Nanostructured semiconductors emit light from electronic states known as excitons. For organic materials, Hund's rules state that the lowest-energy exciton is a poorly emitting triplet state. For inorganic semiconductors, similar rules predict an analogue of this triplet state known as the 'dark exciton'. Because dark excitons release photons slowly, hindering emission from inorganic nanostructures, materials that disobey these rules have been sought. However, despite considerable experimental and theoretical efforts, no inorganic semiconductors have been identified in which the lowest exciton is bright. Here we show that the lowest exciton in caesium lead halide perovskites (CsPbX, with X = Cl, Br or I) involves a highly emissive triplet state. We first use an effective-mass model and group theory to demonstrate the possibility of such a state existing, which can occur when the strong spin-orbit coupling in the conduction band of a perovskite is combined with the Rashba effect. We then apply our model to CsPbX nanocrystals, and measure size- and composition-dependent fluorescence at the single-nanocrystal level. The bright triplet character of the lowest exciton explains the anomalous photon-emission rates of these materials, which emit about 20 and 1,000 times faster than any other semiconductor nanocrystal at room and cryogenic temperatures, respectively. The existence of this bright triplet exciton is further confirmed by analysis of the fine structure in low-temperature fluorescence spectra. For semiconductor nanocrystals, which are already used in lighting, lasers and displays, these excitons could lead to materials with brighter emission. More generally, our results provide criteria for identifying other semiconductors that exhibit bright excitons, with potential implications for optoelectronic devices.

Statistical learning based on a local representation of atomic structures provides a universal model of chemical stability.

The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational cost and its scaling. Techniques based on machine learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the physically relevant space of configurations has remained a challenging goal. Here we present a Gaussian Approximation Potential for silicon that achieves this milestone, accurately reproducing density functional theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calculations that would be very expensive with a first principles electronic structure method, such as finite temperature phase boundary lines, self-diffusivity in the liquid, formation of the amorphous by slow quench, and dynamic brittle fracture. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qualitative estimate of the potential's accuracy for a given atomic configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interatomic potential that comprehensively describes a material, and serves as a template for the development of such models in the future.

We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

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The bright emission observed in cesium lead halide perovskite nanocrystals (NCs) has recently been explained in terms of a bright exciton ground state [Becker et al. Nature 2018, 553, 189−193], a claim that would make these materials the first known examples in which the exciton ground state is not an optically forbidden dark exciton. This unprecedented claim has been the subject of intense experimental investigation that has so far failed to detect the dark ground-state exciton. Here, we review the effective-mass/electron−hole exchange theory for the exciton fine structure in cubic and tetragonal CsPbBr 3 NCs. In our calculations, the crystal field and the short-range electron−hole exchange constant were calculated using density functional theory together with hybrid functionals and spin−orbit coupling. Corrections associated with long-range exchange and surface image charges were calculated using measured bulk effective mass and dielectric parameters. As expected, within the context of the exchange model, we find an optically inactive ground exciton level. However, in this model, the level order for the optically active excitons in tetragonal CsPbBr 3 NCs is opposite to what has been observed experimentally. An alternate explanation for the observed bright exciton level order in CsPbBr 3 NCs is offered in terms of the Rashba effect, which supports the existence of a bright ground-state exciton in these NCs. The size dependence of the exciton fine structure calculated for perovskite NCs shows that the bright−dark level inversion caused by the Rashba effect is suppressed by the enhanced electron−hole exchange interaction in small NCs.

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Structurally disordered materials continue to pose fundamental questions [1][2][3][4] , including that of how different disordered phases ("polyamorphs") can coexist and transform from one to another 5-9 . As a widely studied case, amorphous silicon (a-Si) forms a fourfold-coordinated, covalent network at ambient conditions and much higher-coordinated, metalliclike phases under pressure 10-12 . However, a detailed mechanistic understanding of the structural transitions in disordered silicon has been lacking, due to intrinsic limitations of even the most advanced experimental and computational techniques. Here, we show how atomistic machine-learning (ML) models can break through this long-standing barrier, describing liquid-amorphous and amorphous-amorphous transitions with quantum-mechanical accuracy for a system of 100,000 atoms (ten-nanometre length scale). Our simulations reveal a three-step transformation sequence for a-Si under increasing external pressure. First, polyamorphic low-and high-density amorphous (LDA and HDA) regions are found to coexist, rather than appearing sequentially. Then, we observe a structural collapse into a distinct, very-high-density amorphous (VHDA) phase. Finally, our simulations indicate the transient nature of this VHDA phase: it rapidly nucleates crystallites, ultimately leading to the formation of a poly-crystalline structure, consistent with experiments [13][14][15] but not seen in earlier simulations 11,[16][17][18] . An ML model for electronic densities of states (DOS) confirms the onset of metallicity during VHDA formation and subsequent crystallisation. These results shed new light on liquid and amorphous states of silicon, and, in a wider context, they exemplify a holistic, ML-driven approach to predictive materials mod-