Analogy between the twist-bend nematic and the smectic A phases and coarse-grained description of the macroscopic NTB properties

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ABSTRACTThe twist-bend nematic, NTB, has unusual elastic properties. Contrary to the usual nematic, the NTB director n is spontaneously distorted, resulting in a heliconical structure with small period and doubly degenerate handedness. Different models have been proposed so far, and are still actively debated, to describe the NTB properties on the microscopic scale. On the macroscopic scale, we propose a symmetry-based analogy between the NTB and the SmA* phases. Introducing a complex order parameter, we write the macroscopic NTB energy by analogy with the de Gennes’ SmA* description. By coarse graining, based on the elastic-instability local model, we calculate the macroscopic elastic constants and characteristic lengths in terms of a few Frank-like elastic coefficients. We discuss the inverse elastic anisotropy of the NTB phase, compared with the SmA*, and its impact on the structure of the NTB defects. We extend the coarse-grained (CG) model to investigate the macroscopic response to electric fields, and the surface anchoring alignment and the microscopic distortions of the NTB phase. Finally, we suggest the existence of a NTB analogue of the twist grain boundary phase TGBA, with a penetration of the twist field in the bulk through a network of screw dislocations of the NTB pseudo-layers.