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Dielectric breakdown of physical vacuum (Schwinger effect) is the textbook demonstration of compatibility of Relativity and Quantum theory. Although, the observation of this effect in its original static formulation is practically unachievable, it has been shown that the requirements on field strengths can be significantly reduced for dynamical generalizations of Schwinger effect. Here, we report on observation of an analog dynamical Schwinger effect in gapped Dirac semiconductor lead-halide perovskite MAPbBr$_3$. Specifically, we observe strong photoluminescence of a lead-halide perovskite driven by deep sub-gap irradiation, and use the quasi-adiabatic Landau-Dykhne approach to interpret our data in terms of the dynamical Schwinger effect. Further, the exponential sensitivity of the Schwinger effect to driving fields allows us to measure the local frozen-in fields in a nominally cubic single perovskite crystal at room temperature. Finally, we demonstrate an AC analogue of biasing in our system -- the non-perturbative cooperation between two time-dependent fields simultaneously driving the sample. Our results establish lead-halide perovskites as an excellent platform for simulating effects of strong fields on Dirac fields. In addition, they contribute to the on-going discussion about inversion-breaking in MAPbBr$_3$ single crystal and pave the way for a mid-infrared light detection with lead-halide perovskites.

Lead halide perovskites have recently been reported to demonstrate an exceptionally high nonlinear (Kerr) refractive index n$_2$ of up to 10$^{-8}$ cm$^2$/W in CH$_3$NH$_3$PbBr$_3$. Other researchers however observe different, substantially more conservative numbers. In order to resolve this disagreement the nonlinear Kerr index of a bulk sample of lead halide perovskite was measured directly by means of an interferometer. This approach has many advantages as compared to the more standard z-scan technique. In particular this method allows studying the induced changes to the refractive index in a time-resolved manner, thus enabling to separate the different contributions to $n_2$. The extracted n$_2$ values for CsPbBr$_3$ and MAPbBr$_3$ at $\lambda \approx 1\mu m$ are $n_2=+2.1\times$ 10$^{-14}$ cm$^2$/W and $n_2=+6\times$ 10$^{-15}$ cm$^2$/W respectively hence substantially lower than what has been indicated in most of the previous reports implying the latter should be regarded with a great care.

A rotating organic cation and a dynamically disordered soft inorganic cage are the hallmark features of hybrid organic-inorganic lead-halide perovskites. Understanding the interplay between these two subsystems is a challenging problem but it is this coupling that is widely conjectured to be responsible for the unique behavior of photo-carriers in these materials. In this work, we use the fact that the polarizability of the organic cation strongly depends on the ambient electrostatic environment to put the molecule forward as a sensitive probe of local crystal fields inside the lattice cell. We measure the average polarizability of the C/N--H bond stretching mode by means of infrared spectroscopy, which allows us to deduce the character of the motion of the cation molecule, find the magnitude of the local crystal field and place an estimate on the strength of the hydrogen bond between the hydrogen and halide atoms. Our results pave the way for understanding electric fields in lead-halide perovskites using infrared bond spectroscopy., Comment: version accepted for publication in The Journal of Physical Chemistry Letters

In recent years, halide perovskite materials have been used to make high performance solar cell and light-emitting devices. However, material defects still limit device performance and stability. Here, we use synchrotron-based Bragg Coherent Diffraction Imaging to visualise nanoscale strain fields, such as those local to defects, in halide perovskite microcrystals. We find significant strain heterogeneity within MAPbBr$_{3}$ (MA = CH$_{3}$NH$_{3}^{+}$) crystals in spite of their high optoelectronic quality, and identify both $\langle$100$\rangle$ and $\langle$110$\rangle$ edge dislocations through analysis of their local strain fields. By imaging these defects and strain fields in situ under continuous illumination, we uncover dramatic light-induced dislocation migration across hundreds of nanometres. Further, by selectively studying crystals that are damaged by the X-ray beam, we correlate large dislocation densities and increased nanoscale strains with material degradation and substantially altered optoelectronic properties assessed using photoluminescence microscopy measurements. Our results demonstrate the dynamic nature of extended defects and strain in halide perovskites and their direct impact on device performance and operational stability., Comment: Main text and Supplementary Information. Main text: 15 pages, 4 figures. Supplementary Information: 16 pages, 27 figures, 1 table

