Melting of two dimensional solids on disordered substrate

TL;DR

This paper investigates how weak substrate disorder affects the melting transition in 2D solids, revealing a sharp crossover to a glassy regime with disorder-induced dislocations and discussing experimental implications.

Contribution

It introduces a Coulomb gas renormalisation approach to characterize the crossover from melting to a disordered glassy state in 2D solids with substrate disorder.

Findings

Melting transition replaced by a sharp crossover

Disorder-induced dislocations dominate at large scales

Predicted size effects in vortex flow and AC response

Abstract

We study 2D solids with weak substrate disorder, using Coulomb gas renormalisation. The melting transition is found to be replaced by a sharp crossover between a high $T$ liquid with thermally induced dislocations, and a low $T$ glassy regime with disorder induced dislocations at scales larger than $\xi_{d}$ which we compute ($\xi_{d}\gg R_{c}\sim R_{a}$, the Larkin and translational correlation lengths). We discuss experimental consequences, reminiscent of melting, such as size effects in vortex flow and AC response in superconducting films.