Defect-Mediated Melting of Square-Lattice Solids

TL;DR

This paper extends the KTHNY theory to square-lattice solids, incorporating anisotropy and predicting a two-step melting process with unique features compared to isotropic lattices.

Contribution

It introduces an extended elastic theory for square lattices, accounting for anisotropy and modifying defect interactions in the melting process.

Findings

Predicts a two-step melting with an intermediate tetratic phase.

Identifies a third elastic constant controlling anisotropy.

Shows modified bounds on correlation exponents and non-universal Young's modulus at transition.

Abstract

The Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory successfully explains the melting mechanism of two-dimensional isotropic lattices as a two-step process driven by the unbinding of topological defects. By considering the elastic theory of the square lattice, we extend the KTHNY theory to melting of square lattice solids. In addition to the familiar elastic constants that govern the theory -- the Young's modulus and the Poisson ratio -- a third constant controlling the anisotropy of the medium emerges. This modifies both the logarithmic and angular interactions between the topological defects. Despite this modification, the extended theory retains the qualitative features of the isotropic case, predicting a two-step melting with an intermediate tetratic phase. However, some subtle differences arise, including a modified bound on the translational correlation exponent and the absence of universal values for the Young's modulus at the solid-to-tetratic phase transition.