Observation of strong helical excitons and unexpectedly giant Rashba splitting in single crystal two-dimensional Organic-Inorganic Halide Perovskites

: Two-dimensional (2D) organic-inorganic lead halide perovskites possess strong spin-orbit coupling, and in the presence of broken inversion symmetry, this may lead to helical excitons and Rashba splitting at the band extrema 1-6 . However, a direct and systematic measurement of the helical excitons and the Rashba parameter in the system is still lacking. Here, we report distinct two bright co-helical and two dark anti-helical excitons in single crystal ((CH 3 (CH 2 ) 3 NH 3 ) 2 (CH 3 NH 3 ) n -1 Pb n I 3 n +1 ( n = 1 to 4), where n determines quantum well (QW) thickness of inorganic layer 7 . By comprehensively analyzing the fine structure of helical excitons, we find that the Rashba splitting originates from surface inversion asymmetry and surface-normal electric fields, which are determined by the QW’s dielectric environment, n and temperature. The Rashba splitting parameter is found among the highest recorded of 2.66 and 2.5 eV∙Å for the conduction and valence band of n =1 Iodide, respectively, and reduces for n>1 Iodide. Our result shows the importance of helical excitons and Rashba splitting and presents a direct method to quantify the Rashba parameter in complex halide perovskites. We hope that our study inspires applications of QW materials in novel spintronic devices.


Introduction
Two-dimensional (2D) Ruddlesden-Popper perovskites (RPPs) are a class of quantum well (QW)-like materials represented by the formula (R)2(A)n-1MnX3n+1, where R and A are organic cations, M is a divalent metal cation and X is a halide anion. The value of parameter n indicates the number of the inorganic metal-halide layers between the two layers of the organic chains and determines the QW thickness 7,8 . Therefore, the degree of quantum and dielectric confinements as well as related properties, such as band gaps [9][10][11][12] , excitonic binding energies 9 and Rashba effect 5 are expected to vary with n. The arrangement of RPPs is fundamentally different from transition metal dichalcogenides, in which one layer of the metal ions is sandwiched between two hexagonal layers of S or Se atoms, affording a rigid backbone and dielectric environments [13][14][15] . Therefore, compared with traditional three-dimensional (3D) perovskites and classic dichalcogenide based 2D materials, RPPs offer rich new phenomena for fundamental studies and provide tremendous advantages for various applications. Recently, the synthesis of phase-pure (purified to one n value) 2D single crystal perovskites with high n values was achieved 7,10 .
This opens a new possibility to explore intrinsic physical properties, in particular the electronic structure and optical properties such as helical excitons and Rashba splitting in single crystalline RPPs.
The presence of heavy atoms such as lead and iodine introduces strong spin-orbit coupling (SOC) in the electronic structure 1,16,17 , which makes it highly relevance to spintronics. In non-centrosymmetric crystals, or at surfaces or interfaces where inversion symmetry is broken, the electrons feel an effective electromagnetic field due to the SOC. This interaction, known as the Rashba effect [1][2][3][4]18,19 , removes the electron spin degeneracy and splits the corresponding valence band (VB) and conduction band (CB), resulting in various spin textures at the band edges 2,20 . One compelling observation at the Rashba band edge is energy ordering of excitons. In particular, for 2D RPPs, helical excitons consisting of bright co-helical and dark anti-helical excitons have been predicted due to Rashba splitting (Figs. 1a and b) 20 . Owing to the spin-pair helicities of VB and CB, each exciton state is split into several energy sublevels, known as fine structure. Therefore, finding helical excitons are crucial for fundamental understanding of electronic structure and Rashba effect in 2D RPPs.
For halide perovskites, Rashba-type effects may lead to intriguing and rich phenomena.
