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. This work systematically investigates the electrical transport properties arising from thermal superconducting phase fluctuations in two-dimensional superconductors. Employing the Monte Carlo procedure, we access the numerically exact properties of a microscopic model of superconductivity, in which the classical XY model governs the thermal phase fluctuations of the superconducting order parameter. For both $s$-wave and $d_{x^2-y^2}$-wave pairings, the electrical resistivity exhibits a universal scaling behavior in the temperature range above $T_c$. Our numerical results demonstrate that the scaling behavior of the quasiparticle lifetime is associated with 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. Furthermore, we discuss the dependence of the electrical resistivity coefficient on the pairing amplitude and the possible implication on recent transport experiments.