Coherent phonon dynamics of normal metal in ultrafast spectroscopy: Non-equilibrium gauge invariant Green's function approach

•Coherent phonon dynamics of normal metal in ultrafast spectroscopy is studied.•Non-equilibrium phonon self-energy is found in terms of gauge invariant polarization functions.•Polarization function is obtained by solving gauge invariant quantum Boltzmann equation.

The phonon dynamics of normal metal in the coherent regime of ultrafast spectroscopy is studied based on the non-equilibrium gauge invariant Green's function method. The non-equilibrium phonon self-energy is computed explicitly as a function of time in a gauge invariant way up to the second order of electric field of applied laser pulse. The extension beyond the coherent regime and the incorporation of correlation effects are discussed.