Rashba-Type Band Splitting Effect in 2D (PEA)2PbI4 Perovskites and Its Impact on Exciton–Phonon Coupling

Despite a few recent reports on Rashba effects in two-dimensional (2D) Ruddlesden–Popper (RP) hybrid perovskites, the precise role of organic spacer cations in influencing Rashba band splitting remains unclear. Here, using a combination of temperature-dependent two-photon photoluminescence (2PPL) and time-resolved photoluminescence spectroscopy, alongside density functional theory (DFT) calculations, we contribute to significant insights into the Rashba band splitting found for 2D RP hybrid perovskites. The results demonstrate that the polarity of the organic spacer cation is crucial in inducing structural distortions that lead to Rashba-type band splitting. Our investigations show that the intricate details of the Rashba band splitting occur for organic cations with low polarity but not for more polar ones. Furthermore, we have observed stronger exciton–phonon interactions due to the Rashba-type band splitting effect. These findings clarify the importance of selecting appropriate organic spacer cations to manipulate the electronic properties of 2D perovskites.


Spectroscopic Techniques
All optical measurements were performed on thin films of HP and FP.These films were prepared by spin coating on a clean ozonized coverslip at 1000 rpm for 30 seconds.
Two-Photon Photoluminescence.2] In brief, a mode-locked Ti-Sapphire oscillator (Synergy from Femtolasers) was used to generate laser pulses with a pulse duration of about 10 fs, a repetition rate of 80 MHz, and a central wavelength of 790 nm.The output of the laser was directed to an inverted microscope.A dichroic mirror (FF670-sdi01−25 × 36, Semrock) was used to separate the excitation beam from the PL.To further reduce the scattered light of the excitation beam, a short pass filter (OD4, Edmund optics, no.84-698) with a cut-off wavelength of 625 nm was placed before the spectrometer.A reflective objective (36X/0.5 NA, Edmund optics, part 83684410) was used to focus the excitation beam to the sample.The PL was recorded by a spectrometer with a thermoelectrically cooled CCD detector.The sample was placed in a temperature-controlled stage (Linkam Scientific Instruments, LTS420E-P).The temperature was measured with a platinum resistor sensor in close distance to the surface.A temperature control system was used to change the temperature in a range between 80 and 290 K with a linear cooling rate of 3 K/min.Time-Resolved PL.The lifetimes of the thin-films were probed using a confocal fluorescence microscope (Leica TCS SP8 X).A 470 nm laser with 2.5 MHz repetition rate of 50 ps pulses was employed for the investigation of the FP and HP films.The PL was detected using a fast hybrid photodiode and the exponential decays were fitted with the inbuilt software.

Microscopic Techniques
Transmission Electron Microscopy.High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images, selected area electron diffraction (SAED) patterns and energy-dispersive X-ray spectra in STEM mode (STEM-EDS) were acquired S3 using a Thermo Fisher Titan Themis Z microscope operating at 300 kV supplied with Super-X EDS system.Acquisition time for EDS measurements was around 500 s.Samples were prepared by dripping a diluted sample solution onto a carbon-coated polymer film copper/gold grid.

Grazing-Incidence Wide-Angle X-ray Scattering (GIWAXS).
We performed grazing incidence X-ray diffraction at beamline BL9 of the DELTA synchrotron radiation source (Dortmund, Germany). 3The 2D diffraction images were collected at an incident energy of 13 keV with a beam size of 0.05 × 1.0 mm 2 (v × h) using a MAR345 image plate detector.The angle of incidence was set to 0.25° and the setup was calibrated with a CeO2 powder sample as standard.The 2D diffraction images were converted to reciprocal space and analyzed exploiting the program package pygix/pyFAI. 4The integrations were performed in the azimuthal angular range at 80°±10° and 10°±10° in order to calculate the in-plane and out-ofplane diffraction patterns.In out-of-plane direction the (n00) and (00n) reflections were used to determine the lower limit of the crystallite size in this direction as well as the strain of the second kind for (F-PEA)2PbI4 and (PEA)2PbI4.Moreover, the widths of the (n00) and (00n) diffraction peaks in azimuthal direction were analyzed to determine the tilt-distribution of the flakes.

Computational Methods
6][7] The exchange correlation interactions were treated with the Perdew-Burke-Ernzerhof (PBE) formulation of the generalized gradient approximation (GGA). 8We used a full-potential projected plane-wave framework with a cut-off energy of 350 eV for the plane-wave basis set.We have used ultrasoft pseudopotentials with 14, 7, 7, 4,5 and 1 electrons for Pb, I, F, C, N and H atoms, respectively.The experimental cif files are used to generate the structures.
Additionally, we have applied the tetrahedron method with Blöchl corrections for smearing while optimizing the structures.The structures are optimized until the force per atom is less than -0.02 eV.For band structures, we performed spin-orbit coupling (SOC) corrected calculations.

Material Synthesis
0.8 mmol of phenylethylammonium iodide (PEAI, Greatcellsolarmaterials) or 4-Fluoro-Phenylammonium iodide (4F-PEAI, Greatcellsolarmaterials) and 0.4 of mmol PbI2 (Sigma, 99%) were dissolved in a mixture of 10 mL of DMF and 12.5 μL of n-octylamine to form a perovskite precursor solution.Then, 15 μL of the perovskite precursor solution was quickly dropped into 10 mL of toluene under vigorous stirring.After 30 min, the solution was centrifuged at 3,500 rpm for 5 min, and the precipitates were dispersed in hexane for further use.

Fitting Parameters
Table S1.Fitting parameters determined from the PL kinetics of FP and HP perovskites.

Figure S2 .Figure S3 .S8Fitting
Figure S1.EDS spectra of a) (PEA)2PbI4 and b) (F-PEA)2PbI4.Cu and Au signals emerge from the sample holder, while Si signal originates from the EDS detection system.