Origin of the superconductor-insulator transition in disordered two-dimensional films

Abstract

Theory predicts the superconductor-to-insulator transition (SIT) to emerge from the competition between Anderson localization, which tends to localize single-particle wavefunctions, and superconductivity, which establishes long-range correlations in the superconducting order parameter. In two-dimensional (2D) superconducting films, the transition temperature $T_{\text{c}}$ at which resistance vanishes, $R_{\square }(T_{\text{BKT}})=0$, is set by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism and satisfies $T_{\text{BKT}}<T_{c0}$, where $T_{c0}$ is the mean-field transition temperature. In weakly disordered samples $T_{\text{BKT}}\lesssim T_{c0}$, whereas increasing disorder drives $T_{\text{BKT}}\ll T_{c0}$ near the SIT. Whether the finite-temperature transition retains its BKT character throughout this crossover remains an open question. Here, we investigate the evolution of both sheet resistance $R_{\square }(T)$ and superfluid stiffness $J_s(T)$ over a wide range of disorder strength $W$. We establish that even near the SIT, the finite-temperature transition from the superconducting to the resistive state remains of BKT type. However, as disorder approaches the critical value, the zero temperature superfluid phase stiffness, $J_s(0)$, is found to vanish rapidly while $T_{c0}$ remains finite, which we attribute to quantum phase fluctuations as the drive for the zero-temperature transition. Three decades after its experimental discovery by Haviland, Liu, and Goldman, our measurements clarify the origin of the SIT in 2D films.