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.

Topological insulators (TIs) in the Bi 2 Se 3 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 Bi 2 Se 3 and Bi 2 Te 3 , 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 twodimensional surface state Dirac point.

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 (RIXS) 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.The topological Kondo insulator (TKI) state is a variant of the topological insulator state [1][2][3][4], in which a topologically ordered insulating electronic band structure is obtained from Kondo physics. The realization of a TKI state in mixed-valent SmB 6 was strongly indicated by early theoretical investigations [4,5], and has now been established through direct measurement of the topological surface states via angle resolved photoemission [6][7][8][9][10][11] and transport studies [12,13]. Strong evidence has recently been found suggesting that the surface of polished SmB 6 samples can also host ferromagnetic domains [13], a property that is theoretically associated with exotic axion electrodynamics, an inverse spin-galvanic effect, and ballistic one dimensional transport channels at domain boundaries [2,[14][15][16]. Moreover, surface sensitive X-ray photoemission (XPS) measurements have shown that the surface 4f occupation evolves irreversibly towards 4f 5 as a function of time following cleavage in ultra high vacuum (UHV) [17]. Here, multiplet-dominated X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) measurements in the vacuum ultraviolet (VUV) regime are used as a symmetry-sensitive probe to map the Sm N 4,5 -edge excitations and show that a similarly large change in the density of large-moment samarium sites accompanies this time evolution. This evolution is consistent with expectations for the transition from a Kondo insulating state to magnetism, and represents a means for incrementally tuning the strength of the surface magnetic instability.Measurements were performed at the beamline 4.0.3 (MERLIN) RIXS endstation (MERIXS) [18,19] at the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory. Large single crystals of SmB 6 were grown by the Al flux method as in Ref. [17], cleaved at low temperature, and maintained at a UHV pressure of approximately 3×10 −10 Torr. The photon beam had a grazing 30 o or angle of incidence to the cleaved [001] sample face, and scattered photons were measured at 90 o to the incident beam trajectory. XAS was measured using the total electron yield (TEY) method, and the expecte...

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