Abstract
Many helical compounds can be thought of as a deformation of a highly symmetric structure. This deformation is governed by only one mode, i.e. one irreducible representation, from the high-symmetry phase so that the Landau theory for phase transitions is applicable. It will be shown that the resulting helix has to be described by two (local) symmetry modes, an even and an odd one (with respect to inversion) which are in resonance. The description of a helix with even and odd modes is a consequence only of its geometry. With even and odd components, expressions (chiral functions) which are typical for a helix can be formed. These expressions lead to fourth-order Landau invariants. As examples the helical compounds Se and Te as well as HgO, HgS and HgSe will be treated. The cholesteric state of liquid crystals will be briefly discussed and a generalization will be made for multiple coaxial helices.
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