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

TL;DR

This paper introduces a generalized model for triple-component semimetals with arbitrary monopole charge, revealing their unique surface states, large anomalous Hall effect, and magnetotransport properties influenced by Berry curvature.

Contribution

It extends the theoretical framework of triple-component semimetals to arbitrary monopole charges and constructs corresponding lattice models and transport predictions.

Findings

Supports 2n Fermi arc surface states.

Exhibits large anomalous Hall conductivity proportional to node separation.

Magnetoconductivity and thermal conductivity scale as B^2 at weak fields.

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.