An example is that the band shift in momentum space (k-space) may cause a direct-toindirect band gap transition, and the shift is strongly dependent on the magnitude of Rashba splitting 2-4 . This has a direct consequence on the recombination dynamics of charge carriers. The Rashba effect in 3D RPPs has been studied using angle resolved photoemission spectroscopy 3 , photogalvanic effect 21,22 and electro-absorption 23 , but the Rashba parameters determined showed great disparity. Rashba splitting in 2D (PEA)2PbI4 was reported to be ~1.6 eV Å using a low-energy peak in the electro-absorption spectrum and attributed to transitions between the Rashba spin split bands 19 . However, a direct way to measure helical excitons and spin splitting at the Rashba bands (both VB and CB) is still lacking and challenging.
In this Letter, we use high-resolution and angle-dependent spectroscopic ellipsometry (SE) to directly probe electronic and optical fine structure of ((CH3(CH2)3NH3)2(CH3NH3)n-1PbnI3n+1 (n = 1 to 4) and establish a relationship between the Rashba effect and the thickness of the QW through RPPs. Spectroscopic ellipsometry is the most direct and self-normalized technique to simultaneously probe excitons and spin excitation, which have been shown successfully in transition metal oxides 24 . We perform polarization-dependent X-ray absorption spectroscopy (XAS) measurements at the C K-edge to reveal the surface symmetry broken. corresponds to the change of QW width due to more PbI6 sheets inserted between two organic layers ( Supplementary Fig. S1). In the extreme case where n=∞, the structure becomes a three-dimensional perovskite similar to BaTiO3 25-28 .
The optical fine structure is the most direct and important property in revealing helical excitons 24 as well as Rashba splitting (c.f. Figs. 1a and b). It has been successfully used to study a variety of SOC type of materials, including a polar BiTeI semiconductor 29

and a
Weyl semimetal 30 . The electron dispersion relation near the CB and VB extrema points is described by the effective-mass approximation 2,19 where m * is effective mass of carriers and k is momentum wavevector. The presence of heavy elements in the crystal gives rise to spin-orbit coupling, which, combined with the breaking of the inversion or crystal symmetry, can lift the spin-degeneracy in both momentum space and energy space and thus shift the spin band away from the symmetric points. The new electron/hole dispersion relation can be described by 2,19 where Rashba parameter α=2∆/k0, k0 is the band maximum shifted from the high symmetry point and ∆ is the Rashba energy splitting (see Supplementary Note 4). For n=1 Iodide, we find the lowest interband transition is ~2.80 eV, which is also identified as an optical band gap for n = 1 (Figs. 1c and d).
Our main observation is huge and sharp optical features of helical excitons at ~2.55 (peak II) and ~2.57 eV (peak III) accompanied by two satellite-like features at ~2.46 (peak I) and ~2.62 eV (peak IV) as shown in Figs. 1c and d. Interestingly, the intensity of ε2 of peaks II and III is more than 30 times than that of ε2 at the band-to-band transition.
Generally, an exciton excitation involves a Coulombic pairing of an electron in the conduction band with a hole in the valence band (Fig. 1a). The Rashba interactions cause these excitons to be split into multiple fine structures (Fig. 1b) and lead to an energy splitting of spin texture (counter-clockwise (χ=1) and clockwise (χ= −1)) at band extrema.
The electron-hole interactions with spin selectivity due to excited states from the helical Rashba valence band to the helical Rashba conduction band result in either a bright cohelical exciton (χvb⋅ χcb=1) or a dark anti-helical exciton (χvb⋅ χcb= −1) 2 . In a Rashba split 2D RPPs crystal, we clearly observe two bright co-helical excitons (peaks II and III) and two dark anti-helical excitons (peaks I and IV) at the band edges. The bright co-helical excitons correspond to the spin-allowed transitions (V χ=1 → C χ=1 / V χ=−1 → C χ=−1 ) and the dark co-helical excitons are assigned to the spin-forbidden transitions. This is the first observation of the theoretically predicted multiple helical excitons in 2D RPPs. Because SE is very sensitive to spin excitations 24 ; the energy ordering and huge intensity of ε1 and ε2 below the interband transitions also rule out the origins of these peaks as defect or conventional excitons.
