Carrier transport in two-dimensional topological insulator nanoribbons in the presence of vacancy defects

Using the non-equilibrium Green's function formalism, we study carrier transport through imperfect two-dimensional (2D) topological insulator (TI) ribbons. In particular, we investigate the effect of vacancy defects on the carrier transport in 2D TI ribbons with hexagonal lattice structure. To account for the random distribution of the vacancy defects, we present a statistical study of varying defect densities by stochastically sampling different defect configurations. We demonstrate that the topological edge states of TI ribbons are fairly robust against a high concentration (up to 2%) of defects. At very high defect densities, we observe an increased inter-edge interaction, mediated by the localisation of the edge states within the bulk region. This effect causes significant back-scattering of the, otherwise protected, edge-states at very high defect concentrations (>2%), resulting in a loss of conduction through the TI ribbon. We discuss how this coherent vacancy scattering can be used to our advantage for the development of TI-based transistors. We find that there is an optimal concentration of vacancies yielding an ON-OFF current ratio of up to two orders of magnitude. Finally, we investigate the importance of spin-orbit coupling on the robustness of the edge states in the TI ribbon and show that increased spin-orbit coupling could further increase the ON-OFF ratio.