Coherent acoustic phonons generated by ultrashort terahertz pulses in nanofilms of metals and topological insulators

We report the generation of coherent acoustic phonons in materials with terahertz ultrashort pulses. This is demonstrated in metals and topological insulators by exciting an acoustic eigenmode in nanometric-sized thin films. The efficiency of the coupling is quadratic in the terahertz electric field strength within the range of investigation. Owing to a quantitative comparison between terahertz and near-infrared ultrashort pulse excitations, we show that the process of acoustic phonon generation by terahertz radiation is mainly driven by thermoelastic stress. While for the near-infrared light excitation the lattice temperature increase comes from a rapid energy transfer from the hot carriers to the phonon bath during carrier intraband relaxation, the thermoelastic stress induced by the terahertz electric field is linked to the scattering of the accelerated electrons leading to an ultrafast Joule effect.

Figure 1

(a) Simplified electronic band structure of the metal and of the degenerated $n$-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Simple vertical arrows show the interband optical transition induced by the NIR pulse and double black arrows represent carrier intraband acceleration by the THz electric field. The blue dashed lines represent the spin-polarized Dirac surface states. (b) Dynamic of the photoinduced stresses originating from the electrons ($\mathrm{\Delta }{\sigma }_e$) or from the phonons ($\mathrm{\Delta }{\sigma }_T$) in the case of the prototypical metal aluminum. The NIR light pulse duration is 165 fs, the absorbed energy is $\sim 10$ J/${\mathrm{cm}}^3$, and the thickness is 20 nm. (c) Sketch of the femtosecond time-resolved experiment. (d) Temporal trace of the THz driving field along with its spectrum components (inset).

Figure 2

(a) Transient optical transmission obtained with a THz or NIR pump excitation for a thin Cr film. Dashed lines correspond to the extracted oscillatory parts of the signals (see text). The pulse energy of the NIR is $\sim 0.07\mu \mathrm{J}$ and the THz peak electric field is $\sim 275$ kV/cm. (b) Same as (a) but for a thin 20-nm Al film. The pulse energy of the NIR pulse is $\sim 0.04\mu \mathrm{J}$ and the THz peak electric field is $\sim 250$ kV/cm.

Figure 3

(a) THz peak electric field and NIR pulse energy dependence of the acoustic phonon signal for the Cr thin film. The blue circles indicate the transients shown in Fig. 2. Inset: Coherent acoustic phonon amplitude vs THz pulse energy. (b) Acoustic phonon amplitude as a function of the absorbed density energy for the Cr sample. The THz absorbed energy was calculated by using Eq. (1). The blue circles indicate the transients shown in Fig. 2.

Figure 4

(a) Transient optical transmission obtained with a THz or NIR pump excitation for a 15-nm ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ thin film with 51 nJ and 1.2 $\mu \mathrm{J}$ for NIR and THz excitation, respectively. Inset: Oscillatory part of the signal. (b) THz pulse energy dependence of the acoustic phonon amplitude for the 15-nm thin film. (c) Thickness dependence of the coherent acoustic phonon signal generated by THz excitation. (d) Coherent acoustic phonon oscillation period vs the film thickness. Inset: Phase of the coherent acoustic phonon respect to a cosine function as a function of the samples' thicknesses.