Chiral anomaly and planar Hall conductance in pseudospin-$1$ Fermions

Abstract

Positive longitudinal magnetoconductance (LMC) and planar Hall conductance (PHC) are hallmark transport signatures of the chiral anomaly in Weyl semimetals. Recent theoretical developments have extended Weyl fermions to multifold Fermionic systems with higher-pseudospin quasiparticle excitations, motivating the study of their magnetotransport properties. Here, we employ semiclassical Boltzmann transport theory within the relaxation-time approximation to investigate magnetotransport in pseudospin-1 Weyl semimetals, incorporating momentum-dependent scattering, orbital magnetic moment corrections, and charge-conservation constraints. To obtain a finite PHC, we break azimuthal symmetry through either a generic tilt of the quasiparticle dispersion or a finite misalignment between the electric and magnetic fields. In the untilted case, the PHC is positive and scales quadratically with magnetic field strength. Increasing the scattering strength induces a sign reversal of the PHC, producing a transition from positive to negative values. The PHC further exhibits the characteristic angular dependence $\sin 2γ$, where $γ$ is the angle between the magnetic field and the $x$-axis. Tilt qualitatively alters this behavior: tilt along the $x$- and $z$-directions changes the angular response to $\sinγ$ and $\cosγ$, respectively, generating strong anisotropy in the planar Hall signal. Moreover, the PHC shows a nonmonotonic dependence on tilt magnitude, revealing the interplay between tilt-induced symmetry breaking and chiral-anomaly-driven transport. Our results provide experimentally accessible signatures of multifold fermions and a framework for interpreting magnetotransport measurements in candidate materials of space groups 199, 214, and 220.