Langevin simulations of the out-of-equilibrium dynamics of the vortex glass in high-temperature superconductors

TL;DR

This paper investigates the out-of-equilibrium dynamics of vortex glasses in high-temperature superconductors through numerical simulations, revealing aging, effective temperatures, and similarities to single elastic line behavior.

Contribution

It introduces a detailed numerical analysis of vortex glass dynamics, identifying aging, effective temperature, and finite-size effects, and compares these to single elastic line models.

Findings

Aging in two-times correlation functions.

Modified fluctuation-dissipation relation with an effective temperature.

Vortex glass dynamics similar to single elastic line behavior.

Abstract

We study the relaxation dynamics of flux lines in dirty high-temperature superconductors using numerical simulations of a London-Langevin model of the interacting vortex lines. By analysing the equilibrium dynamics in the vortex liquid phase we find a dynamic crossover to a glassy non-equilibrium regime. We then focus on the out-of-equilibrium dynamics of the vortex glass phase using tools that are common in the study of other glassy systems. By monitoring the two-times roughness and dynamic wandering we identify and characterize finite-size effects that are similar, though more complex, than the ones found in the stationary roughness of clean interface dynamics. The two-times density-density correlation and mean-squared-displacement correlation age and their temporal scaling follows a multiplicative law similar to the one found at criticality. The linear responses also age and the comparison with their associated correlations shows that the equilibrium fluctuation-dissipation relation is modified in a simple manner that allows for the identification of an effective temperature characterizing the dynamics of the slow modes. The effective temperature is closely related to the vortex liquid-vortex glass crossover temperature. Interestingly enough, our study demonstrates that the glassy dynamics in the vortex glass is basically identical to the one of a single elastic line in a disordered environment (with the same type of scaling though with different parameters). Possible extensions and the experimental relevance of these results are also discussed.