Linear and non-linear ac response of the stochastic classical model for sliding charge density waves

A comprehensive study of the ac response properties of the classical stochastic model for sliding charge density waves (CDW) in quasi one-dimensional metals is made by numerically solving the associated Fokker-Planck equation. Above the conductivity threshold a noise mechanism is indispensable to give finite line widths to the resonances of the applied ac signal of frequency with the narrow band noise frequency _OSC inherent in the model. In the present investigation a current noise of strengthT_Nproportional to the CDW current is used in the Fokker-Planck equation in order to model the broad band current noise frequently observed above threshold. The present model thus incorporates three characteristic frequency scales: _OSC,T_N,and a crossover frequency _OSC. Results are evaluated for the ac conductivity (;E₀,E) as function of frequency , dc bias electric fieldE₀ and ac signal field strengthE. ForE0 the linear ac response is obtained by a separate treatment of the Fokker-Planck equation. The resonances near =_OSC are studied in detail. Strong ac signals reduce the response at the fundamental resonance and lead to a harmonic interference structure nearn=_OSC. The overall agreement of the present results with recent measurements of the linear ac response is not good. In reality our results seem to be superimposed on a background not reproduced by the classical model with one cross over frequency. However, the peak in Im (;E₀,E=0) vs.E₀, when the narrow band noise frequency is near , is well reproduced. The spectral width of this peak which corresponds to the inductive dip in the susceptibility is studied as function of current noise strengthT_N.The results stress the need for a complete Fokker-Planck treatment sinceT_Nis not simply related to the line width.