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Fine Structure Splitting of Phonon-Assisted Excitonic Transition in (PEA)_{2}PbI_{4} Two-Dimensional Perovskites

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

_{2}PbI${}_{4}$ crystals.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic view of a 2D perovskite of thickness $n=1$ together with the conduction and valance band alignment and spatial dependence of dielectric screening. (

**b**) Schematic of the band edge exciton fine structure of (PEA)${}_{2}$PbI${}_{4}$ (PEA—phenylethylammonium). G is the ground state of the system (no excitons), D is the dark state, and X, Y, and Z are the three bright states with orthogonally oriented dipole moments. (

**c**) Photoluminescence (grey shading) and reflectance (black line) spectra of (PEA)${}_{2}$PbI${}_{4}$ single crystal. The two in-plane bright exciton states are indicated by X and Y.

**Figure 2.**(

**a**) Broad spectral range reflectance spectrum of (PEA)${}_{2}$PbI${}_{4}$ (black line) and its derivative (red line). The minima in derivative correspond to transition energies. (

**b**) Schematic showing the Franck–Condon model (configurational coordinate diagram). The lower and upper parabolas represent the harmonic potential for the lattice in the ground and excited state. The shaded area corresponds to the spatial probability distribution of the harmonic oscillator. The arrows show examples of the transition from the ground (excited) vibrational level 0 to the vibration level 2 of the excited (ground) state. Such a transition results in the emission of two phonons. (

**c**) Schematic of absorption (green) and emission (grey) spectra of exciton coupled to lattice vibration. The envelope lines represent the merged responses of phonon replicas involving different numbers of phonons also known as phonon wings.

**Figure 3.**(

**a**) Polarization resolved spectra of reflectance for ${\pi}_{X}$ and ${\pi}_{Y}$ polarization. (

**b**–

**d**) Dependence of the reflectance spectrum as a function of the polarization angle. The intensity in each panel is adjusted to emphasize the splitting in a given spectral range. ${\mathsf{\Delta}}_{XY}{sin}^{2}\left(\alpha \right)$ is plotted in dashed black lines, which shows the oscillatory behaviour of the transition energy as a function of detection angle.

**Figure 4.**Polarization resolved PL and reflectance spectra. Blue and red arrows show equal distances of low energy PL peak and SB2 from the zero-phonon line of X and Y exciton.

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**MDPI and ACS Style**

Posmyk, K.; Dyksik, M.; Surrente, A.; Zalewska, K.; Śmiertka, M.; Cybula, E.; Paritmongkol, W.; Tisdale, W.A.; Plochocka, P.; Baranowski, M.
Fine Structure Splitting of Phonon-Assisted Excitonic Transition in (PEA)_{2}PbI_{4} Two-Dimensional Perovskites. *Nanomaterials* **2023**, *13*, 1119.
https://doi.org/10.3390/nano13061119

**AMA Style**

Posmyk K, Dyksik M, Surrente A, Zalewska K, Śmiertka M, Cybula E, Paritmongkol W, Tisdale WA, Plochocka P, Baranowski M.
Fine Structure Splitting of Phonon-Assisted Excitonic Transition in (PEA)_{2}PbI_{4} Two-Dimensional Perovskites. *Nanomaterials*. 2023; 13(6):1119.
https://doi.org/10.3390/nano13061119

**Chicago/Turabian Style**

Posmyk, Katarzyna, Mateusz Dyksik, Alessandro Surrente, Katarzyna Zalewska, Maciej Śmiertka, Ewelina Cybula, Watcharaphol Paritmongkol, William A. Tisdale, Paulina Plochocka, and Michał Baranowski.
2023. "Fine Structure Splitting of Phonon-Assisted Excitonic Transition in (PEA)_{2}PbI_{4} Two-Dimensional Perovskites" *Nanomaterials* 13, no. 6: 1119.
https://doi.org/10.3390/nano13061119