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 biexponential 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 $\mathrm{\Gamma }$ point ($\mathrm{\Gamma }-E_{2g2}$) and $A_1^{\prime }$ optical phonon mode at the $K$ point ($K-A_1^{\prime }$). Both modes have Kohn anomalies at these points in the Brillouin zone. The result is a unique nonequilibrium 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 6.5 ps time scale. 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 $\mathrm{\Gamma }$ point shearing mode of the graphene planes and the out-of-plane motion an acoustic breathing mode response of the film.

Figure 1

Ultrafast electron diffraction of single crystal graphite. (a) The specimen normal can be rotated by an angle $\varphi$ relative to the transmitted electron beam direction. Transient diffraction patterns are captured as a function of time delay $\tau$. (b) Unit cell and Brillouin zone of graphite in the $x\text{−}y$ plane. (c) Unit cell and Brillouin zone of graphite in the $x\mathit{\text{-z}}$ plane.

Figure 2

Incoherent excitation of SCOP modes in graphite as determined through the Debye-Waller suppression of $\{110\}$ peak intensity. (a) Indexed ultrafast electron diffraction pattern of single crystal graphite taken along the [001] direction. (b) Biexponential Debye-Waller suppression of $\{110\}$ peak intensity. The laser deposited energy in the electronic system very rapidly couples to SCOP modes. At longer times, the subpopulation of SCOPs thermalize with lower energy phonon modes as the lattice comes into thermal equilibrium with the electrons. The overall laser-induced $\{110\}$ suppression is linear in excitation fluence as shown in the inset.

Figure 3

Coherent excitation of the transverse optical shearing mode in graphite. The $\{100\}$ family of peaks exhibit oscillatory dynamics, with the (1 $-1$ 0) peak oscillation out of phase by $\pi$ with respect to the other peaks. The frequency and phase of these dynamics are precisely those expected of the $\mathrm{\Gamma }$-point transverse optical shearing mode through its influence on the electron structure factors [Eq. (3)].

Figure 4

Coherent excitation of the thin film breathing mode in graphite. The $c$-axis lattice constant exhibits oscillatory dynamics in addition to simple expansion following photoexcitation. The oscillatory behavior is best explained through excitation of the lowest order longitudinal acoustic phonon quantized by the sample thickness. The measured frequency of 0.2 THz corresponds to a sample thickness of 10 nm. The overall $c$-axis expansion is linear in excitation fluence as shown in the inset.