Anomalous circularly polarized light emission in organic light-emitting diodes caused by orbital-momentum locking

Chiral circularly polarized (CP) light is central to many photonic technologies, from optical communication of spin information to novel display and imaging technologies. As such, there has been significant effort in the development of chiral emissive materials that allow for the emission of strongly dissymmetric CP light from organic light-emitting diodes (OLEDs). A consensus for chiral emission in such devices is that the molecular chirality of the active layer determines the favored light handedness of CP emission, regardless of the light-emitting direction. Here, we discover that, unconventionally, oppositely propagating CP light exhibits opposite handedness, and reversing the current-flow in OLEDs also switches the handedness of the emitted CP light. This direction-dependent CP emission boosts the net polarization rate by orders of magnitude by resolving an established issue in CP-OLEDs, where the CP light reflected by the back electrode typically erodes the measured dissymmetry. Through detailed theoretical analysis, we assign this anomalous CP emission to a ubiquitous topological electronic property in chiral materials, namely the orbital-momentum locking. Our work paves the way to design new chiroptoelectronic devices and probes the close connections between chiral materials, topological electrons, and CP light in the quantum regime.


Introduction
Chirality characterizes parity symmetry-breaking where a molecule cannot be superposed on its mirror image in chemistry and biology 1,2 . Chiral enantiomers exhibit opposite chiroptical activity when coupling to light 3,4 . In physics, chirality usually refers to the spin-momentum locking of particles such as Weyl fermions 5,6 and the circular polarized light. Chiral organics were recently reported to exhibit a topological feature 7 , in which the electronic orbital and momentum are locked together, to rationalize the intriguing spin selectivity in DNA-type molecules 8,9 . Hence given the intimate relationship between electronic states and light-matter interactions, we were inspired to raise a question: Can topological electronic properties (i.e., orbital-momentum locking) enhance chiroptical activity and therefore advance the rapidly developing (chir)optoelectronic technology 10,11 ?
A future industrial application of organic chiral emissive materials is in circularly polarized organic light-emitting diodes (CP-OLEDs) 12 , which should eliminate the ∼50% internal light loss caused by the contrast-enhancing circular polarizer in OLED displays. Such efficiency gains occur via direct circularly polarized electroluminescence (CP-EL) from the CP-OLED, which can pass through the contrast-enhancing polarizer unhindered. 13 The effectiveness of this strategy depends on the degree of circular polarization of EL, where higher polarization gives better efficiency for the display in the presence of such polarizers. 2 Since the first CP-OLED reported in 1977 15 , the circularly-polarized electroluminescence of a material was also assumed to be identical to circular polarization measured in absorption and in photoluminescence (cases without current flow) from the same electronic transition . In another words, CP-EL was considered nearly the same process as CP photoluminescence (CP-PL) [or the inverse process of optical circular dichroism (CD)] due to a shared electronic transition, and the magnitude of CP emission determined by the product of electric and magnetic transition dipole moments. 16,17 Thus most efforts in this field were made on developing more twisted chiral emitters with stronger magnetic transition dipoles to improve optical chirality 18,19 , without taking current flow in an OLED device into consideration.
More importantly, in terms of device engineering, the reflective back-electrode in an OLED device is another key issue. In all prior studies of chiral emissive materials, CP emission is conventionally expected to exhibit the same handedness in both emission directions (forward and back) from the point of recombination, thus any back reflection within the device will invert the handedness of CP emission travelling backwards and cancels out the forward CP emission, reducing the net EL circular polarization that exits the device through the transparent electrode 18,[20][21][22] . Consequently, the magnitude of EL circular polarization from devices is much smaller than the corresponding CP-PL measured in transmittance geometry, which does not suffer issues of reflection 20 (Fig. 1a).
Even though constructing semi-transparent OLEDs can, to some extent, mitigate the problem of reflection, such a strategy reduces the overall the device performance in a displays, negating the original intention of energy saving at the polarizer. 18 Among all CP-OLEDs reported and many other chiral optoelectronic devices based on 2D 23 and perovskite materials 24 , chiral polymeric materials 1, 2, 26-28 demonstrate significant circular polarization in PL and EL, several orders of magnitudes stronger than other chiral emissive systems 18,[29][30][31] (see Fig. 2a). Despite the analysis above, when constructing optoelectronic devices from such materials, their CP-EL remains equal, or sometimes is even enhanced compared to CP-PL or CD.
Although previous theoretical 32, 33 and experimental 1, 2, 26 work attributed the strong optical circular dichroism to a predominately excitonic origin, these analyses cannot account for the comparable or enhanced circular polarization in EL devices, given the expected detrimental effect of back-electrode reflection.
In this work, we discover an anomalous light emission phenomenon from chiral polymeric CP-OLEDs. For the chiral polymeric materials under study, CP-EL exhibits opposite handedness in forward and backward emission directions, counter-intuitive to what is usually expected in EL or PL (Fig. 1b). With such direction-dependent CP emission, the back-reflected light exhibits the same handedness as the forward emission, avoiding the polarization cancellation which occurs in devices using other materials and boosting the net CP-EL exiting the device 18,20 . Furthermore, for the first time, we explain the effect of current flow on CP-EL, where its handedness can also be switched by reversing the current flow in an OLED. We propose that the directional CP-EL observed is caused by the topological nature of the electronic wave functions in chiral polymers.
Because of orbital-momentum locking 7 , the current flow induces nonequilibrium orbital polarization in electron and hole carriers. Therefore, finite angular momentum transfers from electron/hole orbital to the photon spin in the optical transition. When they have the same spin, the counterpropagating CP lights exhibit opposite handedness. This orbital polarization effect rationalizes the fact that the handedness of CP light is determined both by the current direction and the emission direction. Furthermore, this model reveals an exotic CP-EL mechanism caused by current-induced time-reversal breaking. Our work paves they way to design novel chiroptoelectronic devices with strong circular polarization.

