On September 8, 2022, Beijing time, Wu Kaifeng’s team at the Dalian Institute of Chemical Physics of the Chinese Academy of Sciences and others published a research result entitled “Lattice distortion inducing exciton splitting and coherent quantum beating in CsPbI3 perovskite quantum dots” in the journal Nature Materials.

The research team observed the ensemble quantum beat frequency caused by the cleavage of exciton fine structures in CsPbI3 perovskite quantum dots, and proposed a new mechanism to regulate the splitting energy by temperature inducing lattice distortion. This discovery is of great significance for the application of quantum dots in the field of quantum information technology.

The corresponding author is Prof. Kaifeng Wu, Researcher and Dr. Peter Sercel of the U.S. Department of Energy’s Center for Energy Frontier Research (CHOISE); The first author is Dr. Yaoyao Han.

Semiconductor quantum dots (QDs) are one of the important materials for the scientific research of quantum information. In QDs, electron-hole anisotropic exchange due to symmetrical breakdown of morphology or lattice results in fine structure splitting (FSS) of bright exciton energy levels, which can be used for quantum state coherence manipulation or polarization entangled photon pair emission. Observing and regulating FSS is critical for these applications. Since FSS energy is very sensitive to the size and morphology of quantum dots, it is usually necessary to determine the emission spectrum of a single or a small number of quantum dots at liquid helium temperature to determine FSS. Observing FSS at the ensemble level is extremely challenging, and quantitative regulation of FSS has not been reported.

Based on the above background, the research team studied the bright exciton FSS of the solution synthesis CSPbI3 perovskite quantum dot synthesis. For perovskite QDs, electron-hole exchange can divide exciton cracking into a dark state with lower energy and a bright state with higher energy. In addition, as shown in Figure 1a, the symmetry of the morphology and lattice will lead to further cracking of the triple degeneracy bright state, resulting in three energy levels, and its eigenstat also changes from a circular polarization eigenstat to a linear polarization eigenstat. This fine structural splitting energy (ΔFSS) is typically a few to a few hundred μeV. In this case, excitation of QDs using circular polarization light with a wider line width can produce a coherent superposition of the new line polarization eigenstates. Based on this principle, the research team chose to use circularly polarized femtosecond transient absorption spectra (circular polarized TA, that is, transient circular dichromatography) as a research method for this topic.

The research team first synthesized a series of CsPbI3 QDs samples of different sizes using the thermal injection method. The topography of the sample is shown as a cuboid, and a TEM picture of the sample representative is shown in Figure 1b. As the average size of QDs gradually increases from 4.9 nm to 17.3 nm, the quantum limiting effect gradually decreases, and its steady-state absorption spectrum (Figure 1c) and emission spectrum (Figure 1d) also gradually redshift.

**Figure 1: Schematic diagram of CsPbI3 QDs leukor fine structure splitting; (b) Representative CsPbI3 QDs high-resolution electron microscopy diagrams; (c) Steady-state absorption spectra of CsPbI3 QDs of different sizes and corresponding excitation light pulse patterns; (d) Steady-state emission spectra of CsPbI3 QDs of different sizes.**

Subsequently, the research team used circularly polarized femtosecond transient absorption spectroscopy to study the sample’s leucon FSS. Taking CsPbI3 QDs at 4.9 nm as an example, Figures 2a and 2b show a circularly polarized two-dimensional false color TA spectra of the sample at 80 K. Fig. 2a is the TA spectra of the homotropic circular polarization configuration (σ+/σ+, excitation light/detection light) TA spectra of the sample, and Fig. 2b is the inverted circular polarization configuration (σ+/σ-, excitation light/detector light) TA spectra. Where 615 nm is a bleach signal produced by the state fill of a photogenerated exciton, the Coulomb interaction causes QDs to produce photoresorption signals at 570 nm and 630 nm, which can be used to characterize the spin relaxation kinetics of the leukokines. In Figures 2a and 2b, these characteristic signals exhibit periodic oscillations on the ps time scale. Also, the oscillation phases of the TA kinetic curve under the homotropic and reverse circular polarization configurations are reversed (Figure 2c). This quantum beat frequency signal uses circular polarized light (about 27 meV spectral width, Figure 1c) to excite QDs, resulting in the characteristics of the polarization of its bright exciton line eigen-state coherence superposition, and the frequency of the quantum beat frequency corresponds to the size of the bright exciton ΔFSS. It should be noted here that the signal generated by the coherent phonon does not have such a circular polarization dependence feature, and the role of the coherent phonon is excluded herein.

