Interference effects in nonlinear charge-density-wave dynamics

The main features of nonlinear charge-density-wave (CDW) transport in an external dc-ac field are shown to be the natural consequences of resonant phase-slip diffusion. This process is treated numerically within the time-dependent Landau-Ginzburg model, developed by Gor’kov. The resonances in the ac field are manifested as Shapiro steps in the I-V characteristics, present at all rational ratios of the internal frequency of current oscillations and external ac frequency. The origin of Shapiro steps, and their form and heights, are considered in detail. In particular, it is shown that close to resonances the phase-slip voltage acquires a highly nonsinusoidal modulation which leads to the appearance of low-frequency and satellite peaks in the Fourier spectrum. Taking into account the interference of adjacent phase slips and the segment or domain structure of physical samples, we interpret the finite width of steps, side wings, synchronization, incomplete and complete mode locking, and some other effects observed in numerous experiments of ${\mathrm{NbSe}}_3$ and other quasi-one-dimensional materials with the CDW order.