The origin of electronic band structure anomaly in topological crystalline insulator group-IV tellurides

Group-IV tellurides have exhibited exotic band structures. Specifically, despite the fact that Sn sits between Ge and Pb in the same column of the periodic table, cubic SnTe is a topological crystalline insulator with band inversion, but both isovalent GeTe and PbTe are trivial semiconductors with normal band order. By performing first-principles band structure calculations, we unravel the origin of this abnormal behaviour by using symmetry analysis and the atomic orbital energy levels and atomic sizes of these elements. In group-IV tellurides, the s lone pair band of the group-IV element is allowed by symmetry to couple with the anion valence p band at the L -point, and such s–p coupling leads to the occurrence of bandgap at the L -point. We find that such s–p coupling is so strong in SnTe that it inverts the band order near the bandgap; however, it is not strong enough in both GeTe and PbTe, so they remain normal semiconductors. The reason for this is the incomplete screening of the core of the relatively tight-binding Ge 4s orbital by its 3d orbitals and the large atomic size and strong relativistic effect in Pb, respectively. Interestingly, we also find that the rhombohedral distortion removes the inversion symmetry and the reduced s–p coupling transforms the α -SnTe back to a normal semiconductor. Our study demonstrates that, in addition to spin–orbital coupling, strain and interface dipole fields, inter-orbital coupling is another effective way to engineer the topological insulators. Condensed matter: Simulations solve elementary enigma Researchers in China and the USA offer an explanation for why some materials are semiconductors while others exhibit more exotic behavior. Jun-Wei Luo from the Institute of Semiconductors, Chinese Academy of Sciences, and collaborators used first-principles calculations to model the electronic band structure of three related binary compounds: germanium telluride, tin telluride and lead telluride. Germanium, tin and lead are all in the same column on the periodic table, so their properties would be expected to be similar, varying as a function of atomic number. In reality, however, these compounds exhibit starkly different behaviors. Luo and colleagues found explanations for these differences through symmetry analysis and in atomic energy levels and sizes. These findings offer a new solution to this previously unexplained anomaly, and pave the way for more effective engineering of topological insulators.