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.

We report atomic resolution Z-contrast scanning transmission electron microscopy images that reveal the incorporation of I atoms in the form of helical chains inside single-walled carbon nanotubes. Density functional calculations and topological considerations provide a consistent interpretation of the experimental data. Charge transfer between the nanotube walls and the I chains is associated with the intercalation.

The growth of wurtzite GaAs and InAs nanowires with diameters of a few tens of nanometers with negligible intermixing of zinc blende stacking is reported. The suppression of the number of stacking faults was obtained by a procedure within the vapor-liquid-solid growth, which exploits the theoretical result that nanowires of small diameter ( approximately 10 nm) adopt purely wurtzite structure and are observed to thicken (via lateral growth) once the axial growth exceeds a certain length.

The nucleation pathway for single-wall carbon nanotubes on a metal surface is demonstrated by a series of total energy calculations using density functional theory. Incorporation of pentagons at an early stage of nucleation is energetically favorable as they reduce the number of dangling bonds and facilitate curvature of the structure and bonding to the metal. In the presence of the metal surface, nucleation of a closed cap or a capped single-wall carbon nanotube is overwhelmingly favored compared to any structure with dangling bonds or to a fullerene.