Using neutron diffraction and the pair density function analysis, the local atomic structure of the three-dimensional ${\text{Bi}}_2$Se${}_{3-x}$Te${}_x$ ($x=0$, 1, 2, and 3) topological insulator is investigated. The substitution of Te for Se in Bi${}_2$Se${}_{3-x}$Te${}_x$ ($x=0$, 1, 2, and 3) is not random and its preferred site is at the edges of the quintuple layer. This generates a local strain due to the atom size mismatch between Se and Te. The site preference is surprising given that the Bi to chalcogen bonds are strongest when the ions are at the edges than in the middle layer. The (Se/Te) atoms in the middle sublayer of the quintuple are coupled more softly to the Bi atoms than those of the edges and have lower Debye temperatures. This suggests that the atomic properties within the quintuple layer are different than those at the edges. Additionally, the results from band structure and density of state calculations are reported to show the dependence of doping and temperature.

• Received 12 August 2013
• Revised 5 November 2013

DOI:https://doi.org/10.1103/PhysRevB.88.224108