Thermal fluctuations and ac response of weakly pinned charge density waves

Abstract

The Fukuyama-Lee theory for the ac response σ(ω) of weakly pinned charge density waves is extended to include thermal fluctuations. The equation of motion for the local phase includes an extrinsic damping and a distinction is made between static and dynamic parameters in it. It is split into static, thermally fluctuating and response contributions to the phase, respectively. The static problem is treated using a result from Feigel'man's theory which provides a revised value for the weak pinning constant. The impurity averaging of the response equation is performed using the simplifying statistical properties of the stochastic pinning force following Bleher's recent work. The main emphasis is on the treatment of the thermal fluctuations via a thermal field δΦth. The non-linear Langevin equation for δΦth is linearized and further simplified by an RPA type approximation which eliminates the impurity fluctuations from δΦth. The resulting equation is solved exactly. It is shown that the correlation function of the thermal field decays initially with a short time constant. This allows to treat the thermal fluctuations on an equal footing with the impurity fluctuations in the self-consistent Born approximation. The main contribution of the thermal fluctuations results in powers of a thermal factor exp(-〈δΦth2〉/2) to the first and second order self energies of the phason Green's function. Numerical results due to these modifications are given for σ(ω,T). It is found that the absorption peak in Re σ(ω) broadens and shifts to lower frequencies when the temperature is raised. The corresponding treatment for three spatial dimensional is indicated. The thermal factor is evaluated for this case and differences to Maki's result are noted. The questions of analyticity and conductivity sum rule are also dealt with.