The discovery of topological materials hosting spin-polarized Dirac fermion surface states has been driven by surface-sensitive spectroscopic tools. Scanning tunneling microscopy and spectroscopy can, in principle, access the surface state band structure on the nanometer length scale through a combination of one-particle (Landau quantization) and two-particle (quasiparticle interference) techniques. However, quantitative agreement between these techniques has not been shown. We report the surprising simultaneous observation of Landau quantization and quasiparticle interference on the topological semimetal Sb(111), over a range of filled and empty states. We establish the quantitative equivalence of these two momentum-resolved scanning tunneling spectroscopy techniques, and use them to reconstruct the multi-component surface state band structure, which would be inaccessible via either technique alone. Our results clarify the relationship between bulk conductivity and surface state coherence, and provide a quantitative local measure of the mean free path and spin-orbit coupling which will be essential for the fabrication of nanoscale topological devices.
Recent theoretical predictions have suggested that topologically protected surface states may similarly span the hybridization gap in some strongly correlated heavy fermion materials, particularly SmB6. However, the process by which the Sm 4f electrons hybridize with the 5d electrons on the surface of SmB6, and the expected Fermi-level gap in the density of states out of which the predicted topological surface states must arise, have not been directly measured. Local band structure measurements by STM are complicated by interference between two tunneling channels, into the f electron band and the conduction band. We conduct the first atomic resolution spectroscopic study of the cleaved surface of SmB6, and use a cotunneling model to separate the density of states of the hybridized bands. Our spectra reveal a robust hybridization gap which universally spans the Fermi level on four distinct surface morphologies, as well as residual spectral weight spanning the hybridization gap, which may be consistent with a topological surface state.