Orientational correlations of active defects in flat and curved space

Topological defects are salient signatures of active nematics, which are partially-ordered systems intrinsically out of equilibrium. We experimentally study the dynamics of microtubule-kinesin active nematics constrained to both flat 2D space and toroidal surfaces and inquire whether the defects develop any form of order. In flat space, +1/2 defects develop short range ferromagnetic order (mediated by -1/2 defects) and antiferromagnetic order at length scales comparable to the mean defect spacing. Both these effects and the corresponding correlations were seen to persist independent of the total defect density, and without any global orientational order [1]. In contrast, on curved space, we find that defect orientations strongly couple to the surface they live in, resulting in both +1/2 and -1/2 defects developing orientational order in regions of non-zero Gaussian curvature.