Novel time-dependent Ginzburg-Landau simulation of extreme type-II superconductors with a focus on the Nernst signal and its fluctuations

Recently, different transport coefficients have been measured in High-$T_{c}$ superconductors to pinpoint the nature of the pseudogap phase. In particular, the thermoelectric coefficients received a considerable attention both theoretically and experimentally. We numerically simulate the Nernst effect in extreme type-II superconductors using the time-dependent Ginzburg-Landau equations. We report the sign reversal of the thermoelectric coefficient, $\alpha_{xy}$, at temperatures close to the mean-field transition temperature $T^{MF}_{c}(H)$, which qualitatively agrees with recent experiments on high-$T_{c}$ materials. We also discuss the noise power spectrum of $\alpha_{xy}$, which shows $1/f^{\beta}$ behavior. Based on this observation, we propose an experiment to determine different regimes of vortex dynamics by measuring the noise correlations of the Nernst signal.