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We theoretically address the effects of strong magnetic fields inthree-dimensional Weyl semimetals (WSMs) built out of Weyl nodes with amonopole charge $n$. For $n=1$, $2$, and $3$ we realize single, double, andtriple WSM, respectively, and the monopole charge $n$ determines the integertopological invariant of the WSM. Within the linearized continuum description,the quasiparticle spectrum is then composed of Landau levels (LLs), containingexactly $n$ number of chiral zeroth Landau levels (ZLLs), irrespective of theorientation of the magnetic field. In the presence of strong backscattering,for example, (due to quenched disorder associated with random impurities),these systems generically give rise to longitudinal magnetotransport.Restricting ourselves to the quantum limit (and assuming only the subspace ofthe ZLLs to be partially filled) and mainly accounting for Gaussian impurities,we show that the longitudinal magnetoconductivity (LMC) in all members of theWeyl family displays a positive linear-$B$ scaling, when the field is appliedalong the axis that separates the Weyl nodes. But, in double and triple WSM,LMC displays a smooth crossover to a nonlinear $B$-dependence as the field istilted away from such a high-symmetry direction. In addition, due to theenhanced density of states, the LL quantization can trigger instabilitiestoward the formation of translational symmetry breaking density-wave orderingsfor sufficiently weak interaction (BCS instability), which gaps out the ZLLs.Concomitantly as the temperature (magnetic field) is gradually decreased(increased) the LMC becomes negative. Thus WSMs with arbitrary monopole charge($n$) can host an intriguing interplay of LL quantization, longitudinalmagnetotransport (a possible manifestation of one-dimensional chiral or axialanomaly), and density-wave ordering, when placed in a strong magnetic field.

Weyl fermions with arbitrary monopole in magnetic fields: Landau levels, longitudinal magnetotransport, and density-wave ordering