Understanding energy transport in semiconductors is critical for design of electronic and optoelectronic devices. Semiconductor material properties such as charge carrier mobility or diffusion length are measured in bulk crystals and determined using models that describe transport behavior in homogeneous media, where structural boundary effects are minimal. However, most emerging semiconductors exhibit microscale heterogeneity. Therefore, experimental techniques with high spatial resolution paired with models that capture anisotropy and domain boundary behavior are needed. We develop a diffusion tensor-based framework to analyze experimental photoluminescence (PL) diffusion maps accounting for material microstructure. Specifically, we quantify both carrier transport and recombination in single crystal and polycrystalline lead halide perovskites by globally fitting diffusion maps, with spatial, temporal, and PL intensity data. We reveal a 29% difference in principal diffusion coefficients and alignment between electronically coupled grains for CH3NH3PbI3 polycrystalline films. This framework allows for understanding and optimizing anisotropic energy transport in heterogeneous materials., Comment: 47 pages, 19 figures

We use general symmetry-based arguments to construct an effective model suitable for studying optical properties of lead-halide perovskites. To build the model, we identify an atomic-level interaction between electromagnetic fields and the spin degree of freedom that should be added to a minimally-coupled $\mathbf{k\cdot p}$ Hamiltonian. As a first application, we study two basic optical characteristics of the material: the Verdet constant and the refractive index. Beyond these linear characteristics of the material the model is suitable for calculating non-linear effects such as the third-order optical susceptibility. Analysis of this quantity shows that the geometrical properties of the spin-electric term imply isotropic optical response of the system, and that optical anisotropy of lead-halide perovskites is a manifestation of hopping of charge carriers. To illustrate this, we discuss third-harmonic generation., Comment: Version accepted for publication in Phys. Rev. B

Lead-halide perovskites enjoy a number of remarkable optoelectronic properties. To explain their origin, it is necessary to study how electromagnetic fields interact with these systems. We address this problem here by studying two classical quantities: Faraday rotation and the complex refractive index in a paradigmatic perovskite CH$_3$NH$_3$PbBr$_3$ in a broad wavelength range. We find that the minimal coupling of electromagnetic fields to the k$\cdot$p Hamiltonian is insufficient to describe the observed data even on the qualitative level. To amend this, we demonstrate that there exists a relevant atomic-level coupling between electromagnetic fields and the spin degree of freedom. This spin-electric coupling allows for quantitative description of a number of previous as well as present experimental data. In particular, we use it here to show that the Faraday effect in lead-halide perovskites is dominated by the Zeeman splitting of the energy levels, and has a substantial beyond-Becquerel contribution. Finally, we present general symmetry-based phenomenological arguments that in the low-energy limit our effective model includes all basis coupling terms to the electromagnetic field in the linear order., Comment: Version accepted for publication in Phys. Rev. Lett

Halide perovskites have shown great potential for light emission and photovoltaic applications due to their remarkable electronic properties and compatibility with cost-effective fabrication techniques. Although the device performances are promising, they are still limited by microscale heterogeneities in their photophysical properties. In particular, the relation between local heterogeneities and the diffusion of charge carriers at the surface and in the bulk, crucial for efficient collection of charges in a light harvesting device, is not well understood. Here, a photoluminescence tomography technique is developed in a confocal microscope using one- and two-photon excitation to distinguish between local surface and bulk diffusion of charge carriers in methylammonium lead bromide single crystals. The local temporal diffusion is probed at various excitation depths to build statistics of local electronic diffusion coefficients. The measured values range between 0.3 to 2 $cm^2.s^{-1}$ depending on the local trap density and the morphological environment - a distribution that would be missed from analogous macroscopic or surface-measurements. Tomographic images of carrier diffusion were reconstructed to reveal buried crystal defects that act as barriers to carrier transport. This work reveals a new framework to understand and homogenise diffusion pathways, which are extremely sensitive to local properties and buried defects., Comment: C.S. and G.D. contributed equally to this work * corresponding author sds65@cam.ac.uk