Distinct intermediate states in the isostructural $R\text{−}3m$ phase of the topological insulator $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ at high pressure

The electronic state of layered three-dimensional topological insulators at high pressure is a compelling but a puzzling hot topic. The open question is the structural origins for the pressure-induced novel physics of electronic topological transition (ETT), topological superconductivity, and Majorana fermions in the same isostructural $R\text{−}3m$ phase. Here, we report a combined investigation on the local structure and bulk electronic state of topological insulator $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ using x-ray diffraction, high quality x-ray absorption fine-structure spectroscopies both at the $\mathrm{Bi}{L}_3$ edge and at the Se K edge, and first-principles theoretical calculations. We have found three pressure-induced distinct intermediate states in the isostructural rhombohedral phase of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$. The bulk electronic structure of the $R\text{−}3m$ phase was calculated based on the experimental structure. The corresponding distinct electronic states provide the origins of ETT at ∼3 GPa and the metallization at 7–9.5 GPa in the $R\text{−}3m$ phase of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$. Our results demonstrate that the local structure plays a critical role in the electronic states of topological insulator $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$.

Figure 1

Crystal structure of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$. The rhombohedral $R\text{−}3m$ crystal structure of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ consists of hexagonal planes of Bi and Se stacked on top of each other along the $c$ direction forming a QL with Se2-Bi-Se1-Bi-Se2 where Se1 is on the QL central plane whereas Se2 is on the QL surface. The structure of QLs under high pressure is probed by three complementary experiments.

Figure 2

The selected angle-dispersive XRD patterns of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ with NPD anvils under various pressures at room temperature from ambient pressure up to 13 GPa. The vertical bars are the expected diffraction lines of $R\text{−}3m$ and $C2/m$ phases at 0 and 13 GPa, respectively.

Figure 3

Selected $\mathrm{Bi}{L}_3$-edge XAFS of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ as a function of pressure by high-pressure XAFS using NPD anvils. (a) Normalized x-ray absorption $\mu \left(E\right)$ as the x-ray appearance near-edge structure (XANES) region. (b) $k^2$- weighted XAFS spectra $k^2\chi \left(k\right)$ with a noticeable change in the XAFS oscillation profile ($6-11{\AA }^{-1}$) as pressure increases. (c) XAFS Fourier transform $\left|\chi \left(R\right)\right|$ obtained in the range from 2.5 to $12.5{\AA }^{-1}$ with a Hanning window. Note the merging of two peaks (2.8–3.5 Å) above 12.4 GPa.

Figure 4

Selected Se K-edge XAFS of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ as a function of pressure by high-pressure XAFS using NPD anvils. (a) Normalized x-ray absorption $\mu \left(E\right)$ in the XANES region. (b) $k^2$-weighted XAFS spectra $k^2\chi \left(k\right)$ with considerable pressure-induced change in the XAFS oscillation profile ($3-11{\AA }^{-1}$). (c) XAFS Fourier transform $\left|\chi \left(R\right)\right|$ in the range from 2.5 to $12.5{\AA }^{-1}$ with a Hanning window. Note the side peak (3.1–3.5 Å), enhancing (<3 GPa), decreasing (4.2–10.4 GPa), and merging (>12.4 GPa).

Figure 5

(a) Typical Rietveld refinements of the diffraction patterns of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ loaded in a NPD cell using jana2006 software [31]. (b) $\mathrm{Bi}{L}_3$-edge XAFS of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ data $\left|\chi \left(R\right)\right|$ at ambient pressure (black line) together with the theoretical data from the feff calculation (red line). (c) Se K-edge XAFS of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ data $\left|\chi \left(R\right)\right|$ at ambient pressure (black line) together with the theoretical data from the feff calculation (red line).

Figure 6

Upper panel: $\mathrm{Bi}{L}_3$-edge XAFS of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$. (a) Evolution of the nearest Bi-Se1 and Bi-Se2 distances of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ QLs as a function of pressure. (b) Pressure dependence of the DW factor ${\sigma }^2$. Lower panel: Se K-edge XAFS of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$. (c) Structural modeling of XAFS data $\left|\chi \left(R\right)\right|$ for $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ at 8.6 GPa (full circles) using the paths of the $R\text{−}3m$ structure within $4.5{\AA }^{-1}$. (d) Evolution of the Se-Bi and Se-Se bonds of the $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ QL at high pressure.

Figure 7

The optimized $R\text{−}3m$ structure based on the XAFS and XRD experiments: (a) Bi ($6c$) site and (b) Se2 ($6c$) sites. Red lines are the averaged values in the respective pressure ranges for clarification; (c) the obtained $c$/$a$ ratio of the $R\text{−}3m$ phase with previous data [4, 17, 36] for comparison.

Figure 8

(a) Calculated band structure of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ including spin-orbit interaction. Notation for high-symmetric points in the Brillouin zone is the same as in Ref. [11]. (b) Expanded region at the $\mathrm{\Gamma }$ point. We note that the conducting band starts indenting (>3 GPa) and finally splitting (>6 GPa) at the $\mathrm{\Gamma }$ point.

Figure 9

Calculated band gap of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ as a function of pressure: (a) direct band gap at the $\mathrm{\Gamma }$ point and (b) the smallest band gap together with the values of previous studies by Segura et al. [15] and Bera et al. [14].

Figure 10

Influence of atomic local structure on the $e$ states of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ at high pressure: (a) Fermi levels; (b) Values of the band gap with (solid) and without (open) XAFS optimized local structure for comparison.