Electron–phonon coupling and a resonant-like optical observation of a band inversion in topological crystal insulator Pb_1−x Sn _x Se

Abstract

The optical reflectivity of n-type Pb0.865Sn0.135Se and Pb0.75Sn0.25Se solid solutions was measured in the THz spectral region energetically corresponding to optical phonon excitations and in the temperature range from 40 K to 280 K. The first solid solution exhibits an open energy gap with trivial band ordering at all temperatures, while for the second one the transition from trivial insulator to topological crystal insulator phase is expected. The analysis of Pb0.75Sn0.25Se data performed within the dynamic dielectric function formalism revealed an anomaly of resonance-like character in the temperature dependence of LO phonon frequency. The formula for LO phonon energy renormalization reproduced observed anomaly for energy gap equal to zero, the phase transition occurred at T0 = (172 ± 2) K. This effect was absent for Pb0.865Sn0.135Se. Present results show that reflectivity measurements in the THz range in the vicinity of LO phonon frequency can be valuable experimental method for precise determining of band inversion temperature in narrow-gap topological materials.