Magnetoconductivity in Weyl semimetals: Effect of chemical potential and temperature

Abstract

We present detailed analyses of magnetoconductivities in a Weyl semimetal within the Born and self-consistent Born approximations. In the presence of charged impurities, linear magnetoresistance can occur when the charge carriers are mainly from the zeroth (n = 0) Landau level. Interestingly, the linear magnetoresistance is very robust against changes of temperature as long as the charge carriers come mainly from the zeroth Landau level. We denote this parameter regime as the high-field regime. On the other hand, the linear magnetoresistance disappears once the charge carriers from the higher Landau levels can provide notable contributions. Our analysis indicates that the deviation from linear magnetoresistance is mainly due to the deviation of the longitudinal conductivity from 1/B behavior. We found two important features of the self-energy approximation: (i) A dramatic jump of σ xx , when the n = 1 Landau level begins to contribute charge carriers, which is the beginning point of the middle-field regime, when decreasing the external magnetic field from high field; (ii) in the low-field regime, σ xx exhibits B −5/3 behavior, causing the magnetoresistance ρ xx to exhibit B 1/3 behavior. A detailed and careful numerical calculation indicates that the self-energy approximation (including both the Born and the self-consistent Born approximations) does not explain the recent experimental observation of linear magnetoresistance in Weyl semimetals.

Magnetoresistance of a three-dimensional Dirac gas

“…This is consistent with the ∆ = 0 result in Ref. 31. In the high magnetic field limit ( B → 0) only the zeroth Landau level contributes and the equation simply yields…”

“…He only studied the case with zero chemical potential and at very high magnetic fields where only the zeroth Landau level contributes to the conductivity. More recent studies [30][31][32] revisited this calculation in more detail. It was shown that the screened Coulomb impurities used by Abrikosov are crucial for reproducing the linear behavior 30 , since a completely different behavior is achieved for the simple case of short-range scatterers.…”

“…In Ref. 31 Xiao et al calculated the scattering rates for different Landau levels, and they showed that there is Landau level dependence of the scattering rate. In arXiv:1811.06200v1 [cond-mat.mes-hall] 15 Nov 2018 their result they recovered the linear magnetoresistance for high magnetic fields, but at low fields they obtained a B 1/3 behavior.…”

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.…”

“…Using this continuum model previous theoretical papers investigate the magnetoconductivity in the massless [39][40][41] and massive [42][43][44] cases. The experimentally seen linear magnetoresistance is recovered [39][40][41][42] only if screened Coulomb impurities are used. These studies use the linear response theory using the Born approximation 45 to evaluate the self-energy.…”