Abstract
AbstractGroup-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.
Highlights
Topological insulators (TIs) are a group of materials with interesting electronic properties
We find that in the cubic (RS, β-phase) the cation s lone-pair state, which are valence electrons that are not shared with another atom, couples strongly with anion valence p state that leads to band inversion in SnTe, but the coupling is not large enough for GeTe due to its low 4s orbital energy and for PbTe due to its large Pb atom size and relativistic effects, so they remain to be normal semiconductors
By projecting the conduction band minimum (CBM) and valence band maximum (VBM) wavefunctions onto the atomic orbitals, we find in Figure 3 that the CBM of GeTe and PbTe and the VBM of SnTe are cation p predominated with minor contributions from anion s and anion d orbitals, whereas the VBM of GeTe and PbTe and the CBM of SnTe are mainly from anion p with remarkable contributions from cation s
Summary
Topological insulators (TIs) are a group of materials with interesting electronic properties. They can exhibit insulating state in the bulk, but support spin-momentum locked gapless states at the boundaries. For three-dimensional TIs,[1,2] the metallic topological surface states induced by spin–orbit coupling (SOC) are protected by time-reversal symmetry, known as Kramer’s pair. Time-reversal symmetry forbids the elastic backscattering of Kramer’s pair surface states, and the dispassion-less transport of the topological surface states is robust against nonmagnetic weak disorder. The RS structure IV–VI narrow band gap semiconductors such as
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