The research team found that ΔFSS can be regulated by QDs size. Shown in Figure 2d are the dynamic curves of the quantum beat frequencies of QDs of different sizes, which are subjected to a fast Fourier transform (Figure 2e) to extract the characteristic frequencies of the quantum beat frequencies. ΔFSS for QDs of different sizes is shown in Figure 2f. As can be seen from Figure 2f, the smaller the size of the QDs, the larger the ΔFSS. This is the result of the increase in the size of QDs, the enhancement of their quantum limiting effects, and the increase in electron-hole exchange. The ΔFSS of CsPbI3 QDs can be as high as 1.6 meV at liquid nitrogen temperatures.

Here, three additional problems encountered in data analysis need to be pointed out. (1) In Figure 2d, when fitting the quantum beat frequency dynamic curve, in addition to using the damped cosine function, an additional single exponential attenuation term is required to successfully fit the experimental data. (2) The FFT peak in Figure 2e exhibits extreme asymmetry. (3) Considering the sensitivity of QDs ΔFSS to topography and size, ΔFSS will show a huge distribution, and such a non-uniform distribution should erase the beat frequency signal. Even if the beat frequency can be observed for some reason, according to the energy level structure diagram of Figure 1a, three eigenfreques should be visible, while the researchers only observed one eigenfrequency. These phenomena illustrate the uniqueness of this system, which will be analyzed later in conjunction with theoretical calculations.

**Figure 2: (a) 2D false-color TA spectra of the co-directional circular polarization configuration (σ+/σ+) and (b) reverse circular polarization configuration (σ+/σ-) of 4.9 nm CsPbI3 QDs at 80 K; (c) TA kinetic curves at 620 nm under co-directional and reverse circular polarization configurations; (d) Quantum beat frequency dynamic curves of CsPbI3 QDs of different sizes at 80 K; (e) Fast Fourier transform patterns of CsPbI3 QDs of different sizes at quantum beat frequencies at 80 K; (f) CsPbI3 QDs ΔFSS changes with size at 80 K.**

More interestingly, as shown in Figures 3a, 3b, 3c, 3d, the quantum beat frequency characteristic frequency of the same sample is temperature dependent, and the lower the temperature, the faster the frequency. This also shows that the ΔFSS of the same sample has a strong temperature dependence (Figure 3e): the lower the temperature, the greater the ΔFSS. The temperature dependence of ΔFSS has never been observed in previous epitaxial growth QDs.

**Figure 3: Quantum beat frequency dynamics of (a)4.9 nm, (b) 5.4 nm, (c) 7.4 nm, (d) 7.9 nm CsPbI3 QDs at different temperatures; (e) ΔFSS vs. temperature of 4.9 nm, 5.4 nm, 7.4 nm and 7.9 nm CsPbI3 QDs.**

The team realized that the temperature dependence of ΔFSS may come from the influence of temperature on the shape or lattice of perovskites. First, through the determination of variable temperature high-resolution TEM by the research team, it was found that the size of the crystal basically did not change with temperature (negligible in the instrument resolution range), so the temperature-induced QD shape change was not the dominant factor. The change of CsPbI3 perovskite lattice with temperature has been widely studied in the field of perovskite photovoltaics. As shown in Figure 4a, reducing the temperature can cause the deformation of the octahedral frame centered on Pb, resulting in a decrease in lattice symmetry, and the cubic phase perovskite gradually becomes a tetragonal phase and an orthogonal phase. According to the XRD spectra (Figure 4b), CsPbI3 QDs are orthogonal phases at room temperature. As the temperature decreases, the diffraction peaks of the 7.9 nm and 17.3 nm QDs change slightly. By refining the XRD spectra, the CsPbI3 QDs lattice constant changes with temperature (Figure 4c). With the decrease of temperature, the orthogonal lattice constants b and a increase and decrease, respectively. Therefore, the difference between b and a (i.e., lattice anisotropy) increases with decreasing temperature, i.e. lowering the temperature will result in a decrease in lattice symmetry of CsPbI3 QDs.

