  We present a comprehensive numerical study of the gating-induced
insulator-to-metal transition in the charge density wave (CDW) state of the
Holstein model. Large-scale Brownian dynamics method with forces computed from
nonequilibrium Green's function method is employed to simulate the
spatio-temporal dynamics of the CDW state. We show that a threshold voltage,
determined by the energy of the in-gap edge modes, is required to induce the
instability of the CDW. A large bias voltage, on the other hand, induces a
sudden transition to the metallic state similar to a dielectric breakdown. At
intermediate voltages, our extensive simulations show that the transition to
the low-resistance state is initiated by the nucleation of a thin conducting
layer at the gating electrode. The resultant metal-insulator interface is then
swept over the system by the voltage bias, resulting in a growing metallic
domain. We further characterize the voltage and temperature dependence of the
domain-wall dynamics.
