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Calculating Seebeck-Conductivity relations

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Once in a while, people ask how to calculate or plot the Seebeck coefficient (S) vs. electronic conductivity (\sigma) relations reported in my papers. The quantities are parameterized through the (reduced) Fermi-level (\eta), so one should calculate S and \sigma separately for a range of \eta's. Then S and \sigma can be grouped pairwise for each \eta to find the relation. An explicit equation between S and \sigma only exists in the limits of very small or large \eta values.

For people who don’t want to bother with doing Fermi-integrals, here are some values tabulated in Excel sheets:


\eta vs. |S| vs. \sigma (s=1 case): [Download]

\eta vs. |S| vs. \sigma (s=3 case): [Download]


The notation s=1 and s=3 follows that used in [Nature Materials 16 252–257 (2017).] and [Physical Review B 97 235201 (2018).]. Conductivity should be scaled with a coefficient. Seebeck coefficients are tabulated as absolute values (i.e. thermopower).

It has been a while since these papers were published, but I was reminded by another email asking about this Seebeck-conductivity calculation. So I decided to just post it here. Hope this helps!

Last modified: Aug. 13, 2021

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