Abstract
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.
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