Abstract

Three-dimensional topological gapless phases have attracted significant attention due to their unique electronic properties. A flagship example is Weyl semimetals, which require breaking time-reversal or inversion symmetry. In two dimensions, the dimensionality reduction requires imposing an additional symmetry, thereby weakening the phase. Like its three-dimensional counterpart, these "two-dimensional Weyl semimetals" present edge states directly related to Weyl nodes. The direct comparison with the edge states in zigzag-like terminated graphene ribbons is unavoidable, offering the question of how robust these states are and their differences. Here we benchmark the robustness of the edge states in two-dimensional Weyl semimetals without inversion symmetry with those present in zigzag graphene ribbons. Our results show that, despite having a similar electronic band structure, the edge states of two-dimensional Weyl semimetals are more robust against vacancies than graphene ribbons. We attribute this enhanced robustness to a crucial role of the spin degree of freedom in the former case.