To quantitatively assess the Rashba effects on both CB and VB, we fit the fine structure for n=1 Iodide (Fig. 1c). The fine structure can be well-fitted with four peaks associated with bright co-helical and dark anti-helical excitons. Peak I is rather weak due to being spin-forbidden or optically inactive, implying that the spin textures at the band extrema are opposite. To support our analysis, we also measure optical fine structure for n=1 Bromide ((CH3(CH2)3NH3)2PbBr4) and Chloride ((CH3(CH2)3NH3)2PbCl4). We find that for n=1 Br, Rashba splitting is considerably large, showing large SOC ( Supplementary Fig. S4). While for n=1 Chloride, Rashba splitting reduces as evident by the two spin-forbidden transitions that cannot be well-resolved, revealing that the SOC of Cl on VB is negligible ( Supplementary Fig. S5). This further demonstrates that our experimental approach provides the most direct and detailed information and roles of halide are important in determining the Rashba splitting and helical excitons in 2D RPPs.
We next study the effect of temperature on the helical excitons and Rashba splitting in Iodide is mainly from the surface inversion symmetry breaking as discussed later.
Importantly, the spectral weights of the four excitons are increased dramatically at lower temperature and uncover strong spectral weight transfers from well-above optical band gap to the helical excitons. Spectral weight transfer in wide photon energy is a fingerprint of electronic correlation [32][33][34][35] , therefore this reveals that electronic correlation plays an important role in the helical excitons. Furthermore, we also find that the role of electronphonon interactions in which the Rashba splitting energies ∆pb and ∆ Ι are slightly increased as temperature increases (Fig. 2g).
To 2layer. Thus, the crystal structure possesses a polar axis along the stacking direction and leads to a potential gradient (or electric dipole field (Ez)) at the surface due to uncompensated charges 36,37 . The Rashba effect is directly related to the strength of the potential gradient. We argue that the strength of the potential gradient is determined by two factors. The first factor is the QW thickness (l), as the potential gradient is inversely proportional to the QW thickness (α ∝ Ez ∝ Q/l, where Q is uncompensated charges).
The second factor is molecule orientation, as unordered molecule orientation could result in a pronounced polar distortion and counteract the charge dipole field, which further reduces the Rashba energy splitting. Therefore, a narrower QW with higher order of molecule at the surface would prominently increase the Rashba splitting.
The molecule orientation in both organic and inorganic frameworks can be estimated by polarization-dependent X-ray absorption spectroscopy (XAS) and linear dichroism (XLD) at carbon K edge as graphically depicted in Fig. 4a, which describes the relationship between the linear polarization of a photon and the orbital symmetries. In all cases, the interaction would become strongest when photon polarization is along the direction of the orbital lobes of carbon 2p. Therefore, when a molecule is orderly arranged, the absorption spectra show the highest XLD signal. In contrast, there is no XLD that can be measured for a disordered molecular structure. The XLD (IGI-INI) spectra recorded with E polarization of photon along normal (NI) and along grazing (GI) incidence for all four samples (n=1 to 4 Iodides) are shown in Fig. 4b. Interestingly, the XLD signal becomes weak as n increases, implying that the addition of methyl ammonium (n>1) introduces disorder in the system owing to its dynamic rotation and electrostatic effects.
In order to quantitatively determine the potential gradient in one unit cell of each type of sample, we perform in situ high-energy-resolution x-ray photoelectron spectroscopy (XPS) measurements. The binding energy separation between the elements (such as C 4+ , Pb 2+ and I − ) in organic and inorganic frameworks is observed to become more prominent when increasing the internal electric dipole field (Fig. 4c). The relevant energy shift of the four samples (n=1 to 4 Iodides) and a 3D structure (n=∞) as a reference is summarized in Figure 4d. The monotonic energy shift reveals an increased built-in potential between organic and inorganic frameworks with decrease of n, and a maximum of 0.137 eV/Å of potential gradient can be obtained from n=1 Iodide. This highlights the importance of many-body interactions (such as QW confinement, dielectric and polar field) in influencing the Rashba effect in 2D RPPs.
