Influence of vortices and phase fluctuations on thermoelectric transport properties of superconductors in a magnetic field

TL;DR

This paper investigates how vortices and phase fluctuations affect thermoelectric transport in two-dimensional superconductors under magnetic fields, using models of granular Josephson-junction arrays to simulate heat and Nernst effects.

Contribution

It introduces a comprehensive modeling approach combining relaxational and RCSJ dynamics to analyze heat transport and thermoelectric effects in granular superconductors under magnetic fields.

Findings

Heat conductivity diverges logarithmically with system size at low T and zero field.

Nernst signal exhibits a 'tilted hill' profile similar to experiments.

Granularity and randomness significantly influence transport properties at higher magnetic fields.

Abstract

We study heat transport and thermoelectric effects in two-dimensional superconductors in a magnetic field. These are modeled as granular Josephson-junction arrays, forming either regular or random lattices. We employ two different models for the dynamics, relaxational model-A dynamics or resistively and capacitively shunted Josephson junction (RCSJ) dynamics. We derive expressions for the heat current in these models, which are then used in numerical simulations to calculate the heat conductivity and the Nernst coefficient for different temperatures and magnetic fields. At low temperatures and zero magnetic field the heat conductivity in the RCSJ model is calculated analytically from a spin wave approximation, and is seen to have an anomalous logarithmic dependence on the system size, and also to diverge in the completely overdamped limit C -> 0. From our simulations we find at low magnetic fields that the Nernst signal displays a characteristic "tilted hill" profile similar to experiments and a non-monotonic temperature dependence of the heat conductivity. We also investigate the effects of granularity and randomness, which become important for higher magnetic fields. In this regime geometric frustration strongly influences the results in both regular and random systems and leads to highly non-trivial magnetic field dependencies of the studied transport coefficients.