**Figure 4: (a) CsPbI3 perovskite crystal phase changes with temperature; (b) Variable temperature XRD spectra of 17.3 nm and 7.9 nm CsPbI3 QDs; (c) Graphs of lattice parameters b, a, and c as a functioning of temperature for 17.3 nm and 7.9 nm CsPbI3 QDs.**

To reveal the correlation between lattice distortion and ΔFSS, the research team collaborated with Dr. Sercel to perform an effective mass approximation (EMA) of the fine structure of CsPbI3 QDs banded excitons. The theoretical calculation model considers a box QD with side lengths Lx, Ly, and Lz (on Figure 5a). According to high-resolution TEM and related research reports, the crystal edge of QD is parallel to the quasi-cubic < 100>c direction. Thus, the orthogonal pristine lattice vector c is parallel to Lz, and a and b point to the inner angle (bottom of Figure 5a). The temperature dependence of the tetragonal (δ) and quadrature (ζ) should be obtained according to the change of the lattice constant with temperature (Figure 5b). These should variables divide the bright split into exciton states of transition dipole moment and orthogonal axis of symmetry collimated. In order to reveal the reasons why the quantum beat frequency can be observed in this synthesis system, two crystal plane models are used to theoretically calculate the fine structure of bright excitons. One is called the orthogonal crystal plane model (corresponding to the box QD of the boundary plane orthogonal lattice vector), in which the leucons are defined as A, B, and C excitons. Another is called a quasi-cubic crystal plane model (corresponding to the study system model Fig. 5a, with a quasi-cubic {100}c boundary surface of the box QD), in this model, the C exciton is unchanged, A, B excitons coupled to produce new exciton α, β. As can be seen from Figures 5c and 5d, there is an avoidance of cross-energy gap in the α and β exciton energy levels based on the quasi-cubic crystal plane model, and it is the existence of avoidance of cross-energy gaps between exciton α and β that the quantum beat frequency between this energy level can be observed. However, there is no energy cross between α exciton and C exciton, β exciton and C exciton, and its beat frequency phenomenon is affectedThe non-uniform widening of the frequency is eliminated. That’s why the researchers only observed one characteristic frequency. Similarly, for the orthogonal crystal plane model, there is no avoidance energy gap, so the quantum beat frequency is eliminated in the series synthesis. Samples with frequency erasure appear as a simple attenuation in the kinetic curve, which also leads to the asymmetry of FFT. At this point, the results of theoretical calculations have a good explanation of the experimental phenomenon. As can be seen from Figures 5e and 5f, the theoretical calculation results based on the quasi-cubic crystal plane model can well reproduce the shape of the TA beat frequency dynamic curve and its FFT spectrum.

**Figure 5: (a) Schematic diagram of the theoretical calculation model of box CsPbI3 QD; (b)Plot of the tetragonal and quadrature strain components (ζ and δ, respectively) of 7.9 nm CsPbI3 QDs as a function of temperature; (c) When Lz = Le, the bright exciton energy level changes with Ly/Lx; (d) In the case of Lx=Ly, the bright exciton energy level in the quasi-cubic crystal plane model changes with Lz/Lx; (e) TA kinetic comparison plot of theoretical simulation and experimental data at 80 K of 7.9 nm CsPbI3 QDs; (f) FFT spectral comparison charts for theoretical simulations and experimental data.**

In addition, the theoretical calculation results and experimental values of the temperature dependence (Figure 6a) and the size dependence (Figure 6b) of the system ΔFSS are also consistent. The consistency of theoretical calculations and experimental results also confirms the correctness of the theoretical model.

**Figure 6. (a) Comparison of theoretical and experimental data of α, β exciton ΔFSS for 7.9 nm CsPbI3 QDs; (b) ΔFSS theoretical and experimental data comparison chart of CsPbI3 QDs of different sizes at 80 K.**

In summary, this work not only accurately determines the fine structure cracking of the bright excitons of the colloidal quantum dot system synthesis, but also takes the lead in proposing a new principle of regulating the cleavage energy of the bright excitons by temperature inducing CsPbI3 QDs lattice distortion, revealing the huge application potential of this lattice property in the field of quantum information science. (Source: Science Network)

Related paper information:https://doi.org/10.1038/s41563-022-01349-4