2011/07/06 by Gareth P. Alexander, Bryan Gin-ge Chen, Elisabetta A. Matsumoto +1 · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.soft #cond-mat.stat-mech #math.AT
paper · pdf · doi:10.1103/revmodphys.84.497
published as Rev. Mod. Phys. 84 (2012) 497 · Colloquium, 19 pages, 9 figures
arxiv created 2011/07/06 · arxiv updated 2012/04/10
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.