by Maria Troppenz, Patrick Dieu & Santiago Rigamonti for exciting nitrogen
0. Define relevant environment variables and download scripts
Read the following paragraphs before starting with the rest of this tutorial!
Before starting, be sure that relevant environment variables are already defined as specified in How to set environment variables for tutorials scripts.
From now on the symbol $ will indicate the shell prompt.
2. Theoretical background for calculating the transport coefficients by using the Boltzmann equation
The efficiency of a thermoelectric material is determined by the dimensionless figure of merit :
(1)ZT depends on the temperature $T$ and the transport coefficients: Electrical conductivity $\sigma$, Seebeck coefficient $S$, and the thermal conductivity $\kappa$, which is given by the sum of electronic contributions $\kappa_e$ and the lattice contribution $\kappa_l$. The coefficients $\sigma$, $S$ and $\kappa_e$ are mainly related to the electronic structure of the material, whereas $\kappa_l$ is related to the lattice.
Solving the Boltzmann equation in the constant relaxation time approximation (see 1), the transport coefficients can be calculated as follows:
(2)Here, $\mu$ is the chemical potential and $e$ the electron charge, and $ \partial f_0 / \partial \epsilon$ the derivative of the Fermi distribution function $f_0 = [ (\exp( (\epsilon\mu) / k_B T) +1 ]^{1}$.
Using the equation above, the electronic thermal conductivity $\kappa_e$ is obtained by the relation $\kappa_e = \kappa_0  T \sigma S^1$. The lattice part of the thermal conductivity still remains to be calculated by other methods.
The kernal function $\Xi (\epsilon)$ of the three transport coefficients is the transport distribution function,
It is calculated from the group velocities ${ \pmb{v} }_{ \pmb{k} }$ of the charge carriers with cystal momentum $\pmb{k}$ and the corresponding carrier's lifetime $\tau_{\pmb{k}}$, both summed over the first Brillouin zone. In the constant relaxation time approximation, the $\tau$ is independent from $\pmb{k}$.
3. Transport coefficients of Bi_{2}Te_{3}
<input> <title>Bulk Silicon: Plot example</title> <structure speciespath="$EXCITINGROOT/species"> <crystal scale="10.26"> <basevect>0.0 0.5 0.5</basevect> <basevect>0.5 0.0 0.5</basevect> <basevect>0.5 0.5 0.0</basevect> </crystal> <species speciesfile="Si.xml"> <atom coord="0.00 0.00 0.00"></atom> <atom coord="0.25 0.25 0.25"></atom> </species> </structure> <groundstate do="fromscratch" ngridk="5 5 5" rgkmax="8" gmaxvr="14" xctype="GGA_PBE_SOL"> </groundstate> </input>
... <properties> <momentummatrix fastpmat="true"/> <boltzequ nwtdf="1500" windtdf="1.0 0.5" windtemp="300 1200" tgrid="90" windmu="0.2026454363 0.2106454363" mugrid="3" tevout="true" tsiout="true"> <condcomp>1 1</condcomp> <condcomp>2 2</condcomp> <condcomp>3 3</condcomp> </boltzequ> </properties> ...

$ PLOTlossfunction.py LOSS_FXCRPA_OC11_QMT001.OUT.xml LOSS_FXCALDA_OC11_QMT001.OUT.xml