Band inversion mechanism in topological insulators: A guideline for materials design

Alteration of the topological order by band inversion is a key ingredient of a topologically nontrivial material. Using first-principles calculations for HgTe, PtScBi, and Bi${}_2$Se${}_3$, we argue that it is not accurate to ascribe the band inversion to the spin-orbit coupling. Instead, scalar relativistic effects and/or lattice distortions are found to be essential. Therefore, the search for topologically nontrivial materials should focus on band shifts due to these mechanisms rather than spin-orbit coupling. We propose an effective scheme to search for new topological insulators.

Figure 1

Electronic band structure of HgTe obtained from (a) NR, (b) SR, and (c) FR calculations. The wave function symmetry at the $\Gamma$ point is labeled. (d) Band energies at the $\Gamma$ point from the NR, SR, and FR calculations. Percentages of orbital contributions at the $\Gamma$ point from the SR calculation are given as superscripts (for values $\ge$$5\%$). (e)–(h) Analogous to (a)–(d) but for CdTe.

Figure 2

NR, SR, and FR band energies for (a) PtScBi and (b) PtScSb. The orbital contributions refer to the SR calculation. Values below $5\%$ are omitted.

Figure 3

NR, SR, and FR band energies for (a) Bi${}_2$Se${}_3$, (b) $s$-Sb${}_2$Se${}_3$, and (c) Sb${}_2$Se${}_3$. The orbital contributions refer to the SR calculation. Values below 5$\%$ are omitted.

Figure 4

NR, SR, and FR band energies for (a) GaAs, (b) InSb, and (c) $s$-InSb. The orbital contributions refer to the SR calculation. Values below 5$\%$ are omitted.