Geometric stabilisation of topological defects on micro-helices and grooved rods in nematic liquid crystals

Abstract

We demonstrate how the geometric shape of a rod in a nematic liquid crystal can stabilise a large number of oppositely charged topological defects. A rod is of the same shape as a sphere, both having genus g = 0, which means that the sum of all topological charges of defects on a rod has to be −1 according to the Gauss–Bonnet theorem. If the rod is straight, it usually shows only one hyperbolic hedgehog or a Saturn ring defect with negative unit charge. Multiple unit charges can be stabilised either by friction or large length, which screens the pair-interaction of unit charges. Here we show that the curved shape of helical colloids or the grooved surface of a straight rod create energy barriers between neighbouring defects and prevent their annihilation. The experiments also clearly support the Gauss–Bonnet theorem and show that topological defects on helices or grooved rods always appear in an odd number of unit topological charges with a total topological charge of −1.