Columnar phases of three-fold molecular structures

We study the occurrence of both positional and helical orders, for three-fold symmetric flat molecules in a columnar liquid crystal phase D(hd). Working in the group-theoretical Landau's framework, we identify a set of three order parameters giving rise to supercells of intercalated column with helical order and opposite helicities, as observed experimentally. The first-order nature of the transition is also discussed. The degrees of freedom introduced give rise to various other phases, including a new type, having helical order but no positional order along the columns.