Superconducting phase transitions in ultrathin TiN films

We investigate transition to the superconducting state in the ultrathin titanium nitride films on approach to superconductor-insulator transition. Building on the complete account of quantum contributions to conductivity, we demonstrate that the resistance of thin superconducting films exhibits a non-monotonic temperature behaviour due to the competition between weak localization, electron-electron interaction, and superconducting fluctuations. We show that superconducting fluctuations give rise to an appreciable decrease in the resistance even at temperatures well exceeding the superconducting transition temperature, T_c, with this decrease being dominated by the Maki-Thompson process.The transition to a global phase-coherent superconducting state occurs via the Berezinskii-Kosterlitz-Thouless (BKT) transition, which we observe both by power-law behaviour in current-voltage characteristics and by flux flow transport in the magnetic field. The ratio T_{BKT}/T_c follows the universal Beasley-Mooij-Orlando relation. Our results call for revisiting the past data on superconducting transition in thin disordered films.