Topological-sector fluctuations and ergodicity breaking at the Berezinskii-Kosterlitz-Thouless transition

Michael F. Faulkner, Steven T. Bramwell and Peter C. W. Holdsworth

Links: arXiv and DOI.

We found topological-sector fluctuations to be a signal of the high-temperature phase of the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional electrolyte. Our framework augments the charge-interaction representation of Kosterlitz and Thouless to include topological sectors of the electric field, which reflect charges tracing closed paths around the torus. Topological-sector fluctuations are absent in the low-temperature phase, where charges are confined in neutral pairs. This reflects a nonergodicity in the electric field. In contrast, topological-sector fluctuations are nonzero in the ergodic, high-temperature phase, where the charges are deconfined. Topological order is defined by the absence of topological-sector fluctuations. This nonergodicity was cited as a base explanation for the nonergodic dynamics measured in layered cuprates at the superconducting transition. Paper accepted with zero revisions.