Ultrafast Evolution of the Excited-State Potential Energy Surface of ${\mathrm{TiO}}_2$ Single Crystals Induced by Carrier Cooling

We investigate the influence of carrier cooling dynamics in ${\mathrm{TiO}}_2$ on the excited-state potential energy surface along the $A_{1g}$ optical phonon coordinate after above band-gap excitation using ultrashort ultraviolet pulses. The large amplitude coherent oscillation observed in a pump-probe transient reflectivity measurement shows a phase shift of $-0.2\pi$ with respect to a purely instantaneous displacive excitation. The dynamic evolution of the potential energy surface minimum of the coherent phonon coordinate is explored using accurate density functional theory calculations, which confirm a shift of the potential energy surface minimum upon resonant laser excitation and reveal a significant positive contribution to the displacive force due to the cooling of the excited hot electron-hole plasma. We show that this noninstantaneous effect can quantitatively explain the experimentally observed phase using reasonable assumptions for the parameters characterizing the excited carriers. Our work demonstrates that the fast equilibration dynamics of laser-excited nonequilibrium carrier populations can have a pronounced effect on the initial structural response of crystalline solids.

Figure 1

Transient reflectivity of ${\mathrm{TiO}}_2$. The delay-differential reflectivity signal $\delta R/\delta t$ is shown (black solid line), as well as the least-square fit of the coherent phonon oscillation with an exponentially decaying ($\sim 200\mathrm{fs}$) sine function (red dotted line). The inset shows the transient reflectivity signal $\Delta R/R_0$ at $1.3\mathrm{mJ}/{\mathrm{cm}}^2$ pump fluence.

Figure 2

Fit results of the phonons’ phase (a), frequency (b), and amplitude (c) as a function of the pump fluence.

Figure 3

(a) PES of ${\mathrm{TiO}}_2$ along the $A_{1g}$ phonon coordinate in the electronic ground state (black solid line), the hot laser-excited state with an electron temperature of 1 eV (red dashed line), and the cooled excited state with a temperature of 0.027 eV (blue dotted line). The excitation density of both excited states is 0.1 electron-hole pairs per unit cell, corresponding to the experimentally employed fluence regime. The PES of hot and cold excited states are offset by $-414.9$ and $-197.3\mathrm{meV}$, respectively, for clarity of representation. (b) Position of the PES minimum as a function of the number of excited electron-hole pairs per unit cell and the electron temperature. (c) Calculated oxygen atom trajectory (black solid line), in comparison with a cosine oscillation at 17.9 THz that perfectly describes the motion after $t=20\mathrm{fs}$. This cosine oscillation exhibits a phase shift of $-0.16\pi$ (red dashed line), as illustrated with the black dashed lines and black arrows, which allows us to determine the effective phase shift of the atomic motion.

Figure 4

Redistribution of valence electron density around oxygen (yellow) and titanium (green) atoms for hot (a) and (b) cold excited states compared to the electronic ground state, shown for one half of the unit cell. The atomic configuration is fixed at the ground state. Isosurfaces for positive (more charge, red, at Ti sites) and negative (less charge, blue, at O sites) change in charge density are shown at $\pm 0.0005$, $\pm 0.003$, and $\pm 0.0055e/a_0^3$.