Vortex-lattice melting in two-dimensional superconductors in intermediate fields

TL;DR

This study uses Monte Carlo simulations of the 2D Ginzburg-Landau model, including higher Landau levels, to analyze vortex lattice melting in 2D superconductors across different magnetic field strengths.

Contribution

It extends the conventional lowest Landau level approximation by incorporating multiple higher LL modes to better understand vortex melting behavior.

Findings

Nearly vertical melting line in low fields with higher LL modes

First order melting transition weakens at higher fields

No evidence of crossover to continuous melting with hexatic phase

Abstract

To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several {\it higher} LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical melting line in lower fields, which is familiar within the elastic theory, is reached just by including higher LL modes with LL indices less than five, and that the first order character of the melting transition in higher fields is significantly weakened with decreasing the field. Nevertheless, a genuine crossover to the consecutive continuous melting picture intervened by a hexatic liquid is not found within the use of the GL model.