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.

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We present a quasiparticle interference study of clean and Mn surface-doped TaAs, a prototypical Weyl semimetal, to test the screening properties as well as the stability of Fermi arcs against Coulomb and magnetic scattering. Contrary to topological insulators, the impurities are effectively screened in Weyl semimetals. The adatoms significantly enhance the strength of the signal such that theoretical predictions on the potential impact of Fermi arcs can be unambiguously scrutinized.Our analysis reveals the existence of three extremely short, perviously unknown scattering vectors.Comparison with theory traces them back to scattering events between large parallel segments of spin-split trivial states, strongly limiting their coherence. In sharp contrast to previous work [R. Batabyal et al., Science Advances 2:e1600709] where similar but weaker subtle modulations were interpreted as evidence of quasi-particle interference originating from Femi arcs, we can safely exclude this being the case. Overall, our results indicate that intra-as well as inter-Fermi arc scattering are strongly suppressed and may explain why-in spite of their complex multi-band structure-transport measurements show signatures of topological states in Weyl monopnictides.

1 arXiv:1602.03902v1 [cond-mat.mes-hall] 11 Feb 2016 AbstractThe particle-wave duality sets a fundamental correspondence between optics and quantum mechanics. Within this framework, the propagation of quasiparticles can give rise to superposition phenomena which, like for electromagnetic waves, can be described by the Huygens principle. However, the utilization of this principle by means of propagation and manipulation of quantum information is limited by the required coherence in time and space. Here we show that in topological insulators, which in their pristine form are characterized by opposite propagation directions for the two quasiparticles spin channels, mesoscopic focusing of coherent charge density oscillations can be obtained at large nested segments of constant-energy contours by magnetic surface doping. Our findings provide evidence of strongly anisotropic Dirac fermion-mediated interactions. Even more remarkably, the validity of our findings goes beyond topological insulators but applies for systems with spin-orbit-lifted degeneracy in general. It demonstrates how spin information can be transmitted over long distances, allowing the design of experiments and devices based on coherent quantum effects in this fascinating class of materials. 2Coherence is a general property of waves as it describes the capability of keeping a welldefined phase relation while propagating in space and time. Because of the particle-wave duality, which lays at the very foundations of quantum mechanics, the same concept can also be applied to quasiparticles in solids. Quantum coherence is of fundamental importance since it sets the limits up to which information can be transmitted and processed with high fidelity. With the invention of the scanning tunneling microscope it became possible to visualize coherent phenomena in real space by imaging the standing wave pattern produced by scattering events around individual atomic-scale defects [1]. In analogy with electromagnetic waves these results can be interpreted within the Huygens principle. It describes the interference pattern which results from the superposition of waves propagating along all different paths and can be theoretically elegantly expressed by using the quantum-mechanical propagator.The further development of atomic-scale manipulation techniques allowed to engineer these properties at the atomic scale. This capability was used for the creation of exotic effects such as quantum mirages [2], for the extraction of the phase of electron wave functions to analyze how propagating waves in solids are influenced by the periodic potential of the crystal lattice. In particular, it has been shown that the propagation of quasiparticle waves can become anisotropic when the shape of a constant-energy cut (CEC) deviates from an isotropic contour. In analogy to optics, focussing and defocussing lead to an enhanced intensity along certain crystallographic directions and to partial or even complete suppression along others, respectively [5]. However, despite its relevance in s...