Breaking the Rules for Topological Defects: Smectic Order on Conical Substrates

TL;DR

This paper investigates how smectic liquid crystal order is affected by highly localized curvature on conical substrates, revealing the nature of induced singularities through simple, tractable models.

Contribution

It introduces a detailed analysis of smectic order on curved surfaces using paper and tape models, providing new insights into defect formation due to curvature.

Findings

Identification of cusps and singularities induced by curvature

Detailed understanding of defect structures on conical substrates

Insights applicable to small-scale crystalline materials

Abstract

Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are grown on real surfaces; eventually, surface imperfections are on the same scale as the lattice constant. Here, we gain insights into this general problem by studying two-dimensional smectic order on substrates with highly localized intrinsic curvature, constructed from cones and their intersections with planes. In doing so we take advantage of fully tractable "paper and tape" constructions, allowing us to understand, in detail, the induced cusps and singularities.