Melting of two dimensional solids on disordered substrate

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.

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