We propose a spinless symmetry-based three-band tight-binding model with the coexistence of nodal-line and Weyl points, after considering spin-orbital coupling and different magnetization directions. It is confirmed that the number of Weyl points and nodal lines can be tuned by the magnetization direction. The combination of time-reversal symmetry and mirror reflection symmetry plays a crucial role in protecting the degeneracy of nodal lines. Moreover, we put forward a different class of materials ${\mathrm{C}}_4\mathrm{Cr}{X}_3$ ($X=\text{Ge}$ and Si) which host such a nontrivial semimetallic phase.

• Received 8 June 2018

DOI:https://doi.org/10.1103/PhysRevB.98.121103