Magnetoresistance in Weyl-semimetals

Measurements of the longitudinal magnetoresistance are highly non-trivial, when the anisotropy of the conductivity changes with magnetic field. We investigate this classical effect in the proposed Weyl semimetals and were able to show that the field concentrates the current to a narrow path through the sample in commonly used experimental conditions. We try to overcome this problem in order to determine the intrinsic longitudinal magnetoresistance in Weyl semimetals and hence detect the chiral anomaly.

In compensated semimetals the conductivity component perpendicular to the magnetic field decreases strongly in magnetic field due to the orbital effect. On the other hand, the longitudinal conductivity (current parallel to the magnetic field) changes only slightly compared to that, so that the conductivity tensor becomes highly anisotropic in a magnetic field. As nicely explored by K. Yoshida (K. Yoshida, J. Phys. Soc. Jap. **41**, 574 (1976) and later papers), this effect leads to inhomogeneous currents in the sample when the current contacts are smaller than its cross section. **Fig. 2** shows the potential distribution for given values of the conductivity anisotropy A. We study this effect in the resistance and are able to show that it can lead to a decreasing apparent longitudinal magnetoresistance with field, just as expected for the chiral anomaly (see the figure at the top). This puts strong constrains on the experimental determination of the longitudinal magnetoresistance like perfect current contacts over the whole cross section of the sample and a perfect alignment of the magnetic field.

With the aim to find evidence for the chiral anomaly, a signature of Weyl fermions, we investigated the longitudinal magnetoresistance in TaAs, TaP, NbAs and NbP by ensuring homogeneous currents. We find the intrinsic LMR to depend strongly on the crystallographic orientation of the current. The LMR along the c direction rises and saturates for fields above 4 T as depicted in **Fig. 1**. Using Fermi-surface geometries from band-structure calculations that had been confirmed by experiment, we show that this is the behaviour expected from a classical, purely orbital effect. The dashed lines are fits of the orbital magnetoresistance. In configurations where the orbital effect is small, i.e., for B||a in NbAs and NbP, we find a non-monotonous LMR, including regions of negative LMR. A weak-antilocalization scenario can fully account for the overall field dependence, even better than including a chiral anomaly instead. The longitudinal transport in the TaAs family can therefore be explained without including any chiral or topological effects, suggesting that their signatures are either absent or very small.