Twist-bend nematic phase in the presence of molecular chirality

One of the interesting questions related to bent-shaped materials is how structural chirality of the twist-bend nematic (NTB) phase can respond to the presence of molecular chirality, with later being introduced through chiral centers incorporated in the molecules or chiral dopants. We study this problem using minimal coupling Landau-de Gennes theory of NTB, supplemented by a term representing intrinsic molecular chirality. Relative stability and properties of cholesteric (N*), chiral twist-bend nematic with heliconical structure (N*TB), and other homogeneous phases are studied. Besides nematic, chiral twist-bend nematic and cholesteric phases of vanishing global polarization, we find their polar analogues. In particular, a coupling between molecular chirality, alignment tensor and polarization fields can promote a globally polar and chiral twist-bend nematic (N*TBp) with period comparable to that of N*.