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Three-dimensional topological gapless phases have attracted significantattention due to their unique electronic properties. A flagship example areWeyl semimetals, which require breaking time-reversal or inversion symmetry. Intwo dimensions, the dimensionality reduction requires imposing an additionalsymmetry, thereby weakening the phase. Like its three-dimensional counterpart,these two-dimensional Weyl semimetals present edge states directly related toWeyl nodes. The direct comparison with the edge states in zigzag-liketerminated graphene ribbons is unavoidable, offering the question of how robustthese states are and their differences. Here we benchmark the robustness of theedge states in two-dimensional Weyl semimetals without inversion symmetry withthose present in zigzag graphene ribbons. Our results show that, despite havinga similar electronic band structure, the edge states of two-dimensional Weylsemimetal are more robust against vacancies than graphene ribbons. We attributethis enhanced robustness to a crucial role of the spin degree of freedom in theformer case

Robustness of spin-polarized edge states in a two-dimensional topological semimetal without inversion symmetry