Appendix GHall Factor
A magnetic field Hz in the z‐direction applied perpendicularly to an electric current ix in the x‐direction will produce an electric field Ey in the y‐direction. Then the Hall coefficient RH is defined by
In order to obtain the Hall coefficient, we have to solve the Boltzmann transport equation under the relaxation time approximation with the magnetic field. The exact solution, assuming a parabolic single band, eventually leads to the electrical conductivity, Seebeck coefficient, and electronic thermal conductivity, where the detailed derivation can be found in Putley [1] and Goldsmid [2]. Here just the results are presented. The electrical conductivity is
The Seebeck coefficient is
The electronic thermal conductivity is
where
τ is the carrier relaxation time, and g is the carrier density of states. Now we ...
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