Vortex matter in layered superconductors without Josephson coupling: numerical simulations within a mean-field approach

TL;DR

This paper investigates vortex matter in layered superconductors without Josephson coupling using a mean-field approach, employing numerical simulations to analyze phase transitions and thermodynamic properties.

Contribution

It introduces a mean-field simulation method for vortex interactions in layered superconductors without Josephson coupling, combining Monte Carlo and Langevin dynamics.

Findings

Converges to a periodic crystal or vanishes as a liquid depending on temperature.

Accurately computes melting and instability lines.

Finds good agreement with analytical calculations.

Abstract

We study vortex matter in layered superconductors in the limit of zero Josephson coupling. The long range of the interaction between pancake vortices in the c-direction allows us to employ a mean-field method: all attractive inter-layer interactions are reduced to an effective substrate potential, which pancakes experience in addition to the same-layer pancake repulsion. We perform numerical simulations of this mean-field model using two independent numerical implementations with different simulation methods (Monte-Carlo sampling and Langevin molecular dynamics). The substrate potential is updated self-consistently from the averaged pancake density. Depending on temperature, this potential converges to a periodic profile (crystal) or vanishes (liquid). We compute thermodynamic properties of the system, such as the melting line, the instability line of the crystal, and the entropy jump across the melting transition. The simulation results are in good agreement with approximate analytical calculations.