Converting normal insulators into topological insulators via tuning orbital levels

Tuning the spin-orbit coupling strength via foreign element doping and modifying bonding strength via strain engineering are the major routes to convert normal insulators to topological insulators. We here propose an alternative strategy to realize topological phase transition by tuning the orbital level. Following this strategy, our first-principles calculations demonstrate that a topological phase transition in the cubic perovskite-type compounds ${\mathrm{CsGeBr}}_3$ and ${\mathrm{CsSnBr}}_3$ could be facilitated by carbon substitutional doping. Such a unique topological phase transition predominantly results from the lower orbital energy of the carbon dopant, which can pull down the conduction bands and even induce band inversion. Beyond conventional approaches, our finding of tuning the orbital level may greatly expand the range of topologically nontrivial materials.

Figure 1

Schematic illustration of the doping and SOC induced band inversion. (a) The original bands are not inverted. (b, c) The CBM and VBM shift toward each other induced by doping is less/larger than the band gap in (a). Note that a band inversion occurs in (c). (d) The final bands are inverted. For the path (a)-(b)-(d), the doping reduces the band gap, and the SOC induces the band inversion, while for path (a)-(c)-(d) the doping induces the band inversion, and the SOC opens a band gap. The solid and dashed curves denote the sub-bands that have opposite parities. The Fermi level ($E_f$) is denoted by the dashed line.

Figure 2

The calculated band structures of pure ${\mathrm{CsGeBr}}_3$ without (a) and with (b) SOC; the real part of the wave functions of the $R_1^{+}$ (c) and $R_{15}^{-}$ (d) states without SOC, the blue (yellow) isosurfaces represent the “$+$” (“$-$”) sign of the wave functions. The Fermi level is set to zero and indicated by the dashed line.

Figure 3

The PBE calculated electronic band structures of ${\mathrm{CsGe}}_{0.875}{\mathrm{C}}_{0.125}{\mathrm{Br}}_3$ without (a) and with (b) SOC; the calculated energy level of ${\mathrm{\Gamma }}_6^{+},{\mathrm{\Gamma }}_6^{-}$, and ${\mathrm{\Gamma }}_8^{-}$ states (c) as the artificial SOC strength ($\lambda$) increases from zero to original SOC strength (${\lambda }_0$); and the diagrams depicting the signs of the products of parity eigenvalues of all the occupied bands at every TRIM point (d). The inset in (c) zooms into the band inversion between ${\mathrm{\Gamma }}_6^{+}$ and ${\mathrm{\Gamma }}_6^{-}$. In (a) and (b), the Fermi level is set to zero, and indicated by the dashed line.

Figure 4

The calculated LDOS of ${\mathrm{CsGe}}_{0.875}{\mathrm{C}}_{0.125}{\mathrm{Br}}_3$. The Fermi level is set to zero, and indicated by the dashed line. Clearly, Dirac surface states emerge in the bulk gap.