Temperature Effects in the Band Structure of Topological Insulators

We study the effects of temperature on the band structure of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ family of topological insulators using first-principles methods. Increasing temperature drives these materials towards the normal state, with similar contributions from thermal expansion and from electron-phonon coupling. The band gap changes with temperature reach 0.3 eV at 600 K, of similar size to the changes caused by electron correlation. Our results suggest that temperature-induced topological phase transitions should be observable near critical points of other external parameters.

Figure 1

Temperature dependence of the $\mathrm{\Gamma }$-point band gaps of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ family of compounds. The black dotted lines correspond to the static lattice band gaps; the orange dashed and blue dashed-dotted lines show the result of including only thermal expansion or only electron-phonon coupling effects, respectively; the red solid curves give the total temperature dependence.

Figure 2

Phonon dispersion of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ with mode resolved electron-phonon coupling strength without (left) and with (right) spin-orbit coupling. The area of the circles are proportional to the strength of electron-phonon coupling, and the sign of the coupling is positive (widening the gap) for blue circles and negative (reducing the gap) for red circles.

Figure 3

Pressure-temperature phase diagram of ${\mathrm{Sb}}_2{\mathrm{Se}}_3$. Experimentally, the pressure-induced phase transition is observed at 2.5 GPa [3].