Nernst effect and diamagnetism in phase fluctuating superconductors

When a superconductor is warmed above its critical temperature $T_c$, long range order is destroyed by fluctuations in the order parameter. These fluctuations can be probed by measurements of conductivity, diamagnetism, and of the Nernst effect. Here, we study a regime where superconductivity is destroyed by phase fluctuations arising from a dilute liquid of mobile vortices. We find that the Nernst effect and diamagnetic response differ significantly from Gaussian fluctuations -- in particular, a much sharper decay with temperature is obtained. We predict a rapid onset of Nernst signal at a temperature T$_{\rm onset}$ that tracks $T_c$, rather than the pairing temperature. We also predict a close quantitative connection with diamagnetism -- the ratio of magnetization to transverse thermoelectric conductivity $\alpha_{xy}$ reaches a universal value at high temperatures. We interpret Nernst effect measurements on the underdoped cuprates in terms of a dilute vortex liquid over a wide temperature range above $T_c$.