Effective models for multifold Weyl fermions under external magnetic field

While typical Weyl semimetals realize doubly degenerate Weyl points in their bulk, a novel type of Weyl fermions, characterized by a higher degree of degeneracy and protected by crystal symmetry, has been theoretically predicted [1]. These Weyl fermions are synthetic magnetic monopoles in the momentum space, and their presence leads to distinctive physical properties in Weyl semimetals, such as anomalous Hall effects and negative longitudinal magnetoresistance [2,3]. When an external field is applied, the magnetic monopoles associated with multifold Weyl fermions not only shift in momentum space but also display more complex behaviors, including splitting and creation/annihilation. Accounting for these responses could significantly alter physical quantities compared to conventional Weyl semimetals.

In this study, we focus on threefold Weyl fermions (spin-1 fermions). By decomposing the degrees of freedom describing threefold Weyl fermions into the irreducible representations of the space group, we systematically construct a k·p Hamiltonian and an effective tight-binding Hamiltonian that accurately preserves the crystalline symmetry while incorporating an effect of external magnetic fields. Using these models, we investigate how physical properties, such as conductivity and surface states, are modified in the presence of external fields.