One-dimensional Dirac modes in the core of a pentagonal topological crystalline insulator nanowire
We investigate the electronic band topology of recently fabricated pentagonal IV-VI semiconductor nanowires, which contain five radial $\{111\}$ twin planes meeting at the nanowire axis. Tight-binding calculations show that, when the bulk band structure is inverted and the twin planes in the nanowire are cationic, the spectrum contains two spatially separated helical Dirac crossings near $\overline{\Gamma}$: one localized at the core and the other at the outer surface. When the twin planes are anionic, the corresponding spectra remain gapped. The crossings originate from the hybridization of five helical channels associated with the twin-plane edges, whose odd number leaves one Kramers pair near the nanowire axis and the other at the outer boundary. Realistic multiorbital calculations for $\mathrm{Pb}_{0.4}\mathrm{Sn}_{0.6}\mathrm{Te}$ predict well-developed core and surface modes at nanowire thicknesses of approximately 50~nm and above. These results establish pentagonal SnTe-class nanowires as an experimentally accessible realization of spatially separated helical channels bound to the axial defect and the outer boundary.