“…Between them, there exists a secondorder dynamical phase transition, called as the "depinning transition" [1,2,3,4,5,6,7,8]. For several decades, the depinining transition has been the focus of the experimental and theoretical research, which are common to a wide variety of phenomena, including the liquid invasion in porous media [9], the contact line in wetting [10], the vortices in type-II superconductors [11,12], the charge-density waves [13], the fracture propagation [14,15], the dislocation dynamics in crystal plasticity [16], and the domain-wall motions in ferromagnetic and ferroelectric materials [17,18,19,20]. Practically, understanding the fundamental mechanism of the depinning transition plays an important role in predicting and controlling the motions of the magnetic domain walls in nanomaterials [21,22,23], thin films [8,24], and semiconductors [20,25], which is key to the realization of the new classes of potential nonvolatile storage-class devices [26,27].…”