In a cubic topological insulator (TI), there is a band inversion whereby the $s$-like ${\Gamma }_{6\mathrm{c}}$ conduction band is below the $p$-like ${\Gamma }_{7\mathrm{v}}+{\Gamma }_{8\mathrm{v}}$ valence bands by the “inversion energy” ${\Delta }_i<0$. In TIs based on the zinc-blende structure such as HgTe, the Fermi energy intersects the degenerate ${\Gamma }_{8\mathrm{v}}$ state so the insulating gap E${}_g$ between occupied and unoccupied bands vanishes. To achieve an insulating gap E${}_g>0$ critical for TI applications, one often needs to resort to structural manipulations such as structural symmetry lowering (e.g., Bi${}_2$Se${}_3$), 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 ${\Gamma }_{8\mathrm{v}}$ below ${\Gamma }_{7\mathrm{v}}$ (“negative spin-orbit splitting”), one can realize band inversion (${\Delta }_i<0$) 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${}_g>0$ with ${\Delta }_i<0$, albeit in a metastable form of FTS.

• Received 7 February 2012

DOI:https://doi.org/10.1103/PhysRevB.86.075316