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 alpha-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.