In the Drude formula, the scattering rate is taken as a constant. But in the extended Drude formula, the scattering rate becomes frequency dependent. Is this only reason for frequency dependent term due to the spin-scattering, particle interactions? If yes, then how can one derive the extended Drude formula?
Consult Chapter 9 (Optical Properties of Solids) of the book by Gerald D. Mahan, Many-Particle Physics, 3rd ed. (Kluwer Academic / Plenum, New York, 2000). See also the following two on-line lecture notes by M.S. Dresselhaus (see in particular Chapter 2 in Part II):
http://web.mit.edu/course/6/6.732/www/6.732-pt1.pdf
http://web.mit.edu/course/6/6.732/www/6.732-pt2.pdf
This is just a quick response that might help on the way. Below plasma frequency, the conductivity of Drude electron(s) becomes quickly a constant - sigmadc=Re{sigma}. For metals plasma frequency can be as high as some 10^13 Hz ,for ultra pure Silicon as low as some 10^9 Hz. Below these frequencies, nothing is frequency dependent. The scattering rates/relaxation times/the mobilities might be strong functions of temperature (the effect of quantum mechanical statistics and proper consideration of phonon scattering rates), but they are not time dependent until frequencies where they are not well defined . This is in the high GHz region even for (very slow) polaron motion, where the hopping rates (not the scattering rates) are already time independent. It might be that the electron or hole spin scattering mechanism might extend to these "low" frequency regions, but I doubt it. If I am wrong, I would be very interested to hear more. Usually, in the various transport theories, the spin effect are not really relevant .
With best regards
Petr
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