Broadening of the Berezinskii-Kosterlitz-Thouless superconducting transition by inhomogeneity and finite-size effects

We discuss the crucial role played by finite-size effects and inhomogeneity on the Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional superconductors. In particular, we focus on the temperature dependence of the resistivity, that is dominated by superconducting fluctuations above the BKT transition temperature T₁₊ₓ and by inhomogeneity below it. By means of a renormalization-group approach we establish a direct correspondence between the parameter values used to describe the BKT fluctuation regime and the distance between T₁₊ₓ and the mean-field Ginzburg-Landau transition temperature. Below T₁₊ₓ a resistive tail arises due to finite-size effects and inhomogeneity, that reflects also on the temperature dependence of the superfluid density. We apply our results to recent experimental data in superconducting LaAlO₃/SrTiO₃ heterostructures, and we extract several informations on the microscopic properties of the system from our BKT fitting parameters. Finally, we compare our approach to recent data analysis presented in the literature, where the physical meaning of the parameter values in the BKT formulas has been often overlooked.