Results
A chiral polymer blend consisting of an achiral light-emitting polymer (i.e., poly(9,9-dioctylfluorenealt-benzothiadiazole), F8BT, Fig. 1) and a non-emissive chiral additive (i.e., [P]-aza [6]helicene) was selected for the investigation of CP-EL. Upon thermal annealing of spin-casted thin-films, the chiral additive (10 wt%) induces a strong and robust chiral structure and optical CD to the originally achiral polymer with an absorption dissymmetry factor (g abs ) of ∼ 0.6 (see Fig. S1) 1,13 , calculated in the following way: where I L/R is the irradiance recorded from the CP-OLEDs. However, despite a fixed absolute stereochemistry of chiral material in the emissive layer of both devices, the sign of the CP-EL signals was found to be dependent on the device structure. When the emission direction relative to the current direction is switched, the inverted CP-OLED emits right-handed circularly polarized light through ITO with a g EL of ?0.33. Apart from the emission direction-dependent CP-EL signals in conventional versus inverted devices, we detected no evidence of erosion of g EL by the reflective electrodes. Compared with other reported CP-OLEDs 18, 29-31 , the polyfluorene-based CP-OLEDs we developed exhibit one of the highest known g EL values (Fig. 2a). In contrast, lanthanide complexes exhibit intrinsically high PL dissymmetry (g P L ) 20 , but the g EL recorded from the transparent electrode of lanthanide-based CP-OLEDs dramatically decreases when increasing the thickness of the reflective metal electrode. This is similarly observed in other small molecule CP-OLEDs 18, 29-31 ( Fig. 2b).
To compare our results with other previously reported CP-OLEDs, we performed CP-EL measurements on semi-transparent OLEDs in both conventional and inverted CP-OLEDs (Fig. 2c).
Surprisingly, emission direction-dependent CP-EL behavior was observed in both device structures, where the CP-EL from forward and backward emission (i.e., through a semi-reflective electrode) exhibit the opposite handedness. Considering this emission direction-dependent dissymmetry factor is only observable in EL but not for CP-PL or CD of the chiral thin films ( Theoretical model It is known that helicene additive promotes the F8BT polymer to form chiral assemblies in solid-state thin films 32,34 . The chiral polymer blend is the real-space channel for both current flow and light emission. In the following, we will discuss the light emission in the presence of TRS-breaking due to the current flow.
We first will revisit the general theory that describes the CP emission effect and interpret our experiments from an anomalous term. According to Fermi's golden rule, the emission rate of CP light is, where |0 (|1 ) represents the ground (excited) state with energy 0 ( 1 ), H is the light interaction Hamiltonian H = −eE · r − m · B with m being the magnetic moment, E and B are the light electric and magnetic fields, respectively, and ω is the photon energy. For right/left-handed light traveling along the z axis, the electric and magnetic fields are E = E 0 (1, ±i, 0)/ √ 2 and Therefore, the leading term of CP light emission can be derived as, where x 01 = 0| x |1 and m 01 x = 0| m x |1 represent the electric and magnetic transition dipoles, respectively, and I 0 = |E 0 | 2 . We note m = (m x , m y , m z ), r = (x, y, z) and δ for the same δ-function in Eq. 3.
The second term in Eq. 4 is routinely employed to understand CD, CP-PL or CP-EL for organic/inorganic systems and has been called natural chiroptical activity 37  Therefore, the first term was generally ignored when studying organic molecules. It was referred to as the magnetic CD 41,42 in absorption of magnetic materials or in a external magnetic field.
However, if electrons and holes carry finite velocities before recombination, the first term cannot be naively neglected. In other words, the current flow can induce magnetization, more specifically the orbital magnetization as we will show. The nonequilibrium phase breaks TRS in chiral molecules.
We refer to the first term as the anomalous circular polarization effect (ACPE) here. In such a case, ACPE may contribute more to the net circular polarization than NCPE because the electric field is much stronger than magnetic field in light. wave function reduces from |ψ to |ψ ± . We point out that |ψ ± themselves violate TRS, although |ψ does not.

