Defect generation and deconfinement on corrugated topographies

TL;DR

This paper explores how complex surface topographies influence defect formation in liquid crystal films, revealing transitions in defect behavior driven by surface geometry and boundary conditions.

Contribution

It introduces a detailed analysis of defect generation and deconfinement on curved surfaces with varying Gaussian curvature, including the effects of boundary conditions and surface aspect ratio.

Findings

Defect generation is driven by surface topography and Gaussian curvature.

Transitions in defect behavior depend on aspect ratio and boundary conditions.

Deconfinement transitions occur as the surface aspect ratio is lowered.

Abstract

We investigate topography-driven generation of defects in liquid crystals films coating frozen surfaces of spatially varying Gaussian curvature whose topology does not automatically require defects in the ground state. We study in particular disclination-unbinding transitions with increasing aspect ratio for a surface shaped as a Gaussian bump with an hexatic phase draped over it. The instability of a smooth ground state texture to the generation of a single defect is also discussed. Free boundary conditions for a single bump are considered as well as periodic arrays of bumps. Finally, we argue that defects on a bump encircled by an aligning wall undergo sharp deconfinement transitions as the aspect ratio of the surface is lowered.