Quantum and classical ratchet motions of vortices in a 2D trigonal superconductor

Dynamical behavior of vortices plays central roles in the quantum phenomena of two-dimensional (2D) superconductors. Quantum metallic state, for example, showing an anomalous temperature-independent resistive state down to low-temperatures, has been a common subject in recently developed 2D crystalline superconductors, whose microscopic origin is still under debate. Here, we unveil a new aspect of the vortex dynamics in a noncentrosymmetric 2D crystalline superconductor of MoS$_{2}$ through the nonreciprocal transport measurement. The second harmonic resistance $R^{2w}$ at low temperature with high current indicates the classical vortex flow accompanying the ratchet motion. Furthermore, we found that $R^{2w}$ is substantially suppressed in the quantum metallic state with low current region, allowing identification of the quantum and classical ratchet motions of vortices by the magnitude of the second harmonic generation. This suggests that nonreciprocal transport measurement can be a powerful tool to probe the vortex dynamics in noncentrosymmetric 2D superconductors.