Orbital-momentum locking in chiral molecules
Next, |ψ ± carry opposite OAM (±l) in a chiral molecule 7 . As illustrated in Fig. 3b, electrons that travel along a chiral pathway pick up a self-rotation, i.e., the OAM, in analogue to the spinning bullet out of a rifled barrel. Mathematically, we can generally describe a positive-moving plane wave by |ψ + = A(ρ, z)e ilφ+ikz , where A(ρ, z) is a general coefficient depending on z and the radial distance ρ, k is the momentum, and l = 0, ±1, ±2? represents OAM. |ψ + is a chiral plane wave if l = 0 and reduces to a normal plane wave for l = 0. Because both the inversion symmetry and mirror symmetry, either of which forces l = 0, are broken l = 0 generically holds in a chiral system. It is obvious that |ψ − with −k carries opposite OAM −l because |ψ + = |ψ − * . Such orbital(l)-momentum(k) locking represents the wave function topology, in which the parallel or antiparallel l − k relation depends on the molecular chirality and chemical potential. It is similar to the monopole-like spin-momentum locking in the topological Weyl fermion 5, 6 .

Angular momentum transfer from electrons to light The injected electrons and holes carry
finite OAM because of the polymer chirality in the OLED. Given the low mobility in the organic semiconductor, the linear momentum is quickly relaxed, for instance, by interface scattering between neighboring aggregate clusters. But the OAM relaxation time should be much longer than the momentum relaxation time because neighboring clusters share the same chirality. Due to the same chirality protection, we also expect that OAM is robust against electron-electron interactions.
Therefore, electrons and holes can preserve the OAM polarization when they form excitons for light emission. In the following, we discuss the OAM transfer from carriers to CPL in the electron-hole recombination.
The ACPE term in Eq. 4 is equivalent to the OAM shift in the optical transition [41][42][43] ∆l = L z 0→1 = x 01 p 10 y − y 01 p 10 x , whereL z = xp y − yp x is the OAM operator (see more information in Supplementary Information).
In the presence of current along −z, we need replace |0 + (|1 + ) for |0 (|1 ) to evaluate the ACPE in Eq. 4. In this case, ∆l is nonzero in the optical transition from |1 + to |0 + , both of which carry finite OAM, as illustrated in Fig. 3d. In addition, reversing current leads to −∆l (Fig. 3e). We note that ∆l is gauge invariant although l of a given band depends on the specific gauge. Ab initio calculations Furthermore, we quantitatively estimate the ACPE and NCPE for the chiral F8BT polymer assembly by ab initio calculations. It is challenging to refine the accurate atomic structure of such chiral aggregates. Without losing generality, we simulate chiral stacking of F8BT molecules and focus on the intermolecular chirality that is associated with the dominant charge transport direction along the layered packing structure (noted as z axis here) 44 . Although |0, 1 can be generally many-body wave functions, we use the highest occupied molecule orbital (HOMO) and lowest unoccupied molecule orbital (LUMO) to represent |0 and |1 , respectively, by ignoring higher-order corrections (like the distortion in excited states) in the calculations. As shown in Fig.   4, two layer stacking with a counter-clockwise twisting angle 30 • reshapes HOMO and LUMO wave functions dramatically compared to a single layer of molecule. By calculating the ACPE involving the +z moving HOMO and LUMO, we obtain a large dissymmetry factor |g EL | = 0.48 (0.44) for two (three) layer stacking, which is in the same order of magnitude as experimental g EL . The OAM can be evaluated from the phase winding number in the xy plane (see Fig. 4c and the Methods section), verifying the orbital-momentum locking in |0 ± and |1 ± . Because |0, 1 is usually composed by many plane waves, the total value of l is unnecessarily an integer.
Better knowledge on the molecular arrangement of chiral polymer assemblies will help improve the prediction power of calculations in the future work.
Additionally, the current-induced magnetization in our experiments is relevant to the orbital rather than spin of electronic states. If electron-spin polarization matters, it would require substantial spin-orbit coupling (SOC) in the device. We know that these organic polymers made of light elements exhibit negligible SOC. Despite that metal electrodes may include heavy elements, the circular polarization rate remains the same for Al, Ag and Au electrodes with largely varied SOC (Fig. S8). Thus, the role of electron spin may be negligible in ACPE although ACPE may also appear in systems with strong SOC. The ACPE is caused by the chirality-induced orbital polarization, different from the chirality-induced spin selectivity effect discussed in literature 8

