I want to calculate the thermoelectric properties of a material via BoltzTrap. Should I calculate the effective mass at the crossing point? What if there are two different crossing points at the same band?
If there are two different crossing points at the same band, then it is necessary to calculate the effective mass at both points. In this case, the effective mass at each crossing point may contribute differently to the transport properties, depending on the details of the band structure and the Fermi level.
It is also possible that the two crossing points may merge into a single band extrema, in which case only one effective mass needs to be calculated. In any case, the calculation of the effective mass is an important step in determining the thermoelectric properties of a material via BoltzTrap.
Here is a reference that you may find helpful:
Madsen, G. K. H., and Singh, D. J. (2006). BoltzTraP. A code for calculating band-structure dependent quantities. Computer Physics Communications, 175(1), 67-71.
This paper describes the BoltzTraP code, which is widely used for calculating transport properties of materials, and provides a detailed explanation of the theory and methodology behind the code. In particular, Section 3 of the paper discusses the calculation of effective mass and its role in determining the transport properties of a material.
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