Weyl semimetals such as the TaAs family (TaAs, TaP, NbAs, NbP) host quasiparticle excitations resembling the long sought after Weyl fermions at special band-crossing points in the band structure denoted as Weyl nodes. They are predicted to exhibit a negative longitudinal magnetoresistance (LMR) due to the chiral anomaly if the Fermi energy is sufficiently close to the Weyl points. However, current jetting effects, i.e. current inhomogeneities caused by a strong, field-induced conductivity anisotropy in semimetals, have a similar experimental signature and therefore have hindered a determination of the intrinsic LMR in the TaAs family so far. This work investigates the longitudinal magnetoresistance of all four members of this family along the crystallographic $a$ and $c$ direction. Our samples are of similar quality as those previously studied in the literature and have a similar chemical potential as indicated by matching quantum oscillation (QO) frequencies. Care was taken to ensure homogeneous currents in all measurements. As opposed to previous studies where this was not done, we find a positive LMR that saturates in fields above 4 T in TaP, NbP and NbAs for $B||c$. 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, independent on the distance of the Weyl node to the Fermi energy. The TaAs family of compounds is the first to show such a simple LMR without apparent influences of scattering anisotropy. 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. We discuss a weak antilocalisation scenario as an alternative interpretation than the chiral anomaly for these results, since it can fully account for the overall field dependence.
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