Origin of the thermal expansion anomaly in layered Bi2X3 topological insulators: Ultrafast time-resolved pump-probe experiments and theory

Recent experiments on the thermal expansion of ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$, a prototypical example of strong three-dimensional topological insulators, have shown an intriguing anomaly in the thermal expansion coefficient along the hexagonal axis $({\ensuremath{\alpha}}_{{}_{\ensuremath{\parallel}}})$, which drops sharply to almost zero in a narrow range of temperature around $\ensuremath{\sim}225$ K. With no accompanying signatures in other properties, the origin of this anomaly is not understood. We present here femtosecond pump-probe differential reflectivity measurements on single crystals of ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ as a function of temperature from 3 to 300 K to determine the temperature dependence of coherent optical and acoustic phonons along with the dynamics of the photoexcited carriers. We find clearly anomalous temperature dependence of the parameters associated with vibrational and electronic relaxation in the narrow temperature range of 200--250 K. Within first-principles density functional theoretical analysis, we show that the observed anomalies can be explained with a mechanism of formation of stacking faults stabilized by vibrational entropy above 200 K. As a similar anomaly in the thermal expansion is also observed in other chalcogenides in the same family, the proposed mechanism may also be applicable to these layered strong topological insulators.