Corrections to the magnetoresistance formula for semimetals with Dirac electrons: the Boltzmann equation approach...

The magnetoresistance (MR) in semimetals with Dirac (or Weyl) electrons and free holes is investigated on the basis of the Boltzmann theory. The MR is modified from the conventional results with free electrons and holes in a very complex way due to the correction of the Dirac dispersion. The obtained formula explicitly includes the magnetic field dependence, which is very useful for the analysis of experimental results. In order to verify the validity of our results, the results obtained by the Boltzmann approach are compared with those by the Kubo theory. It is revealed that, by taking into account the field dependence of carrier density, the MR obtained by the Boltzmann theory almost perfectly agrees with that based on the Kubo theory even in the high-field region (in the quantum limit) except for the quantum oscillations. It is also shown that the MR in semimetals increases linearly with respect to the field in the quantum limit due to the drastic change of the carrier density, which is a significant characteristic of semimetals.