Frustrated Polyelectrolyte Bundles and T=0 Josephson-Junction Arrays

TL;DR

This paper establishes a theoretical link between polyelectrolyte bundle behavior and Josephson-junction arrays, revealing a universal transition characterized by symmetry breaking and a response to shear.

Contribution

It introduces a novel mapping between classical and quantum models, connecting polyelectrolyte physics with superconducting array phenomena.

Findings

Continuous liquid-to-solid transition in polyelectrolyte bundles

Spontaneous chiral symmetry breaking at the transition

Universal shear response of the bundle at criticality

Abstract

We establish a one-to-one mapping between a model for hexagonal polyelectrolyte bundles and a model for two-dimensional, frustrated Josephson-junction arrays. We find that the T=0 insulator-to-superconductor transition of the {\it quantum} system corresponds to a continuous liquid-to-solid transition of the condensed charge in the finite temperature {\it classical} system. We find that the role of the vector potential in the quantum system is played by elastic strain in the classical system. Exploiting this correspondence we show that the transition is accompanied by a spontaneous breaking of chiral symmetry and that at the transition the polyelectrolyte bundle adopts a universal response to shear.