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

## TL;DR

This paper investigates the relationship between the Nernst effect and fluctuation diamagnetism in strongly fluctuating superconductors, revealing a universal ratio that links these phenomena across different regimes.

## Contribution

It introduces a comprehensive model connecting phase and amplitude fluctuations to experimentally measurable quantities, and calculates a novel ratio that characterizes their correlation in cuprates.

## Key findings

- The ratio M/(T α_xy) is consistent across the phase diagram.
- The correlation between the Nernst signal and magnetization is primarily due to their equilibrium properties.
- No sharp boundary exists between phase and Gaussian fluctuation regimes for this ratio.

## Abstract

We study the Nernst effect in fluctuating superconductors by calculating the transport coefficient $\alpha_{xy}$ in a phenomenological model where relative importance of phase and amplitude fluctuations of the order parameter is tuned continuously to smoothly evolve from an effective XY model to 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 ${\bf M}$ over the entire range of experimentally accessible values of field, temperature and doping. We argue that $\alpha_{xy}$ and ${\bf M}$ are 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 ${\bf M}$. Further, there exists a dimensionless ratio ${\bf M}/(T \alpha_{xy})$ 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 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 ${\bf M}$ 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.