Topological crystalline insulators are materials in which the crystalline symmetry leads to topologically protected surface states with a chiral spin texture, rendering them potential candidates for spintronics applications. Using scanning tunneling spectroscopy, we uncover the existence of one-dimensional (1D) midgap states at odd-atomic surface step edges of the threedimensional topological crystalline insulator (Pb,Sn)Se. A minimal toy model and realistic tightbinding calculations identify them as spin-polarized flat bands connecting two Dirac points. This non-trivial origin provides the 1D midgap states with inherent stability and protects them from backscattering. We experimentally show that this stability results in a striking robustness to defects, strong magnetic fields, and elevated temperature. Main Text:The recent theoretical prediction and experimental realization of topological insulators (TIs) have considerably extended the notion of a phase of matter. Within this framework, it has been shown that-based on some topological invariants-the electronic properties of materials can be classified into distinct topological classes (1,2). In topologically non-trivial materials, unconventional boundary modes have been experimentally detected by several different techniques (3-9). In two-dimensional (2D) TIs, counter-propagating spin-momentum-locked one-dimensional (1D) edge modes develop along the sample boundary; in contrast, threedimensional (3D) TIs (4) have boundary modes that are linearly dispersing chiral surface states.Although a large variety of 3D TIs have been reported, only very few 2D TIs are known [HgTe (3), InAs (10) quantum wells, and Bi bilayers (11)]. These 2D TIs are delicate and difficult to realize experimentally because they all require the fabrication of precisely controlled thin film heterostructures. Properties such as small band gaps (3,10), strong substrate-induced hybridization effects (11), or the existence of residual trivial states (10,11) make helical edge states not only challenging to study, but also of limited appeal for applications. Furthermore, their topological properties are protected only as long as time-reversal symmetry is preserved.Here we report that two-dimensional (2D) topological surfaces, in turn, can be the mother state for non-trivial one-dimensional (1D) midgap states, suggesting a dimensional hierarchy of boundary states in topological insulators. Specifically, we report on the discovery of 1D topological spin-filtered channels that naturally develop at step edges of 3D topological crystalline insulators (TCIs), i.e., materials where the existence of surface Dirac states is guaranteed by crystal symmetries.

Topological insulators interacting with magnetic impurities have been reported to host several unconventional effects. These phenomena are described within the framework of gapping Dirac quasiparticles due to broken time-reversal symmetry. However, the overwhelming majority of studies demonstrate the presence of a finite density of states near the Dirac point even once topological insulators become magnetic. Here, we map the response of topological states to magnetic impurities at the atomic scale. We demonstrate that magnetic order and gapless states can coexist. We show how this is the result of the delicate balance between two opposite trends, that is, gap opening and emergence of a Dirac node impurity band, both induced by the magnetic dopants. Our results evidence a more intricate and rich scenario with respect to the once generally assumed, showing how different electronic and magnetic states may be generated and controlled in this fascinating class of materials.

We have studied cleaning procedures of Nb(110) by verifying the surface quality with low-energy electron diffraction, Auger electron spectroscopy, and scanning tunneling microscopy and spectroscopy. Our results show that the formation of a surface-near impurity depletion zone is inhibited by the very high diffusivity of oxygen in the Nb host crystal which kicks in at annealing temperatures as low as a few hundred degree Celsius. Oxygen can be removed from the surface by heating the crystal up to T = 2400 • C. Tunneling spectra measured on the clean Nb(110) surface exhibit a sharp conductance peak in the occupied states at an energy of about −450 meV. Density functional theory calculations show that this peak is caused by a d z 2 surface resonance band at theΓ point of the Brillouin zone which provides a large density of states above the sample surface. The clean Nb(110) surface is superconducting with a gap width and a critical magnetic field strength in good agreement to the bulk value. In an external magnetic field we observe the Abrikosov lattice of flux quanta (vortices). Spatially resolved spectra show a zero-bias anomaly in the vortex core.

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We provide a detailed microscopic characterization of the influence of defects-induced disorder onto the Dirac spectrum of three dimensional topological insulators. By spatially resolved Landau-levels spectroscopy measurements, we reveal the existence of nanoscale fluctuations of both the Dirac point energy as well as of the Dirac-fermions velocity which is found to spatially change in opposite direction for electrons and holes, respectively. These results evidence a scenario which goes beyond the existing picture based on chemical potential fluctuations. The findings are consistently explained by considering the microscopic effects of local stain introduced by defects, which our model calculations show to effectively couple to topological states, reshaping their Dirac-like dispersion over a large energy range. In particular, our results indicate that the presence of microscopic spatially varying stain, inevitably present in crystals because of the random distribution of defects, effectively couple to topological states and should be carefully considered for correctly describing the effects of disorder.