Finally, from the Rashba splitting energies, we can readily estimate the offset, k0, in momentum space using a parabolic dispersion relation with an electron effective mass for both VB and CB. The electron effective mass can be obtained by the following equation: 38 where 3D g E is the band gap of the 3D (n=∞) reference material, µ is the electron and hole effective mass, and Leff is the QW effective thickness. For simplification, we assume that QW effective thickness is correlated with both QW and barrier, and Leff can be expressed as A*LQW+B*Lb, where A, B and as well electron effective mass can be obtained by best fitting of equation (3) with experimental data as shown in Fig. 1e. The experimental band gap of RPPs with various QW thicknesses can be well reproduced by equation (3) and the reduced effective mass µ≅0.23me (me is the mass of a free electron) can be determined by this best fitting. We thus are able to obtain k0 both at the CB and VB by using ∆=ħ 2 k0 2 /2m * (summarized in Supplementary Note 4); consequently, the Rashba splitting parameter α can be deduced with α=2∆/k0 and the results are shown in Fig. 1f.
The spin splitting of helical excitons at the band extrema is the 'smoking gun' evidence for Rashba splitting and it is observed for the first time in 2D complex halide perovskites.
The Rashba parameter decreases monotonously with the increase the n of Iodide (Fig. 1 f), indicating that the Rashba splitting is highly dependent on the QW thickness and electronic structure. We also find that the Rashba parameter reduces faster for higher n Iodides, suggesting that the strength of Rashba splitting can also be elevated by the internal electric field formed by the polar structure. Note that the probing depth of a photon at the energy range of helical excitons is only tenths of nanometers (see Supplementary Fig. S18) and the XAS technique is also sensitive within tenth of nanometers, these support that the huge Rashba splitting is mostly from the surface effect. Spectroscopic ellipsometry measurement. The ellipsometry studies were carried out on J. A. Woollam ellipsometer which is monochromator based with photon energies ranging from 0.6 to 6.5 eV. Spectroscopic ellisometry directly measures the changes of the polarization states, which can be expressed by two parameters ѱ and Δ. Then the Fresnel reflection coefficient ratio (ρ) between the two polarized (s-and p-) (rp and rs) light can be obtained by calculating the equation as following: where Δ is the change in phase and ѱ is the intensity ratio for p-and s-components of the light after it has interacted with the sample. For the bulk materials, the real and imaginary parts of the complex dielectric function ε1 and ε2 can be directly extracted from the Fresnel equations, which are defined as where n and θ represent the complex refractive index and incidence (transmission) angles, respectively. a and b signify the ambience and sample for the modeling.
Synchrotron radiation based X-ray diffraction measurement. (θ-2θ) measurements were carried out at the X-ray Demonstration and Development (XDD) beamline (Singapore Synchrotron Light Source, SSLS) which was equipped with a Huber 4-circle system diffractometer having a high precision of 0.0001° step size for w and 2q acquisitions. The incident x-ray having a wavelength of 1.5406Å (8.048 keV) and spotsize of 0.5 mm × 0.5 mm with angular divergence of 0.005° after passing through a Si(111) channel-cut monochromator was used.
Angle-dependence X-ray absorption spectra at the C K-edges. X-ray absorption spectroscopy measurements were performed at the SINS beamline of SSLS. The energy resolution was set ~0.1eV. The C K-edge absorption data are collected in total electron yield (TEY) mode monitoring total current. The base pressure in the UHV chamber is maintained at ∼2 × 10 −10 mbar throughout the measurements. Author Contributions X.C., K.P.L and A.R. conceived the idea. X.C. and A.R. performed spectroscopic ellipsometry measurements and analysis. X.C, X.Y and A.R. performed X-ray absorption measurements and analysis. X.C. and P.Y. performed XRD measurements. K.L. prepared samples. X.C. and A.R. analyze all data comprehensively and write paper with inputs from all other co-authors. A.R. leads the project.    The C 1s and Pb 4f have been shifted slightly so that all C 1s peaks are aligned at 285 eV as a means of visualizing the separation between the C 1s and Pb 4f peaks, that is to say, we can estimate the change of potential gradient by this energy separation 39 . d, The summary of energy shift of Pb 4f as a reference of 3D (n=∞).