Anomalous terahertz nonlinearity in disordered s-wave superconductor close to the superconductor-insulator transition

Detection of the Higgs mode in superconductors using nonlinear terahertz spectroscopy is a key area of interest in condensed matter physics. We investigate the influence of disorder on the nonlinear terahertz response and the Higgs mode in NbN thin films with varying Ioffe-Regel parameters ($k_Fl$). In strongly disordered films near the superconductor-insulator transition (SIT), we observe an anomalous third-harmonic generation (THG) signal above $T_c$, which is absent in both cleaner superconducting and non-superconducting counterparts. The persistence of this normal-state THG signal in a high magnetic field excludes superconducting fluctuations as its origin. Below $T_c$, the THG intensity increases sharply, indicating a dominant contribution from the driven Higgs mode. The THG spectrum of the strongly disordered sample exhibits a broadened, multi-peak structure, which we attribute to quantum path interference between distinct channels involving unpaired electrons and Cooper pairs within emergent superconducting islands. Our findings not only demonstrate how disorder tunes the nonlinear terahertz response but also uncover a strong coupling between electrons responsible for normal-state THG and the superconducting Higgs mode below $T_c$ in strongly disordered samples.