Coherent and incoherent structural dynamics in laser-excited antimony

We investigate the excitation of phonons in photoexcited antimony and demonstrate that the entire electron-lattice interactions, in particular coherent and incoherent electron-phonon coupling, can be probed simultaneously. Using femtosecond electron diffraction (FED) with high temporal resolution, we observe the coherent excitation of the fully symmetric ${\mathrm{A}}_{1g}$ optical phonon mode via the shift of the minimum of the atomic potential energy surface. Ab initio molecular dynamics simulations on laser excited potential energy surfaces are performed to quantify the change in lattice potential and the associated real-space amplitude of the coherent atomic oscillations. Good agreement is obtained between the parameter-free calculations and the experiment. In addition, our experimental configuration allows observing the energy transfer from electrons to phonons via incoherent electron-lattice scattering events. The electron-phonon coupling is determined as a function of electronic temperature from our DFT calculations and the data by applying different models for the energy transfer.

Figure 1

(a) Sketch of the experimental configuration. (b) Diffraction image of tilted, polycrystalline antimony with (110) texture. The axis of rotation is shown as a dotted line. (c) Radial averages, calculated by integrating selected angular regions (colored bars) of the diffraction pattern shown in (b). [The different ratios of the intensity of closely spaced peaks allows a better determination of relative intensity changes with pump-probe delay (not shown).] The lines indicate the positions of Bragg peaks that remain (gray) or vanish (orange) in the more symmetric phase.

Figure 2

Measured and simulated evolution of the intensity of different Bragg peaks in (a) the first picosecond after excitation and (b) in a window of 15 picoseconds. Diamond symbols are used for PD peaks and circles denote Bragg peaks which are also present in the high-symmetry phase. The thick solid lines in (a) are obtained from the MD simulations by convolution with a Gaussian function to account for the temporal resolution of the experiment. Peak labels only denote the most prominent peaks of the fit.

Figure 3

(a) Electronic heat capacity of Sb as a function of electronic temperature, calculated by DFT. (b) Electron temperature dependence of the electron-phonon coupling strength. The blue solid line is the retrieved coupling strength from the TTM fit with the light blue area denoting its error. The blue dashed line is $G_{ep}$ from the DFT calculations, and the red dashed lines are the partial couplings $G_{ep,i}$ to optical and acoustic phonon branches, respectively. (c) Measured change in atomic mean square displacement (black squares) as a function of pump-probe delay. The blue solid line is derived from the two-temperature model fit, the dotted blue line is the MSD obtained by running a TTM with the DFT values of $G_{ep}$ as an input. The red dashed line is the result of the nonthermal lattice model using the ab initio partial coupling strengths.