Electronic Gr\"{u}neisen Parameter in the Non-equilibrium Regime

The Gr\"{u}neisen parameter is a fundamental parameter characterizing the relationship between thermal expansion and specific heat of a solid. Conventionally, electronic Gr\"{u}neisen parameter\textit{ $\gamma $}$_{e}$ is measured in a solid by minimizing the lattice contribution to thermal expansion at low temperatures, and the value of \textit{$\gamma $}$_{e}$ is believed to be a constant. In this report, we perform pump-probe experiments using surface plasmon as the probe technique to resolve the dynamics of acoustic phonons that are impulsively excited in Ag film using fs laser pulses. Our study shows that the conventional value of electronic Gruneisen parameter is not necessarily valid in thermal non-equilibrium distribution immediately following ultrafast pulse excitation. A revised \textit{$\gamma $}$_{e}$ is proposed here to precisely take into account the role of electron pressure in driving acoustic phonons in solids.