Third-order topological insulators with wallpaper fermions in Tl4PbTe3 and Tl4SnTe3

Abstract

Abstract Nonsymmorphic symmetries open up horizons of exotic topological boundary states and even generalize the bulk–boundary correspondence, which, however, the third-order topological insulator in electronic materials are still unknown. Here, by means of the symmetry analysis and k · p models, we uncover the emergence of long-awaited third-order topological insulators and the wallpaper fermions in space group I4/mcm (No.140). Based on this, we present the hourglass fermion, fourfold-degenerate Dirac fermion, and Möbius fermion in the (001) surface of Tl4 XTe3 (X = Pb/Sn) with a nonsymmorphic wallpaper group p4g. Remarkably, 16 helical corner states reside on eight corners in Kramers pair, rendering the real electronic material of third-order topological insulators. More importantly, a time-reversal polarized octupole polarization is defined to uncover the nontrivial third-order topology, as is implemented by the 2nd and 3rd order Wilson loop calculations. Our results could considerably broaden the range of wallpaper fermions and lay the foundation for future experimental investigations of third-order topological insulators.