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We have studied spectral evolution of the $E_u^1$ phonon line of atopological insulator Bi$_{2-x}$Sr$_x$Se$_3$ with temperature. Unlike theRaman-active phonons, the $E_u^1$ mode demonstrates softening upon cooling thecrystal, and the corresponding spectral line acquires a pronounced Fano-likeshape at temperatures $T\lesssim100$ K. We interpret the latter effect as asignature of specific coupling of the bulk infrared active phonons to surfaceDirac electrons. Using coherent resonant excitation of the $E_u^1$ mode as asurface sensitive tool, we have detected softening of the surface counterpartof the bulk $E_u^1$ phonon mode upon strontium doping. This observation can bean evidence of enhanced electron-phonon interaction at the surface of theBi$_{2-x}$Sr$_x$Se$_3$ crystal.

Anomalous behavior of the $E_u^1$ infrared-active phonon mode in a Bi$_{2-x}$Sr$_x$Se$_3$ crystal