Topological insulators are a class of quantum materials in which time-reversal symmetry, relativistic effects and an inverted band structure result in the occurrence of electronic metallic states on the surfaces of insulating bulk crystals. These helical states exhibit a Dirac-like energy dispersion across the bulk bandgap, and they are topologically protected. Recent theoretical results have suggested the existence of topological crystalline insulators (TCIs), a class of topological insulators in which crystalline symmetry replaces the role of time-reversal symmetry in ensuring topological protection. In this study we show that the narrow-gap semiconductor Pb(1-x)Sn(x)Se is a TCI for x  =  0.23. Temperature-dependent angle-resolved photoelectron spectroscopy demonstrates that the material undergoes a temperature-driven topological phase transition from a trivial insulator to a TCI. These experimental findings add a new class to the family of topological insulators, and we anticipate that they will lead to a considerable body of further research as well as detailed studies of topological phase transitions.

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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.