Monte-Carlo calculation of longitudinal and transverse resistivities in a model Type-II superconductor

TL;DR

This paper uses Monte Carlo simulations to analyze how a transport current affects the vortex lattice in type-II superconductors, revealing a two-stage melting process with implications for resistivity behavior.

Contribution

It introduces a detailed Monte Carlo approach to study resistivities and vortex lattice melting in type-II superconductors under thermal fluctuations and transport currents.

Findings

Vortex lattice melts in two stages at different temperatures.

Transverse resistivity becomes finite at the first melting point.

Longitudinal coherence is lost at a higher temperature.

Abstract

We study the effect of a transport current on the vortex-line lattice in isotropic type-II superconductors in the presence of strong thermal fluctuations by means of 'driven-diffusion' Monte Carlo simulations of a discretized London theory with finite magnetic penetration depth. We calculate the current-voltage (I-V) characteristics for various temperatures, for transverse as well as longitudinal currents I. From these characteristics, we estimate the linear resistivities R_xx=R_yy and R_zz and compare these with equilibrium results for the vortex-lattice structure factor and the helicity moduli. From this comparison a consistent picture arises, in which the melting of the flux-line lattice occurs in two stages for the system size considered. In the first stage of the melting, at a temperature T_m, the structure factor drops to zero and R_xx becomes finite. For a higher temperature T_z, the second stage takes place, in which the longitudinal superconducting coherence is lost, and R_zz becomes finite as well. We compare our results with related recent numerical work and experiments on cuprate superconductors.