Universal scaling behavior of resistivity under two-dimensional superconducting phase fluctuations

In superconductors with relatively low superfluid density, such as cuprate high-$T_c$ superconductors, the phase fluctuations of the superconducting order parameter are remarkable, presumably playing a nonnegligible role in shaping many distinctive physical properties. Despite existing phenomenological arguments for many years, a comprehensive quantitative analysis of the electrical transport properties resulting from thermal superconducting phase fluctuations in two-dimensional superconductors has been lacking. This study employs Monte Carlo simulations to explore the numerically exact transport properties of a microscopic model of superconductivity, where the thermal phase fluctuations of the superconducting order parameter are described by the classical XY model. For both s-wave and d _{x ²} − _{y ²} -wave pairings, the electrical resistivity exhibits a universal scaling behavior at temperatures above the critical temperature T _c . Our numerical results demonstrate that the scaling behavior of the quasiparticle lifetime is closely linked to the correlation length of the superconducting order parameter, yielding the universal scaling behavior of electrical resistivity determined by the Berezinskii-Kosterlitz-Thouless critical scaling of the correlation length. While this behavior aligns formally with the phenomenological framework of Halperin and Nelson in the critical region, our findings suggest that the resistivity scales with the inverse of the correlation length with a power less than one. Additionally, we examine the dependence of the electrical resistivity coefficient on the pairing amplitude and potential implications for recent transport experiments.