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Temperature-dependent chirped coherent phonon dynamics in Bi$_{2}$Te$_{3}$ using high intensity femtosecond laser pulses

Degenerate pump-probe reflectivity experiments have been performed on a single crystal of bismuth telluride (Bi$_2$Te$_3$) as a function of sample temperature (3K to 296K) and pump intensity using $\sim$ 50 femtosecond laser pulses with central photon energy of 1.57 eV. The time resolved reflectivity data show two coherently generated totally symmetric A$_{1g}$ modes at 1.85 THz and 3.6 THz at 296K which blue shift to 1.9 THz and 4.02 THz, respectively at 3K. At high photoexcited carrier density of $\sim$ 1.7 $\times$ 10$^{21}$cm$^{-3}$, the phonon mode at 4.02 THz is two orders of magnitude higher positively chirped (i.e the phonon time period decreases with increasing delay time between the pump and the probe pulses) than the lower frequency mode at 1.9 THz. The chirp parameter, $β$ is shown to be inversely varying with temperature. The time evolution of these modes is studied using continuous wavelet transform of the time-resolved reflectivity data.