Quantum phase transition in NbN superconducting thin films

We systematically investigated the low-temperature transport properties of two series of NbN epitaxial films. The first series of films with thickness ranging from $\ensuremath{\sim}2.0$ to $\ensuremath{\sim}4.0\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ are two-dimensional (2D) with respect to superconductivity, while another series with thickness around $\ensuremath{\sim}20\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ is quasi-three-dimensional (quasi-3D). Those 2D NbN films undergo a superconductor-insulator transition (SIT) with decreasing film thickness, and the critical sheet resistance for the SIT is close to the quantum resistance of Cooper pairs $h/4{e}^{2}$ (6.45 $\mathrm{k}\mathrm{\ensuremath{\Omega}}$). Besides the Berezinski-Koterlitz-Thouless transition, a magnetic-field-driven SIT is observed in those 2D superconducting films ($2.6\phantom{\rule{0.16em}{0ex}}\mathrm{nm}\ensuremath{\lesssim}t\ensuremath{\lesssim}4.0\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$). The field-driven quantum metal state does not appear in these 2D superconducting films. However, it is found that both in the 2D and quasi-3D superconducting films the low-temperature magnetoresistance isotherms do not cross at a very narrow region (generally treated as a single point) but cross at a well-distinguished wide region. The dynamical critical exponent obtained by analyzing these magnetoresistance isotherms is divergent as the quantum critical point is approached. The divergence of the dynamical critical exponent near the critical point is consistent with the quantum Griffiths singularity behavior. Our results suggest that the quantum Griffiths singularity can also occur in a 2D superconductor with SIT or a quasi-3D superconductor. The origin of the infinite-randomness point of the quantum phase transition is attributed to the emergence of superconducting rare regions due to the quench disorder in low temperatures.