Anomalous temperature dependence of optical and acoustic phonons in Bi₂Se₃ arising from stacking faults

The class of layered 3D-topological insulators have shown intriguingly anomalous temperature dependence in their thermal expansion coefficients. It was proposed that stacking faults are the origin of the observed anomalous thermal expansion. Here, using femtosecond pump-probe differential reflectivity measurements we probe the carrier and coherently generated totally symmetric A_1g optical phonons in Bi₂Se₃. Transient signals also show a low frequency (∼GHz) oscillations due to coherent longitudinal acoustic phonons. We extract temperature dependence of optical constants, sound velocity and Young's modulus of Bi₂Se₃ using the strain pulse propagation model. A remarkable anomalous behavior around ∼180 K is observed in the temperature dependence of optical and acoustic phonons as well as the optical constants. First-principles density functional theory reveals that thermally activated formation of stacking faults is responsible for the anomalies observed in Bi₂Se₃, similar to case of Sb₂Te₃. We also show that inclusion of spin–orbit coupling plays an important role in reducing the total energy difference between the pristine and the faulted structures. (paper)