Signatures of thermally excited vortices in a superconductor with competing orders

Abstract

Experimental evidence for the existence of a fluctuating charge-density wave order in the pseudogap regime of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ has renewed interest in its interplay with superconductivity. Here, we consider the problem within a nonlinear sigma model, which was recently proposed to describe the apparent competition between the two order parameters. In particular, we use a saddle-point approximation to calculate the properties of superconducting vortex excitations within such a model. In addition, we analytically calculate a collection of experimentally observable quantities, which probe both the superconducting and charge-density wave fluctuations, and identify expected signatures of thermally excited vortices. Specifically, we find that the magnetization and Nernst signal decay rapidly with temperature for a range of temperatures above the Kosterlitz-Thouless transition, while the x-ray structure factor increases in the same temperature range. At higher temperatures, the system enters a regime of Gaussian fluctuations where vortices are no longer well defined, and as a result the magnetization, Nernst signal, and x-ray structure factor all decrease moderately with temperature.