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

Three-dimensional topological gapless phases have attracted significant attention due to their unique electronic properties. One of the flagships is the Weyl semimetals, which requires breaking time-reversal or inversion symmetry in three dimensions. 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 with those present in zigzag graphene ribbons. To such end, we use a Dirac Hamiltonian model proposed by Young and Kane, adding new terms for inducing a two-dimensional Weyl semimetal phase and use a scattering picture for the transport calculation. Our results show that despite having a similar electronic band structure, the edge states of two-dimensional Weyl semimetal 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.