Eightfold Degenerate Fermions in Two Dimensions.

Multifold degenerate fermions have attracted a lot of research interest in condensed matter physics and materials science, but always lack in two dimensions. In this Letter, from symmetry analysis and lattice model construction, we demonstrate that eightfold degenerate fermions can be realized in two-dimensional systems. In nonmagnetic materials with negligible spin-orbit coupling, the gray magnetic space groups together with SU(2) spin rotation symmetry can protect the two-dimensional eightfold degenerate fermions on a certain high-symmetry axis in the Brillouin zone, no matter whether the system is centrosymmetric or noncentrosymmetric. In antiferromagnetic materials, the eightfold degenerate fermions can also be protected by certain ``spin space groups.'' Furthermore, by first-principles electronic structure calculations, we predict that the paramagnetic phase of the monolayer ${\mathrm{LaB}}_{8}$ on a suitable substrate is a two-dimensional eightfold degenerate as well as Dirac node-line semimetal. Especially, the eightfold degenerate points are close to the Fermi level, which makes monolayer ${\mathrm{LaB}}_{8}$ a good platform to study the exotic physical properties of two-dimensional eightfold degenerate fermions.