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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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In this contribution, field-induced interactions of magnetizable particles embedded into a soft elastomer matrix are analyzed with regard to the resulting mechanical deformations. By comparing experiments for two-, three- and four-particle systems with the results of finite element simulations, a fully coupled continuum model for magneto-active elastomers is validated with the help of real data for the first time. The model under consideration permits the investigation of magneto-active elastomers with arbitrary particle distances, shapes and volume fractions as well as magnetic and mechanical properties of the individual constituents. It thus represents a basis for future studies on more complex, realistic systems. Our results show a very good agreement between experiments and numerical simulations—the deformation behavior of all systems is captured by the model qualitatively as well as quantitatively. Within a sensitivity analysis, the influence of the initial particle positions on the systems’ response is examined. Furthermore, a comparison of the full three-dimensional model with the often used, simplified two-dimensional approach shows the typical overestimation of resulting interactions in magneto-active elastomers.

The extraction of noise source levels from ambient noise measurements requires accounting for the seismoacoustic propagation from the surface generated noise sources to the field measurement positions. At frequencies below 100 Hz, the waveguide nature of the environment strongly influences the distribution of ambient noise. Only when these propagation effects are considered can measurements from different experiments taken in different environments be combined to ascertain the global properties of surface noise sources. Here, such a previous analysis of a shallow water experiment [Schmidt et al., in Natural Mechanisms of Surface Generated Noise, edited by B. Kerman (Reidel, Dordrecht, The Netherlands, 1988)] is used and the results are combined with Kibble-white and Ewans' lower-frequency results [J. Acoust. Soc. Am. 78, 981– 994 (1985)], the latter also containing a summary of previous experimental results obtained by others. These data are treated in the same way by accounting for the environments using a wave theory model of distributed noise [W. A. Kuperman and F. Ingenito, J. Acoust. Soc. Am. 67, 1988– 1996 (1980)]. When the particular environments are used, the spread in the reprocessed noise levels is substantially reduced, showing more consistency in the frequency dependence of the noise sources, suggesting that there are only a few (or possibly only one) dominant natural noise source mechanisms that primarily contribute to ocean ambient noise below 100 Hz. The importance of appropriately including propagation factors in processing noise data for estimating source levels is therefore strongly demonstrated.

Recently the doping of topological insulators has attracted significant interest as a potential route towards topological superconductivity. Because many experimental techniques lack sufficient surface sensitivity, however, a definite proof of the coexistence of topological surface states and surface superconductivity is still outstanding. Here we report on highly surface sensitive scanning tunneling microscopy (STM) and spectroscopy (STS) experiments performed on Tl-doped Bi 2 Te 3 , a three-dimensional topological insulator which becomes superconducting in the bulk at T C = 2.3 K.Landau level spectroscopy as well as quasiparticle interference mapping clearly demonstrated the presence of a topological surface state with a Dirac point energy E D = −(118 ± 1) meV and a Dirac velocity v D = (4.7 ± 0.1) · 10 5 m/s. Tunneling spectra often show a superconducting gap, but temperature-and field-dependent measurements show that both T C and µ 0 H C strongly deviate from the corresponding bulk values. Furthermore, in spite of a critical field value which clearly points to type-II superconductivity, no Abrikosov lattice could be observed. Experiments performed on normal-metallic Ag(111) prove that the gapped spectrum is only caused by superconducting tips, probably caused by a gentle crash with the sample surface during approach. Nearly identical results were found for the intrinsically n-type compound Nb-doped Bi 2 Se 3 . Our results suggest that the superconductivity in superconducting-doped V-VI topological insulators does not extend to the surface where the topological surface state is located.

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