Phase diagram of chiral biopolymer Wigner crystals

We study the statistical mechanics of counterion Wigner crystals associated with hexagonal bundles of chiral biopolymers. We show that, due to spontaneous chiral symmetry breaking induced by frustration, these Wigner crystals would be chiral even if the biopolymers themselves were not chiral. Using a duality transformation of the model onto a spin-charge Hamiltonian, we show that melting of the Wigner crystal is due to the unbinding of screw dislocations and that the melting temperature has a singular dependence on the intrinsic chirality of the biopolymers. Finally, we report that, if electrostatic interactions are strongly screened, the counterions can condense in the form of an intermediate achiral Wigner solid phase that melts by the unbinding of fractional topological charges.