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

We generalize the construction of time-reversal symmetry-breaking triple-component semimetals, transforming under the pseudospin-1 representation, to arbitrary (anti-)monopole charge 2n, 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) = +/- 1 and energy dispersions E-k = +/-root alpha(2)(n)k(perpendicular to)(2n) + v(z)(2)k(z)(2), where k(perpendicular to) = root k(x)(2) + k(y)(2), 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 2n branches of topological Fermi arc surface states and also accommodate a large anomalous Hall conductivity (in the xy plane), given by sigma(3D)(xy) proportional to 2nx the separation of the triple-component nodes (in units of e(2)/h). Furthermore, we compute the longitudinal magnetoconductivity, planar Hall conductivity, and magnetothermal 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.