Lead halide perovskites have emerged as promising semiconductors for high-performance photovoltaics, light-emitting devices as well as quantum information technologies. In this review, we highlight the magneto-optical effects in these materials from both fundamental research and practical application perspectives. We summarize the experimental results measured for basic physical quantities and the assignment of various spectral peaks using the magneto-optical spectroscopy. These results provide a solid foundation underlying the excellent photo-electronic properties of lead halide perovskites. Additionally, we provide an overview of carrier spin precession and its hyperfine interaction with the nuclear spin bath in response to the applied magnetic field, which is essential for developing perovskite-based spintronic devices. We also illustrate the magnetic-field effects in optoelectronic devices, aiming at providing instructions for performance optimization. Finally, we discuss several challenging research directions towards a comprehensive understanding of the perovskite family and their potential applications in quantum physics, which might be accessed with the magneto-optical techniques. Overall, this review highlights the intriguing possibilities for lead halide perovskites in magneto-optical research and technology, and provides insights for future investigations to advance this promising field.

Bulk photovoltaic effect (BPVE), a second-order nonlinear optical effect governed by the quantum geometric properties of materials, offers a promising approach to overcome the Shockley-Quiesser limit of traditional photovoltaic effect and further improve the efficiency of energy harvesting. Here, we propose an effective platform, the nano edges embedded in assembled van der Waals (vdW) homo- or hetero-structures with strong symmetry breaking, low dimensionality and abundant species, for BPVE investigations. The BPVE-induced photocurrents strongly depend on the orientation of edge-embedded structures and polarization of incident light. Reversed photocurrent polarity can be observed at left and right edge-embedded structures. Our work not only visualizes the unique optoelectronic effect in vdW nano edges, but also provides an effective strategy for achieving BPVE in engineered vdW structures.

The well-known ion migration in mixed halide perovskites has been intensely investigated within the area under uniform light illumination. Here, the authors demonstrate that the anion segregation in these materials is a nonlocal effect of which the ion redistribution may occur at a macroscopic or mesoscopic scale beyond.

Lead halide perovskite nanocrystals (NCs) have emerged as novel semiconductor nanostructures possessing great potential for optoelectronic, photovoltaic, and quantum information processing applications. Success in these applications requires a comprehensive understanding of the perovskite NCs' electronic structures, which mysteriously exhibit either doublet or triplet peaks of exciton luminescence at the single-particle level. Here we show that the transition from doublet- to triplet-exciton peaks can be triggered in single CsPbI3 NCs from the same batch of samples when they are stored in the ambient environment. We propose theoretically that the doublet-exciton peaks originate from two in-plane dipole moments, while the optical transition arising from the out-of-plane dipole moment becomes prominent only after the crystal-field splitting is strongly reduced by the structural transformation in the deterioration process. Furthermore, the quantum-confinement effect is strongly reinforced in the single CsPbI3 NCs with a triplet-exciton configuration, leading to enhanced Auger recombination and allowing us to extract the emission-energy dependence of the exciton-energy-level fine structure.

Coherent manipulation of the exciton wave function in a single semiconductor colloidal nanocrystal (NC) has been actively pursued in the past decades without any success, mainly due to the bothersome existence of the spectral diffusion and the photoluminescence (PL) blinking effects. Such optical deficiencies can be naturally avoided in the newly developed colloidal NCs of perovskite CsPbI3, leading to the PL spectrum with a stable intensity at the single-particle level. Meanwhile, from the first-order photon-correlation measurement, a PL line width smaller than 20 μeV is estimated for the emission state of the neutral exciton in a single CsPbI3 NC. Moreover, a dephasing time of about 10 ps can be extracted from the quantum interference measurement on the absorption state of the charged exciton. This stable demonstration of a coherent optical feature will advance single colloidal NCs into the quantum information regime, opening up an alternative yet prospective research direction beyond their traditional applications such as in optoelectronic devices and bioimaging.

利用贝叶斯估计方法研究一类带有小干扰项的二阶随机微分方程的参数估计问题,得到了估计量的形式,并且讨论了ε →0或T→ ∞ 时估计量的性质,证明了估计量的渐近正态性和渐近一致性.

The asymptotic behavior of the stochastic FitzHugh–Nagumo system with small excitability is concerned. It is proved that solutions of the stochastic FitzHugh–Nagumo system converge in probability to the unique solution of the limit system as the excitability tends to zero. In our approach the proof of tightness of the distributions of solutions in some appropriate functional space is a key step. Furthermore, we establish the existence of a global random attractor for the stochastic FitzHugh–Nagumo system, then construct a local random attractor for the limit system and prove the upper semicontinuity between global random attractors for the original system and the local random attractor for the limit system as the excitability goes to zero. As the semigroup is not compact, a novel part is to introduce the D–α-contracting to prove the existence of global random attractor for stochastic FitzHugh–Nagumo system.

The asymptotic behavior of Zakharov equations driven by random force is studied. The force, which is smooth enough and homogeneous in space and white noise in time, acts on both equations of the Zakharov system independently. By some a priori estimates we prove the existence of a solution in energy spaces E-1 and E-2 via the Galerkin approximation. This solution is defined on the given probability space rather than a martingale solution. Then a global random attractor is constructed in energy space E-2 equipped with weak topology. Further the existence of a stationary measure is proved in energy space E-2 with usual topology.

Convergence dynamics of reaction–diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some sufficient conditions to guarantee the almost sure exponential stability, mean value exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov functional method, M-matrix properties, some inequality technique and nonnegative semimartingale convergence theorem are used in our approach. These criteria ensuring the different exponential stability show that diffusion and delays are harmless, but random fluctuations are important, in the stochastic continuously distributed delayed reaction–diffusion RNNs with the structure satisfying the criteria. Two examples are also given to demonstrate our results.