Predictive power of the Berezinskii-Kosterlitz-Thouless theory based on renormalization group throughout the BCS-BEC crossover in two-dimensional superconductors

Recent experiments on 2D superconductors allow the characterization of the critical temperature and of the phase diagram across the BCS-BEC crossover as a function of density. We obtain from these experiments the microscopic parameters of the superconducting state at low temperatures by the BCS mean-field approach. For ${\mathrm{Li}}_{x}\mathrm{ZrNCl}$, the extracted parameters are used to evaluate the superconducting phase stiffness and the Berezinskii-Kosterlitz-Thouless (BKT) critical temperature throughout the BCS-BEC crossover by implementing the corresponding renormalization group (RG) approach. In this way, we make a quantitative test of the predictive power of the BKT theory for evaluating the critical temperature. The RG flow equations turn out to give a sizable renormalization of the phase stiffness and of the critical temperature, which is crucial to obtain a satisfactory agreement between the BKT theory and the experiments, in particular, in the BCS-BEC crossover regime. We predict the temperature range where phase stiffness renormalization can be measured in ${\mathrm{Li}}_{x}\mathrm{ZrNCl}$ across the BCS-BEC crossover. Contrary to other microscopic theories of superconductivity, we find that the BKT theory can be exploited to evaluate quantitatively the critical temperature of 2D superconductors in different pairing regimes.