Strong electron-phonon coupling and enhanced phonon Grüneisen parameters in valence-fluctuating metal EuPd2Si2

We study the valence crossover and strong electron-phonon coupling of ${\mathrm{EuPd}}_{2}{\mathrm{Si}}_{2}$ by polarization-resolved Raman spectroscopy. The fully symmetric phonon mode shows strongly asymmetric line shape at low temperature, indicating Fano-type interaction between this mode and a continuum of electron-hole excitations. Moreover, the frequency and linewidth of the phonon modes exhibit anomalies across the valence-crossover temperature, suggesting the coupling between valence fluctuations and lattice vibration. In particular, two phonon modes show a significantly enhanced Gr\"uneisen parameter, possibly related to a nearby critical elastic regime. The relative contribution of the structural change and valence change to the phonon anomalies is evaluated by density-functional-theory calculations.