Disclination Loops, Hedgehogs, and All That

TL;DR

This paper reviews the topological classification of defects in uniaxial nematic liquid crystals, emphasizing recent experimental advances and the subtle ambiguities unique to these systems compared to classical models.

Contribution

It provides a detailed analysis of defect classification in nematic liquid crystals, highlighting novel ambiguities and their implications for topological defect theory.

Findings

Experimental progress in colloidal inclusions in liquid crystals

Identification of unique topological ambiguities in nematic systems

Enhanced understanding of defect classification complexities

Abstract

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, we review and expound upon the classification of defects in uniaxial nematic liquid crystals. Particular attention is paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet.