The spin-dependent Seebeck coefficient for a given spin channel is defined in terms of K0 and K1 calculated for this spin channel, which corresponds to either spin_up or spin_down transmission spectrum. This is now corrected in the 'seebeck_coefficient.py' script enclosed.
The total Seebeck coefficient is not defined correctly in the PRB 2016 paper cited in a previous post. It is neither (S_up + S_down) nor (S_up + S_down)/2 as defined in the PRB paper. The total thermopower is given as (conductance_up S_up + conductance_down S_down)/(conductance_up + conductance_down), see two slides (in the enclosed zip file) with a formal derivation of this formula. These slides also contain a complete set of equations for calculating S, S_up, S_down, conductance_up, conductance_down as well as useful references used to derive these physical quantities.
Enclosed you can find an updated python script that calculates the spin-dependent and total Seebeck coefficient as well as the conductance for spin up and down channels. An important update is that the definition of the Seebeck coefficient sign has been corrected; it is now S = -K1/(K0*e*T), where the elemental charge e>0 (positive). This definition of the thermopower is now consistent with the definition given in a textbook on Solid State Physics by Ashcroft & Mermin, see Chapter 13.
To test the script, one can use an nc-file (Device_New_Configuration.nc in the zip-file) with the spin-dependent transmission spectrum calculated for a 1D carbon chain with parallel magnetization configuration of the electrodes. The description of how to run the script is given in the script header.
NOTE: we are working on updating the thermoelectrics plugin in the VNL to fix the sign problem in the definition of the Seebeck coefficient.
