Commensurate polar smectic structures with a two-component order parameter

Recently Wang [Phys. Rev. Lett. 104, 027801 (2010)]10.1103/PhysRevLett.104.027801 discovered a novel smectic- C^∗ liquid-crystal commensurate structure with six-layer period. Challenged by this discovery, we show that the observed novel structure and the unusual sequence of polar phases can be explained in the framework of the discrete Landau model of phase transitions with a two-component order parameter. Peculiarities of the six-layer phase and the influence of short-range and long-range interactions on the formation of different phases and phase sequences are discussed.