Magnetoresistance of a three-dimensional Dirac gas

Abstract

We study the transversal magnetoconductivity and magnetoresistance of a massive Dirac fermion gas. This can be used as a simple model for gapped Dirac materials. In the zero mass limit the case of gapless Dirac semimetals is also studied. In the case of Weyl semimetals, to reproduce the non-saturating linear magnetoresistance seen in experiments, the use of screened charged impurities is inevitable. In this paper these are included using the first Born approximation for the self-energy. The screening wavenumber is calculated using the random phase approximation with the polarization function taking into account the electron-electron interaction. The Hall conductivity is calculated analytically in the case of no impurities and is shown to be perfectly inversely proportional to the magnetic field. Thus, the magnetic field dependence of the magnetoresistance is mainly determined by σxx. We show that in the extreme quantum limit at very high magnetic fields the gapped Dirac materials are expected to have σxx ∝ B −3 leading to xx ∝ B −1 , in contrast with the gapless case where σxx ∝ B −1 and xx ∝ B. At lower fields we find that the effect of the mass term is negligible and in the region of the Shubnikov-de Haas oscillations the two systems behave almost identically. We suggest a phenomenological scattering rate that is able to reproduce the linear behavior at the oscillating region. We show that in the case of the scattering rate calculated using the Born approximation the strength of the relative permittivity and the density of impurities affects the magnetic field dependence of the conductivity significantly.

Thermoelectric transport coefficients of a Dirac electron gas in high magnetic fields

“…The screened charged impurities are necessary to reproduce the B −1 dependence of the conductivity and thus the linear magnetoresistance, consistently with previous studies for the 2 × 2 Weyl Hamiltonian [39][40][41] . We calculated the vertex correction and showed that it is negligible for realistic parameter regimes, which justifies the assumptions in previous studies 39,40,42 . In the case of finite mass term we showed that the high field limit is qualitatively the same as in the massless case i.e.…”

“…We show the analytic asymptotic behaviors of the chemical potential the screening wavenumber and the scattering rate based on the results obtained in Ref. 42. The important energy scale is ∆ B = 2π 2 n e 2 B and the mass term ∆ becomes relevant when ∆ B < ∆.…”

“…In the case of σ xx impurities are necessary to get a non-zero result. In our previous study 42 we have shown that the magnetic field dependence of the scattering rate directly affects the magnetic field dependence of the conductivity. The screened charged impurities are necessary to reproduce the B −1 dependence of the conductivity and thus the linear magnetoresistance, consistently with previous studies for the 2 × 2 Weyl Hamiltonian [39][40][41] .…”

“…39 and 42. The scattering rate in the Landau level representation (Γ n = − Im{Σ n }) becomes diagonal and can be expressed as 42 :…”

“…We calculate the chemical potential, the screening and the scattering rate and we give their asymptotic behavior at high magnetic fields based on our results in Ref. 42. Then, we move on to the calculation of the thermoelectric transport coefficients.…”