| Summary: | Dynamical behavior of vortices plays central roles in the quantum phenomena of two-dimensional (2D) superconductors. The quantum metallic state, for example, showing an anomalous temperature-independent resistive state down to low temperatures, has been a topical subject in recently developed 2D crystalline superconductors, whose microscopic origin is still under debate. Here, we unveil an interesting aspect of the vortex dynamics in a noncentrosymmetric 2D crystalline superconductor of gated MoS_{2} through the nonreciprocal transport measurement. The second-harmonic resistance R^{2ω} at low temperature with high current indicates the classical vortex flow accompanying the ratchet motion. Furthermore, we found that R^{2ω} is substantially suppressed in the quantum metallic state with the low current region, allowing identification of the quantum and classical ratchet motions of vortices by the magnitude of the second-harmonic resistance. Combining R^{2ω} with the linear resistance R^{ω} allowed us to establish a comprehensive vortex phase diagram for crystalline 2D superconductors with minimal disorder.
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