The Role of the Core Energy in the Vortex Nernst Effect

We present an analytical study of diamagnetism and transport in a film with superconducting phase fluctuations, formulated in terms of vortex dynamics within the Debye-H\"uckle approximation. We find that the diamagnetic and Nernst signals decay strongly with temperature in a manner which is dictated by the vortex core energy. Using the theory to interpret Nernst measurements of underdoped La$_{2-x}$Sr$_x$CuO$_4$ above the critical temperature regime we obtain a considerably better fit to the data than a fit based on Gaussian order-parameter fluctuations. Our results indicate that the core energy in this system scales roughly with the critical temperature and is significantly smaller than expected from BCS theory. Furthermore, it is necessary to assume that the vortex mobility is much larger than the Bardeen-Stephen value in order to reconcile conductivity measurements with the same vortex picture. Therefore, either the Nernst signal is not due to superconducting phase fluctuations, or that vortices in underdoped La$_{2-x}$Sr$_x$CuO$_4$ have highly unconventional properties.