although there is no topological necessity for defects in the ground state, we find that excess disclination defects are nevertheless energetically favored for fat torii or moderate vesicle sizes. Some experimental consequences are discussed.