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.

The spin-momentum locking of topological states offers an ideal platform to explore novel magnetoelectric effects. These intimately depend on the ability to manipulate the spin texture in a controlled way. Here we combine scanning tunnelling microscopy with single-atom deposition to map the evolution of topological states under the influence of different magnetic perturbations. We obtain signatures of Dirac fermion-mediated magnetic order for extremely dilute adatom concentrations. This striking observation is found to critically depend on the single adatoms' magnetic anisotropy and the position of the Fermi level. Our findings open new perspectives in spin engineering topological states at the atomic scale and pave the way to explore novel spin-related topological phenomena with promising potential for applications.

Hybrid organic/inorganic interfaces have been widely reported to host emergent properties that go beyond those of their single constituents. Coupling molecules to the recently discovered topological insulators, which possess a linearly dispersing and spin-momentum-locked Dirac fermions, may offer a promising platform towards new functionalities. Here, we report a scanning tunneling microscopy and spectroscopy study of the prototypical interface between MnPc molecules and a Bi 2 Te 3 surface. MnPc is found to bind stably to the substrate through its central Mn atom. The adsorption process is only accompanied with a minor charge transfer across the interface, resulting in a moderately n-doped Bi 2 Te 3 surface. More remarkably, topological states remain completely unaffected by the presence of the molecules, as evidenced by the absence of scattering patterns around adsorption sites. Interestingly, we show that, while the HOMO and LUMO orbitals closely resembles those of MnPc in the gas phase, a new hybrid states emerges through interaction with the substrate. Our results pave the way towards hybrid organic-topological insulator heterostructures, which may unveil a broad range of exciting and unknown phenomena.2

The success of topological insulators (TI) in creating devices with unique functionalities is directly connected to the ability of coupling their helical spin states to well-defined perturbations. However, up to now, TI-based heterostructures always resulted in very disordered interfaces, characterized by strong mesoscopic fluctuations of the chemical potential that make the spin-momentum locking ill-defined over length scales of few nanometers or even completely destroy topological states. These limitations call for the ability to control topological interfaces with atomic precision. Here, we demonstrate that molecular self-assembly processes driven by inherent interactions among the constituents offer the opportunity to create well-defined networks at TIs surfaces. Even more remarkably, we show that the symmetry of the overlayer can be finely controlled by appropriate chemical modifications. By analyzing the influence of the molecules on the TI electronic properties, we rationalize our results in terms of the charge redistribution taking place at the interface. Overall, our approach offers a precise and fast way to produce tailor-made nanoscale surface landscapes. In particular, our findings make organic materials ideal TIs counterparts, because they offer the possibility to chemically tune both electronic and magnetic properties within the same family of molecules, thereby bringing us a significant step closer toward an application of this fascinating class of materials.