Harmonic mixing by weakly pinned charge density waves

Third order harmonic mixing voltageE ₀ in case of frequency matching, =₂–₁=0, and third order pseudo harmonic mixing currentj() in the detuned case, 0, are evaluated for the one-dimensional Fukuyama-Lee-Rice model for weakly pinned charge density waves in the region of sub-threshold bias electric fields. After a perturbation expansion of the phase response to the ac driving fields the impurity averaging is performed diagrammatically. Specific statistical properties of the charge density wave phase in the weak pinning limit and a non-trivial result for the pinning of the static phase are utilized to expressE ₀ andj() in terms of the dielectric function (). A recent evaluation of () within the self-consistent Born approximation is used to present the results explicitly in a number of diagrams. In comparison to the overdamped anharmonic oscillator the following differences are found: Randomness leads to interference contributions which increase the amplitudes and decrease the phase shifts. The more realistic form for () at lower frequencies lead to a downward shift in the maximum ofj() when ₁ is decreased below the cross-over frequency _c . The present theory retains inertia in the dynamical equations and remains valid for frequencies near and above the pinning frequency. It fails, however, for small frequencies _{1 c} due to the neglect of metastable states and screening.