Probing the electronic structure at the boundary of topological insulators in the Bi₂Se₃ family by combined scanning tunneling and atomic force microscopy

We develop a numerical scheme for the calculation of tunneling current I and differential conductance dI/dV of metal- and CO-terminated STM tips on the topological insulators Bi₂Se₃, Bi₂Te₂Se as well as Bi₂Te₃, and find excellent agreement with experiment. The calculation is an application of Chen's derivative rule, whereby the Bloch functions are obtained from Wannier-interpolated tight-binding Hamiltonians and maximally localized Wannier functions from first-principle DFT+GW calculations. We observe signatures of the topological boundary modes, their hybridization with bulk bands, Van Hove singularities of the bulk bands, and characterize the orbital character of these electronic modes using the high spatial resolution of STM and AFM. Bare DFT calculations are insufficient to explain the experimental data, which are instead accurately reproduced by many-body-corrected GW calculations.