Origin of the isostructural electronic states of the topological insulator Bi2Te3

The novel physics, such as the pressure-induced electronic topological transition (ETT), topological superconductivity and Majorana fermions in the isostructural $R\text{\ensuremath{-}}3m$ phase of three-dimensional topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, holds considerable interest in condensed-matter physics. We carried out a combined investigation of single-crystal x-ray diffraction, high-quality x-ray absorption fine structure, and first-principles theoretical calculations to decipher the puzzling origin of the intriguing electronic states in the isostructural $R\text{\ensuremath{-}}3m$ phase of ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ at high pressure. Three distinct regions with two isostructural phase transitions (IPTs) in the $R\text{\ensuremath{-}}3m$ phase have been identified. The first IPT, which is known as the ETT, occurs at the boundary of region I (0--2 GPa) and region II (2--5 GPa) with a sharp minimum in the $c/a$ ratio of $R\text{\ensuremath{-}}3m$ structure, while the second IPT happens as pressure increases from region II (2--5 GPa) to region III (5--7 GPa). The positions of the Bi ($6c$) and Se ($6c$) sites in the unit cell change rapidly in region II (2--5 GPa), but there is little change at these sites in region III (5--7 GPa). The band-gap closure in region I reflects the pressure-induced metallization. At higher pressures, the band gap opens in region II but remains almost constant after the second IPT in region III, which agrees well with the topological superconductivity of ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$. Our results demonstrate that the combination of local structure, long-range crystal structure, and first-principles calculation is critically important for understanding the isostructural electronic states and the connection between the structure and function as in ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ at high pressure.