Two-dimensional Weyl semimetal with coexisting fully spin-polarized type-I and type-II Weyl points

As novel topological states of matter, Weyl semimetals (WSM) have been well studied in three-dimensional (3D) system. However, two-dimensional (2D) WSMs, especially type-II ones, are rarely reported. Here, we propose that monolayer Cr2C is a 2D WSM with coexisting fully spin-polarized type-I and type-II Weyl points. The material is ferromagnetic and has a high Curie temperature of 562 K. It is metallic in the spin-up channel but insulating in the spin-down channel, showing a half metal band structure. The low-energy bands in the spin-up channel form one pair type-I Weyl points and three pairs of type-II Weyl points, which are protected by the rotation symmetry in high-symmetry path. The Weyl points can survive under spin-orbit coupling with magnetization along y direction. The Weyl points show fully spin-polarized Fermi arc of edge states within the projected Weyl points. Most interestingly, we find the 2D type-II Weyl points show unusual Magnetoresponse with complete Landau levels (LLs) collapse independent with the magnetic-field. Such LLs collapse is different with type-II Weyl points in 3D system. The material provides a promising platform to study the fundamental physics of 2D type-I and type-II Weyl points, as well potential entanglements between them.