Summary
In summary, we report an anomalous phenomenon where the handedness of CP light emission depends on the emission direction. This effect enables us to design unconventional CP-OLED devices with large g EL and without errosion from the back-electrode reflection. We highlight that the orbit-momentum locking causing ACPE is strongly associated with the charge transport mode in the polymer systems and therefore suggest the following design principles for further development of CP-OLEDs with strong CP-EL. To ensure the entire stack of molecular assemblies exhibit strong ACPE, it is necessary that the emissive sites should strongly couple with chiral transport sites or ideally within the same sites as in our polymer systems, to induce strong orbital-momentum locking in conduction electrons. If charge carriers are independently transported, such as in host materials, then they get scattered to random adjacent chiral emissive sites, the net momentum and OAM will be quenched and only NCPE will appear. In this case, CP-EL can no longer be considered as the same origin as CP-PL and circular dichroism where no charge transport and current flows exist.
We propose an ACPE that involves finite angular momentum transfer in the optical transition.
Because ACPE and NCPE come from the first and second-order optical transitions in Eq. 4, ACPE is often much larger than NCPE when TRS is broken. We highlight that the unusual TRS-breaking in ACPE is driven by the nonequilibrium orbital magnetization, which originates in the chiral orbital nature in wave functions. In CP-OLED, such orbital magnetization is caused by the current flow (rather than static magnetization or magnetic field), the impact of which was rarely recognized in previous studies on chiral materials 45 . Our work reveals an intriguing unification of chirality in seemingly unrelated aspects: structure geometry, electronic topology, and the light handedness. The chirality information can be transferred from the material geometry to electronic wave function and further to the spin of light.    Table S1 and Scheme S1. |g P L | and |g EL | represent photo-and electro-luminescence   too thick films, compared to previous studies 1, 2 . Organic film thicknesses was monitored using a Dektak 150 surface profiler and the metal thickness was used as displayed from QCM monitor.
Photophysical characterization: Circular dichroism measurements were performed using a Chirascan (Applied Photophysics) spectrophotometer. CP-PL was measured in a transmittance geometry using a CPL-300 JASCO spectrometer. GIWAXS data was measured in ALBA beamline (Spain). The incidence angles of the X-ray beam were set to be 0.2 for all films. The GIWAXS patterns were recorded with a 2D CCD detector and an X-ray irradiation time 10-20s, dependent on the saturation level of the detector.

CP-EL:
Left-handed and right-handed CP emission spectra were collected using a combination of linear polarizer and zero-order quarter-wave plate (546 nm, Thorlabs) placed before detectors.  [P]-aza [6]helicene-blended F8BT deposition was the same as for the thin film studies, followed by the thermal evaporation of a 10 nm TPBi (Sigma-Aldrich), 10 nm from DFT wave functions. The charge density is ρ 0 = | |0 | 2 . Besides G z z, the phase of the G z propagating wave in Fig. 4 is argφ 0 (G z ). Under electrical current along −z, the CP electric dipole transition amplitudes are calculated as: where * represents taking complex conjugate. One can analyze the symmetry constrain on CP emission from Eq. (7). If inversion symmetry is present, then c 0,1 G = p 0,1 c 0,1 −G with p 0,1 = ±1 refers to the parity eigenvalue of |0 or |1 . On the other hand the time-reversal symmetry requires that c 0,1 G = (c 0,1 −G ) * . Thus, if inversion and time-reversal symmetries exist simultaneously, the coefficient c 0,1 G is purely real (imaginary) for the parity even (odd) state. Therefore, I R = I L always holds according to Eq. (7). When inversion is broken, the circular polarization (I R = I L ) can appear.
OAM and winding number: The OAM l is a topological number charactering the phase winding of the wave function in real space, which is defined as 5 : where ϕ(r) is the real-space distribution of wave function phase, and C refers to the integration contour (dashed circle in Fig. 4c). l represents the total phase change (in multiples of 2π) after circulating the contour C. Generally, a nonzero winding number indicates a topological defect inside the contour C which cannot be removed by continuously varying the wave function without