Generalized triple-component fermions: Lattice model, Fermi arcs, and anomalous transport

Abstract

We generalize the construction of time-reversal symmetry-breaking triple-component semimetals, transforming under the pseudospin-1 representation, to arbitrary (anti-)monopole charge $2 n$, with $n=1,2,3$ in the crystalline environment. The quasiparticle spectra of such systems are composed of two dispersing bands with pseudospin projections $m_s=\pm 1$ and energy dispersions $E_{\bf k}=\pm \sqrt{ \alpha^2_n k^{2n}_\perp +v^2_z k^2_z}$, where $k_\perp=\sqrt{k^2_x+k^2_y}$, and one completely flat band at zero energy with $m_s=0$. We construct simple tight-binding models for such spin-1 excitations on a cubic lattice and address the symmetries of the generalized triple-component Hamiltonian. In accordance to the bulk-boundary correspondence, triple-component semimetals support $2 n$ branches of topological Fermi arc surface states and also accommodate a \emph{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 magnetoconductivity, planar Hall conductivity, and magneto thermal conductivity in these systems, which increase as $B^2$ for sufficiently weak magnetic fields ($B$) due to the nontrivial Berry curvature in the medium. A generalization of our construction to arbitrary integer spin systems is also highlighted.