Electric field effects in incommensurate smectic phases

Abstract

We discuss electric properties of frustrated smectics in the general framework of two coupled order parameters, characterized by two incommensurate preferred lengths. We find the existence of modulated phases locked on subharmonics of the layer period, equivalently described as discommensuration lattices, which period is an integer number of layer spacing. They can be induced by the action of an external electric field, either through an infinite number of steps, or through a finite sequence beyond a threshold value; they can also exist in the absence of any external field, and correspond to longitudinal ferroelectric states.