Evidence of superconductivity-induced phonon spectra renormalization in alkali-doped iron selenides

Polarized Raman scattering spectra of superconducting K$_x$Fe$_{2-y}$Se$_2$ and nonsuperconducting K$_{0.8}$Fe$_{1.8}$Co$_{0.2}$Se$_2$ single crystals were measured in a temperature range from 10 K up to 300 K. Two Raman active modes from the $I4/mmm$ phase and seven from the $I4/m$ phase are observed in frequency range from 150 to 325 cm$^{-1}$ in both compounds, suggesting that K$_{0.8}$Fe$_{1.8}$Co$_{0.2}$Se$_2$ single crystal also has two-phase nature. Temperature dependence of Raman mode energy is analyzed in terms of lattice thermal expansion and phonon-phonon interaction. Temperature dependence of Raman mode linewidth is dominated by temperature-induced anharmonic effects. It is shown that change of Raman mode energy with temperature is dominantly driven by thermal expansion of the crystal lattice. Abrupt change of the A$_{1g}$ mode energy near $T_C$ was observed in K$_x$Fe$_{2-y}$Se$_2$, whereas it is absent in non-superconducting K$_{0.8}$Fe$_{1.8}$Co$_{0.2}$Se$_2$. Phonon energy hardening at low temperatures in the superconducting sample is a consequence of superconductivity-induced redistribution of the electronic states below critical temperature.