Pressure-induced topological phase transitions in rocksalt chalcogenides

By means of a comprehensive theoretical investigation, we show that external pressure can induce topological phase transitions in IV–VI semiconducting chalcogenides with a rocksalt structure. These materials satisfy mirror symmetries that are needed to sustain topologically protected surface states, at variance with time-reversal symmetry that is responsible for gapless edge states in ${\mathcal{Z}}_2$ topological insulators. The band inversions at high-symmetry points in the Brillouin zone that are related by mirror symmetry are brought about by an “asymmetric” hybridization between cation and anion $sp$ orbitals. By working out the microscopic conditions to be fulfilled in order to maximize this hybridization, we identify materials in the rocksalt chalcogenide class that are prone to undergo a topological phase transition induced by pressure and/or alloying. Our model analysis is fully confirmed by complementary advanced first-principles calculations and ab initio-based tight-binding simulations.

Figure 1

(a) Crystal structure and (b) Brillouin zone of rocksalt chalcogenides, showing one mirror plane (green) containing the high-symmetry points $\Gamma$, $L$, and $X$ as well as their projection onto the [001] surface. Schematic representation of the band structure at the $L$ point in the topologically trivial phase (c) and upon pressure-induced enhancement of $sp$ hybridization (d). Dashed lines separate occupied from unoccupied energy levels.

Figure 2

Topological phase transition in PbTe upon pressure, calculated by a TB method. For selected volume ratios $V/V_0$, the spectral density of the topmost layer of the (001) surface is represented in a color scale [(b), in states $/eV$]. Topological trivial phases with mirror Chern number 0 appear for the equilibrium volume (a) and close to the critical pressure (b). A topological nontrivial phase (c) shows a mirror Chern number of $-2$. Its Dirac surface state is depicted in a constant-energy cut around $\overline{X}$ at $E_{\mathrm{F}}-0.05$ eV [inset in (c)]. A $k$ path shown also in (c) is marked by arrowed lines. The $k$ axis common to (a)–(c) shows $2/5$ of the $\overline{M}$-$\overline{X}$ and $\overline{X}$-$\overline{\Gamma }$ lines around $\overline{X}$ [cf. Fig. 1b].

Figure 3

DFT electronic structures of selected rocksalt chalcogenides for different volume ratios $V/V_0$, with band characters highlighted by a color scale (anions: blue; cations: red).