Large p olaron evidence in the u ltrafast THz response of Lead-Halide Perovskites

. We unveil the large polaron fingerprints in the transient THz dielectric response of lead-halide perovskites. We clarify the mechanism underlying the physics of charge transport of full-inorganic lead-halide perovskites by combining ultrafast Thz spectroscopy with DFT calculations.


Introduction
Hybrid Organic-Inorganic Perovskites (HOIPs) represent a promising platform for emerging optoelectronics devices due to their exceptional physical properties. Although their low carrier mobility and the presence of static and dynamic disorder, HOIPs behave as defect-free semiconductors with long carrier lifetime and high diffusion length, hence promoting them as reliable candidates, for instance, for high efficiency solar cells [1].
Intriguingly, the formation of large polaron has been proposed as a possible explanation for the exceptional HOIPs dielectric response combined to their peculiar structure composed by a lead halide cage (PbX3) and a disordered inorganic/organic cation sublattice (A + ) [2,3]. To explain the relative moderate mobility of this class of materials, Zhu and Podzorov have proposed the presence of the large polarons formed due to the dielectric electron-phonon coupling combined with the light effective masses for bare carriers [4,5] spectroscopy and demonstrated a phonon dressing of the photo-generated species in the fsps time regime [6].
To unveil the presence of large polarons, we studied all-inorganic CsPbBr3 nanocrystals by means of Optical-Pump-THz probe spectroscopy that is capable to investigate excitations in the few meV range such as the carrier-lattice coupling. Figure 1 Normalized ∆E/E signal at 160, 80 and 20 µJ/cm 2 (green diamonds, blue squares and black circle respectively) together with the biexponential curves (continuous red line).

Results and Discussion
We excite the sample with a 400-nm, 25-fs 1-kHz laser pulses focused on the sample with a spot size diameter of 3 mm at different fluences, from 10 to 160 µJ/cm 2 .  [7]. The fast decay component becomes dominant when the initial carrier density N0 is larger than 0.5•10 18 /cm 3 . At these densities, traps states are saturated and many-body processes start to play a role, therefore we assign this fast dynamic to the increase of fast free carrier recombination and three-body processes.
To more deeply investigate the carriers transport mechanism in CsPbBr3 NCs, we studied the frequency-resolved optical conductivity. Transient spectra at different pump probe delays reveal resonances that reflect the presence of electron-phonon coupling following the photoexcitation. Remarkably, the transient conductivity reported in Figure  2a) shows three main peaks in the 0.4-1.9 THz (15-60 cm -1 ) region that bare almost the whole intensity at 3ps. Theory predicts that the formation of a large polaron is expected for CsPbBr -3 NCs after the carrier's photo-injection due to the coupling with lattice IR modes. The largest intensity is predicted for four Pb-Br-Pb bending modes at 0.75, 0.84, 1.35 and 1.88 Thz [6] that finely matches the experimental features (0.81, 1.26 and 1.74 THz). Figure 2b) shows the real part of the Lorentzian curves used for the fitting procedure. Remarkably, a redshift affects the curves at 200 ps. We rationalize this observation in terms of lattice shrinking and expansion: once the photoexcitation creates a hole in the top of the valence band, which is a Pb-Br anti-bonding, then the Pb-Br bonds shorten and the lattice shrinks with the resulting phonons blueshift; as the injected charge starts to relax, then the lattice can expand again with the consequent stretch of the Pb-Br bonds and phonons softening.

Conclusions
By combining Ultrafast THz spectroscopy with density-functional theory calculations we demonstrated the presence of large polaron in all-inorganic lead-halide Perovskites. We observed the fingerprints of the coupling between the photoinjected charge and the bending modes of the deformed PbBr lattice in the pump-induced conductivity spectra. Our findings agree with the recent results present in the literature [6] and explain the peculiar dielectric response that make lead halide perovskites the more intriguing playground for beyond thestate-of-the-art optoelectronics devices.