Disclination Asymmetry in Deformable Hexatic Membranes and the Kosterlitz-Thouless Transitions

Abstract
A disclination in a hexatic membrane favors the development of Gaussian curvature localized near its core. The resulting global structure of the membrane has mean curvature, which is disfavored by curvature energy. Thus a membrane with an isolated disclination undergoes a bluckling transition from a flat to a buckled state as the ratio of the bending rigidity k to the hexatic rigidity is decreased. In this paper we calculate the buckling transition and the energy of both a positive and a negative disclination. A negative disclination has a larger energy and a smaller critical value of at buckling than does a positive disclination. We use our results to obtain a crude estimate of the Kosterlitz-Thouless transition temperature in a membrane. This estimate is higher than the transition temperature recently obtained by the authors in a renormalization calculation.