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

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.