How to measure the spatial correlations in disordered Berezinski-Kosterlitz-Thouless transition ?

TL;DR

This paper proposes an experimental method to measure local spatial correlations in disordered systems undergoing the Berezinski-Kosterlitz-Thouless transition, revealing a percolation-like propagation of coherence near criticality.

Contribution

It introduces a novel experimental approach to probe local paths of coherence and demonstrates their percolation-like behavior near the transition in disordered superconducting films.

Findings

Coherence propagates along ramified networks near the transition

The method can experimentally access spatial correlation information

Coherence pathways resemble percolation clusters

Abstract

The Berezinski-Kosterlitz-Thouless transition is a unique two dimensional phase transition, separating two phases with exponentially and power-law decaying correlations, respectively. In disordered systems, these correlations propagate along favorable paths, with the transition marking the point where global coherence is lost. Here we propose an experimental method to probe locally these particular paths in superconducting thin films, which exhibit this transition, and demonstrate theoretically that close to the transition the coherence propagate along a ramified network, reminiscent of a percolation transition. We suggest and calculate experimentally accessible quantities that can shed light on the spatial correlations in the system as it approaches the critical point.