Fully spin-polarized double-Weyl fermions with type-III dispersion in the quasi-one-dimensional materials X2RhF6 ( X=K , Rb, Cs)

Abstract

Double-Weyl fermions, as novel topological states of matter, have been mostly discussed in nonmagnetic materials. Here, based on density-functional theory and symmetry analysis, we propose the realization of fully spin-polarized double-Weyl fermions in a family ferromagnetic materials ${\mathrm{X}}_{2}{\mathrm{RhF}}_{6}$ ($X=\text{K}$, Rb, Cs). These materials have the half-metal ground states, where only the bands from the spin-down channel present near the Fermi energy. The spin-down bands form a pair of triply degenerate nodal points (TDNPs) if spin-orbit coupling (SOC) is not included. Under SOC, one TDNP splits into two double-Weyl points featuring quadratic dispersion along two momentum directions with the chiral charge of $\ifmmode\pm\else\textpm\fi{}2$, and they are protected by the three-fold rotation (${C}_{3}$) symmetry. Unlike most double-Weyl semimetals, the Weyl points proposed here have the type-III dispersion with one of the crossing bands being saddle-shaped. An effective model is constructed, which describes well the nature of the Weyl points. These Weyl points are fully spin-polarized, and are characterized with double Fermi arcs on the surface spectrum. Breaking ${C}_{3}$ symmetry by lattice strain could shift one double-Weyl point into a pair of type-II single-Weyl points. The ${\mathrm{X}}_{2}{\mathrm{RhF}}_{6}$ materials proposed here are excellent candidates to investigate the novel properties of type-III double-Weyl fermions in ferromagnetic system, as well as generate potential applications in spintronics.