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

TL;DR

This paper investigates how finite-size effects and inhomogeneity influence the BKT transition in 2D superconductors, linking theoretical models with experimental data to better understand the microscopic properties of systems like LaAlO3/SrTiO3 heterostructures.

Contribution

It introduces a renormalization-group approach connecting BKT fluctuation parameters with the mean-field transition temperature, accounting for finite-size and inhomogeneity effects.

Findings

Finite-size effects cause a resistive tail below T_BKT.

Inhomogeneity affects the temperature dependence of superfluid density.

The approach provides insights into microscopic properties from experimental data.

Abstract

We discuss the crucial role played by finite-size effects and inhomogeneity on the Beresinkii-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 $T_{BKT}$ 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 $T_{BKT}$ and the mean-field Ginzburg-Landau transition temperature. Below $T_{BKT}$ a resistive tail arises due to finite-size effect and inhomogeneity, that reflects also on the temperature dependence of the superfluid density. We apply our results to recent experimental data in superconducting LaAlO$_3$/SrTiO$_3$ 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.