Large insulating gap in topological insulators induced by negative spin-orbit splitting

Abstract

In a cubic topological insulator (TI), there is a band inversion whereby the s-like Γ 6c conduction band is below the p-like Γ 7v+Γ 8v valence bands by the "inversion energy" Δ i<0. In TIs based on the zinc-blende structure such as HgTe, the Fermi energy intersects the degenerate Γ 8v state so the insulating gap E g between occupied and unoccupied bands vanishes. To achieve an insulating gap E g0 critical for TI applications, one often needs to resort to structural manipulations such as structural symmetry lowering (e.g., Bi 2Se 3), strain, or quantum confinement. However, these methods have thus far opened an insulating gap of only <0.1 eV. Here we point out that there is an electronic rather than structural way to affect an insulating gap in a TI: if one can invert the spin-orbit levels and place Γ 8v below Γ 7v ("negative spin-orbit splitting"), one can realize band inversion (Δ i<0) with a large insulating gap (E g up to 0.5 eV). We outline design principles to create negative spin-orbit splitting: hybridization of d orbitals into p-like states. This general principle is illustrated in the "filled tetrahedral structures" (FTS) demonstrating via GW and density functional theory (DFT) calculations E g0 with Δ i<0, albeit in a metastable form of FTS. © 2012 American Physical Society.