Stability of Majorana modes in Coulomb-disordered topological insulator nanowires

We evaluate theoretically the possibility to realize Majorana zero modes in hybrid devices made from topological-insulator (TI) nanowires proximity-coupled to a superconductor. Such systems have been suggested as building blocks of future topological quantum computers, as they have been predicted to realize Majorana zero modes protected by large gaps. A main obstacle is, however, the presence of a relatively large density of charged impurities, $n_\text{imp}\sim 10^{19}$cm$^{-3}$. Based on extensive numerical simulations, we show that the proximity to the superconductor leads to an efficient screening of the disorder potential. By analyzing the Majorana splitting energy, the size of the Andreev gap and the localization of edge modes, we show that robust Majorana modes can be realized for realistic levels of impurity concentrations and wire radii.