The correlation between the Nernst effect and fluctuation diamagnetism in strongly fluctuating superconductors

We study the Nernst effect in fluctuating superconductors by calculating the transport coefficient alpha(xy) in a phenomenological model where the relative importance of phase and amplitude fluctuations of the order parameter is tuned continuously to smoothly evolve from an effective XY model to the more conventional Ginzburg-Landau description. To connect with a concrete experimental realization we choose the model parameters appropriate for cuprate superconductors and calculate alpha(xy) and the magnetization Mover the entire range of experimentally accessible values of field, temperature and doping. Weargue that alpha(xy) and Mare both determined by the equilibrium properties of the superconducting fluctuations (and not their dynamics) despite the former being a transport quantity. Thus, the experimentally observed correlation between the Nernst signal and the magnetization arises primarily from the correlation between alpha(xy) and M. Further, there exists a dimensionless ratio M/(T alpha(xy)) that quantifies this correlation. We calculate, for the first time, this ratio over the entire phase diagram of the cuprates and find it agrees with previous results obtained in specific parts of the phase diagram. We conclude that there appears to be no sharp distinction between the regimes dominated by phase fluctuations and Gaussian fluctuations for this ratio in contrast to alpha(xy) and M individually. The utility of this ratio is that it can be used to determine the extent to which superconducting fluctuations contribute to the Nernst effect in different parts of the phase diagram given the measured values of magnetization.