Disorder effects of vacancies on the electronic transport properties of realistic topological insulators nanoribbons: the case of bismuthene

The robustness of topological materials against disorder and defects is presumed but has not been demonstrated explicitly in realistic systems. In this work, we use state-of-the-art density functional theory and recursive nonequilibrium Green's functions methods to study the effect of disorder on the electronic transport of long nanoribbons, up to $157\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$, as a function of vacancy concentration. In narrow nanoribbons, a finite-size effect gives rise to hybridization between the edge states erasing topological protection. Hence, even small vacancy concentrations enable backscattering events. We show that the topological protection is more robust for wide nanoribbons, but surprisingly it breaks down at moderate structural disorder. Our study helps to establish some bounds on defective bismuthene nanoribbons as promising candidates for spintronic applications.