Phonon hardening due to the small-polaron effect

The influence of the small-polaron effect on the vibrational properties of the strongly coupled electron-phonon system is investigated. It was found that polaron-phonon interaction may cause a noticeable renormalization of the phonon spectra. These changes may be observed by the measurements of the speed of sound for which a very specific dependence on temperature, values of coupling constant and adiabatic parameter is expected. We also found that the rise of the small-polaron effective mass as a function of the coupling constant should be considerably moderated than that anticipated without taking into account the modification of the vibrational spectra