Coherent and incoherent electron-phonon coupling in graphite observed with radio-frequency compressed ultrafast electron diffraction

Radio-frequency compressed ultrafast electron diffraction has been used to probe the coherent and incoherent coupling of impulsive electronic excitation at 1.55 eV (800 nm) to optical and acoustic phonon modes directly from the perspective of the lattice degrees of freedom. A bi-exponential suppression of diffracted intensity due to relaxation of the electronic system into incoherent phonons is observed, with the 250 fs fast contribution dominated by coupling to the $E_{2g2}$ optical phonon mode at the $\Gamma$-point ($\Gamma-E_{2g2}$) and $A_1^{'}$ optical phonon mode at the $K$-point ($K-A_1^{'}$). Both modes have Kohn anomalies at these points in the Brillouin zone. The result is a unique non-equilibrium state with the electron subsystem in thermal equilibrium with only a very small subset of the lattice degrees of freedom within 500 fs following photoexcitation. This state relaxes through further electron-phonon and phonon-phonon pathways on the 6 ps timescale. In addition, electronic excitation leads to both in-plane and out-of-plane coherent lattice responses in graphite whose character we are able to fully determine based on spot positions and intensity modulations in the femtosecond electron diffraction data. The in-plane motion is specifically a $\Gamma$-point shearing mode of the graphene planes with an amplitude of approximately 0.06 pm and the out-of-plane motion an acoustic breathing mode response of the film.