Coarse-graining elastic theory for twist-bend nematic phases

By use of a standard theoretical method, we arrive at a coarse-grained elastic energy density for twist-bend nematic (N-tb) phases which features two fields, a director t designating the outer macroscopic optic axis and a variable cone angle # reflecting the inner heliconical microscopic structure. The theory describes the N-tb phase through a nematic-like energy with an extra scalar order parameter. The coupling with an external field is similarly described at the same coarse-grained level and a field-induced transition to the ordinary nematic phase is also predicted to take place in a confined Frederiks cell, in the simplified setting where natural boundary conditions are prescribed on the cell's plates. [GRAPHICS] .