Locked-to-running transition in the two-dimensional underdamped driven Frenkel-Kontorova model

We study the nonlinear dc response of a two-dimensional underdamped system of interacting atoms subject to an isotropic periodic external potential with triangular symmetry. We consider various values of the effective elastic constant of the system, two different atomic interaction potentials, and different concentrations of atoms. In the case of a closely packed layer, when its structure is commensurate with the substrate, there is a locked-to-running transition as a function of the driving force, whose mechanism depends on the effective elastic constant. For a low elastic constant, where the layer is weakly coupled, the transition is achieved via the creation of an avalanche of moving particles that leaves a depleted region in its wake. On increasing the effective elastic constant the depleted region becomes less marked and there is a crossover to a scenario in which an island of moving particles nucleates the transition. In the case of a partially filled atomic layer, several dynamical phase transitions between states with different atomic mobility are observed. The mobility of atoms as a function of the external force can vary nonmonotonically with increasing force. For the case of a small external damping, the system can be trapped at a large force in an immobile metastable state, thus demonstrating a ``fuse-safety device'' on an atomic scale.