Generalized Triple-Component Fermions: Lattice Model, Fermi arcs and Anomalous Transport

A generalization of time-reversal symmetry-breaking triple-component semimetals, transforming under the pseudo-spin-1 representation, to arbitrary (anti-)monopole charge $2 n$, with $n=1,2,3$ in the crystalline environment will be presented. The quasiparticle spectra of such systems are composed of two dispersing bands with pseudo-spin projections $m_s=\pm 1$ and one completely flat band at zero energy with $m_s=0$. In this talk we will show simple tight-binding models for such spin-1 excitations in a cubic lattice and address the symmetry protection of the generalized triple-component nodes. In accordance to the bulk-boundary correspondence, triple-component semimetals support $2 n$ branches of topologically protected Fermi arc surface states and accommodate a large anomalous Hall conductivity (in the $xy$ plane), given by $\sigma^{\rm 3D}_{xy} \propto 2 n \times$ the separation of the triple-component nodes (in units of $e^2/h$). Furthermore, we compute the longitudinal magneto-, planar Hall and magneto thermal-conductivities in this system, which increase as $B^2$ (due to the non-trivial Berry curvature in the medium) with the external magnetic field ($B$), when it is sufficiently weak. A generalization of our construction to arbitrary integer spin system is also highlighted.