The sign of longitudinal magnetoconductivity and the planar Hall effect in Weyl semimetals

Abstract

The manifestation of chiral anomaly in Weyl semimetals typically relies on the observation of longitudinal magnetoconductance (LMC) along with the planar Hall effect, with a specific magnetic field and angle dependence. Here we solve the Boltzmann equation in the semiclassical regime for a prototype of a Weyl semimetal, allowing for both intravalley and intervalley scattering, along with including effects from the orbital magnetic moment (OMM), in a geometry where the electric and magnetic fields are not necessarily parallel to each other. We construct the phase diagram in the relevant parameter space that describes the shift from positive to negative LMC in the presence of OMM and sufficiently strong intervalley scattering, as has been recently pointed out for only parallel electric and magnetic fields. On the other hand, we find that the chiral anomaly contribution to the planar Hall effect always remains positive (unlike the LMC) irrespective of the inclusion or exclusion of OMM, or the strength of the intervalley scattering. Our predictions can be directly tested in experiments, and may be employed as new diagnostic procedures to verify chiral anomaly in Weyl systems.

Longitudinal magnetoconductance and the planar Hall effect in a lattice model of tilted Weyl fermions

“…The reduction of the critical intervalley strength can again be understood as a combination of the two factors like the previous case (i) a finite tilt t 1 z and α i (when γ = π/2) drives the system to change the LMC sign from positive to negative (as seen in Fig. 4), and secondly γ = π/2 along with a finite α i (when t 1 z = 0) drives the system to change LMC sign from positive to negative much below α i = 0.5 [66]. The different shape of the contour (negative LMC filling out the parameter space instead of a curved trapezoid) is essentially because the cones are now tilted along the x-direction and the magnetic field has an x-component to it, which is qualitatively different from the tilt occurring in the zdirection.…”

“…When α i crosses threshold value α c i (t 1 z ) the linear coefficient dominates and LMC switches sign as a function the magnetic field. Note that there is a special case of t 1 z = 0, where the linear coefficient is always zero and the LMC switches sign when α i = 0.5 [66]. However, for even small values of t 1 z , the linear coefficient dominates over the quadratic coefficient and the sign reversal in LMC occurs below α i = 0.5.…”

“…This feature can be understood as a combination of two factors: when γ = π/2, a finite tilt t 1 z and α i drives the system to change the sign of LMC from positive to negative (as seen in Fig. 3), and secondly when γ = π/2 along with a finite α i (even when t 1 z = 0) drives the system to change LMC sign from positive to negative much below α i = 0.5 [66]. The combination of these two assisting factors shapes the zero LMC contour in the current scenario.…”

“…However, a detailed analysis shows that positive longitudinal magnetoconductance is neither a necessary, nor a sufficient condition to prove the existence of chiral anomaly in WSMs. It has now been well established that both positive or negative magnetoconductance can arise from chiral anomaly in WSMs [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66]. In the presence of strong magnetic field, when Landau quantization is relevant, the sign of magnetoconductance depends on the nature of scattering impurities [49][50][51][52][53][54][55].…”