Phase Diagram of Chiral Biopolymer Wigner Crystals

TL;DR

This paper investigates the phase behavior of chiral biopolymer Wigner crystals, revealing how chirality influences melting transitions and the emergence of intermediate phases due to electrostatic screening effects.

Contribution

It introduces a duality transformation approach to analyze melting mechanisms and uncovers the role of chirality and screening in phase transitions of biopolymer Wigner crystals.

Findings

Melting involves unbinding screw dislocations.

Chirality causes a singular dependence of melting temperature.

Screening leads to an intermediate achiral Wigner solid phase.

Abstract

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.