Dynamics of dislocations in the Twist-Grain-Boundary-A phase of liquid crystals

The superconductor-smectic A analogy by de Gennes has been successfully applied by Renn and Lubensky to predict the existence and mean field properties of the Twist-Grain-Boundary-A phase, which was independently discovered experimentally by Goodby and coworkers. We explore the possibility of extending this powerful analogy to aspects of the Twist-Grain-Boundary-A phase which require treatments going beyond the static mean field regime. Careful analysis reveals (1)the motion of a grain boundary as a liquid crystal analogue of the current-induced flux flow of the Abrikosov vortices, which can be realized either by applying the electric field in the helical axis direction, or by imposing a temperature gradient, and (2) the dynamical renormalization of effective Frank elastic constants resulting from the motion of the grain boundary. Implications of our findings for the vulnerability of the TGBA phase to thermal fluctuation is briefly discussed.