Delayed switching in a phase-slip model of charge-density-wave transport

We analyze the dynamics of the depinning transition in a many-body model of charge-density-wave (CDW) transport in switching samples. The model consists of driven massless phases with random pinning and a coupling term that is periodic in the phase difference, thus allowing phase slip. When the applied field in our model exceeds the depinning threshold by a small amount, there is a delay before the appearance of a coherent moving solution. This delay is also seen experimentally in switching CDW materials. We find that close to threshold the switching delay is approximately proportional to the inverse distance above threshold. Analytical results agree with numerical integration of the model equations. Results are also compared to available experimental data on delayed switching.