Many-impurity scattering on the surface of a topological insulator

We theoretically address the impact of a random distribution of non-magnetic impurities on the electron states formed at the surface of a topological insulator. The interaction of electrons with the impurities is accounted for by a separable pseudo-potential method that allows us to obtain closed expressions for the density of states. Spectral properties of surface states are assessed by means of the Green’s function averaged over disorder realisations. For comparison purposes, the configurationally averaged Green’s function is calculated by means of two different self-consistent methods, namely the self-consistent Born approximation (SCBA) and the coherent potential approximation (CPA). The latter is often regarded as the best single-site theory for the study of the spectral properties of disordered systems. However, although a large number of works employ the SCBA for the analysis of many-impurity scattering on the surface of a topological insulator, CPA studies of the same problem are scarce in the literature. In this work, we find that the SCBA overestimates the impact of the random distribution of impurities on the spectral properties of surface states compared to the CPA predictions. The difference is more pronounced when increasing the magnitude of the disorder.