Anomalous high-temperature THz nonlinearity in superconductors near the metal-insulator transition

The interplay of strong disorder and superconductivity is a topic of long-term interest in condensed matter physics. Here we explore the nonlinear THz response of superconducting NbN films close to the 3D metal-insulator transition. For the least disordered samples, the magnitude of the nonlinear $\chi^{(3)}$ response follows the temperature dependence of the superfluid density as expected. In contrast, for high disorder samples near the metal-insulator transition the $\chi^{(3)}$ nonlinearity persists to temperatures as high as even 4 times the $T_c$ of the cleanest sample. We discuss the possible origins of this remarkably large nonlinearity, including the possibility that it arises in an enhancement of the temperature scales of superconductivity close to localization. Our work highlights the importance of finite frequency nonlinear THz experiments in detecting superconducting correlations even into regions where long-range ordered superconductivity does not persist.