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

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

vs. vs. (s=1 case): [Download]

vs. vs. (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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