It depends on which model you use to fit your data. The general procedure is to used the least square method for calculations. Use Matlab or similar softwares to write a program to fit your data.

Just a word of warning. This is one of the fundamental fallacies in physics (both experimental and "theoretical") of localised transport (diffusional, (multi-phonon) polaron and other hopping of localised charges). Jump rate - hopping mobility, is NOT frequency dependent until some GHz region even in the polaron case. Number of hops per second has nothing to do with frequency dependence of measured impedance, it just determines the dc value of measured current (the dc conductivity of the sample).

Looking at your data (incomplete !!, the imaginary part is missing), it is not clear at all whether you are looking at the bulk or at the combined effect of the bulk and interface regions. Your impedance in the entire frequency region measured has to scale with thickness of the sample, before you can embark on the analysis in terms of various bulk hopping "models". Twice the thickness, twice the real part of the measured impedance and half the measured real part of the capacitance. If this is so, you measure bulk properties. 

The apparent frequency dependence of your complex "conductivity" is a result of two physical processes taking place in parallel - the dc current from the free(hopping) charges and the polarisation current from the bound charges - these two currents are 90 degrees out of phase with the respect to each other .-> therefore frequency dependence of the measured conductivity. Your data indicate a slow, frequency dependent polarisation process, nothing necessarily to do with hopping motion !

Because of the above general comments, I would be very sceptical to interpret the intercept of the conductivity ~ w^s line with the dc conductivity line as "hopping frequency.

Sorry for not helping, but I hope  this might help as well.

With best regards

Petr

Petr Viscor, interesting comment. Just like Kotagiri, who wrote this question, I'm working on the same analysis, trying to find hopping characteristics from AC conductivity data (1 Hz - 5 MHz). For now, the papers I read about this (Pollack & Geballe (1961), Bisquert & Garcia-Belmonte (2003), etc.) work with the same frequency ranges for their analysis.

Since you suggest to go to GHz frequencies, can you recommend some literature on AC conductivity analysis?

Thanks in advance.

Dear Robin,

My suggestion was not to go necessarily to GHz range of frequencies with your measurements, my point was that until GHz frequencies, that is below ~1 GHz, you can assume that the dc conductivity is constant and frequency independent. And that is the necessary condition to derive various hopping parameters from the measured impedance, if, what you measure, is the bulk impedance.

As far as the literature is concerned , I am not very good at searching, and therefore the best one to ask to suggest the best sources.

Therefore, please look at my recent publication dealing with AC conductivity (Electrical Impedance Spectroscopy) and analysis. The article is a general one, but it touches on the question of the density and the mobility of mobile electrical charges in anything:

Viscor&Viscor : El.Imp.Spectroscopy: "The First Principles" analysis of....,

in Pure and Applied Chemistry 91(11) (2019), p.1837-1856.

See also references there. The monograph by Mott&Davis is probably the most useful for you at this point.

with best regards

Petr

Thanks a lot for your comment and your interesting and extensive paper, Petr.

Best, Robin

You are welocomed Robin, I hope it will help.

With best regards

Petr