Topological insulators (TIs) in the Bi2Se3 family manifest helical Dirac surface states that span the topologically ordered bulk band gap. Recent scanning tunneling microscopy measurements have discovered additional states in the bulk band gap of Bi2Se3 and Bi2Te3, localized at one-dimensional step edges. Here numerical simulations of a TI surface are used to explore the phenomenology of edge state formation at the single-quintuple layer step defects found ubiquitously on these materials. The modeled one-dimensional edge states are found to exhibit a stable topological connection to the two-dimensional surface state Dirac point.

Three-dimensional topological insulators are bulk insulators with Z₂ topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by non-magnetic disorder, and have been adopted as the basis for a wide range of proposals to achieve new quasiparticle species and device functionality. Recent studies have yielded a surprise by showing that in spite of resisting localization, topological insulator surface electrons can be reshaped by defects into distinctive resonance states. Here we use numerical simulations and scanning tunnelling microscopy data to show that these resonance states have significance well beyond the localized regime usually associated with impurity bands. At native densities in the model Bi₂X₃ (X=Bi, Te) compounds, defect resonance states are predicted to generate a new quantum basis for an emergent electron gas that supports diffusive electrical transport.

The compound SmB6 is the best established realization of a topological Kondo insulator, in which a topological insulator state is obtained through Kondo coherence. Recent studies have found evidence that the surface of SmB6 hosts ferromagnetic domains, creating an intrinsic platform for unidirectional ballistic transport at the domain boundaries. Here, surface-sensitive x-ray absorption (XAS) and bulk-sensitive resonant inelastic x-ray scattering spectra are measured at the Sm N4,5 edge, and used to evaluate electronic symmetries, excitations, and temperature dependence near the surface of cleaved samples. The XAS data show that the density of large-moment atomic multiplet states on a cleaved surface grows irreversibly over time, to a degree that likely exceeds a related change that has recently been observed in the surface 4f orbital occupation.