  Superconductor-insulator transition is one of the remarkable phenomena driven
by quantum fluctuation in two-dimensional (2D) systems. Such a quantum phase
transition (QPT) was investigated predominantly on highly disordered thin films
with amorphous or granular structures using scaling law with constant
exponents. Here, we provide a totally different view of QPT in highly
crystalline 2D superconductors. According to the magneto-transport measurements
in 2D superconducting ZrNCl and MoS2, we found that the quantum metallic state
commonly observed at low magnetic fields is converted via the quantum Griffiths
state to the weakly localized metal at high magnetic fields. The scaling
behavior, characterized by the diverging dynamical critical exponent (Griffiths
singularity), indicates that the quantum fluctuation manifests itself as
superconducting puddles, in marked contrast with the thermal fluctuation. We
suggest that an evolution from the quantum metallic to the quantum Griffiths
state is generic nature in highly crystalline 2D superconductors with weak
pinning potentials.
