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Defect engineering in two-dimensional semiconductors has been exploited to tune the optoelectronic properties and introduce new quantum states in the band gap. Chalcogen vacancies in transition metal dichalcogenides in particular have been found to strongly impact charge carrier concentration and mobility in 2D transistors as well as feature subgap emission and single-photon response. In this Letter, we investigate the layer-dependent charge-state lifetime of Se vacancies in ${\mathrm{WSe}}_2$. In one monolayer ${\mathrm{WSe}}_2$, we observe ultrafast charge transfer from the lowest unoccupied orbital of the top Se vacancy to the graphene substrate within $(1\pm 0.2)\mathrm{ps}$measured via the current saturation in scanning tunneling approach curves. For Se vacancies decoupled by transition metal dichalcogenide (TMD) multilayers, we find a subexponential increase of the charge lifetime from $(62\pm 14)\mathrm{ps}$in bilayer to a few nanoseconds in four-layer ${\mathrm{WSe}}_2$, alongside a reduction of the defect state binding energy. Additionally, we attribute the continuous suppression and energy shift of the $dI/dV$in-gap defect state resonances at very close tip-sample distances to a current saturation effect. Our results provide a key measure of the layer-dependent charge transfer rate of chalcogen vacancies in TMDs. Published by the American Physical Society2025 

We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the form where is a degree polynomial and is a degree polynomial. This function class generalizes the single-index model, which corresponds to , and is a natural class of functions possessing an underlying hierarchical structure. Our main result shows that for a large subclass of degree polynomials , a three-layer neural network trained via layerwise gradient descent on the square loss learns the target up to vanishing test error in samples and polynomial time. This is a strict improvement over kernel methods, which require samples, as well as existing guarantees for two-layer networks, which require the target function to be low-rank. Our result also generalizes prior works on three-layer neural networks, which were restricted to the case of being a quadratic. When is indeed a quadratic, we achieve the information-theoretically optimal sample complexity , which is an improvement over prior work (Nichani et al., 2023) requiring a sample size of . Our proof proceeds by showing that during the initial stage of training the network performs feature learning to recover the feature with samples. This work demonstrates the ability of three-layer neural networks to learn complex features and as a result, learn a broad class of hierarchical functions. 

Abstract. The chemical compound 1,2-dichloroethane (DCE), or ethylene dichloride, is an industrial very short-lived substance (VSLS) whose major use is as a feedstock in the production chain of polyvinyl chloride (PVC). Like other chlorinated VSLSs, transport of DCE (and/or its atmospheric oxidation products) to the stratosphere could contribute to ozone depletion there. However, despite annual production volumes greatly exceeding those of more prominent VSLSs (e.g. dichloromethane), global DCE observations are sparse; thus, the magnitude and distribution of DCE emissions and trends in its atmospheric abundance are poorly known. In this study, we performed an exploratory analysis of the global DCE budget between 2002 and 2020. Combining bottom-up data on annual production and assumptions around fugitive losses during production and feedstock use, we assessed the DCE source strength required to reproduce atmospheric DCE observations. We show that the TOMCAT/SLIMCAT 3-D chemical transport model (CTM) reproduces DCE measurements from various aircraft missions well, including HIPPO (2009–2011), ATom (2016–2018), and KORUS-AQ (2016), along with surface measurements from Southeast Asia, when assuming a regionally varying production emission factor in the range of 0.5 %–1.5 %. Our findings imply substantial fugitive losses of DCE and/or substantial emissive applications (e.g. solvent use) that are poorly reported. We estimate that DCE's global source increased by ∼ 45 % between 2002 (349 ± 61 Gg yr−1) and 2020 (505 ± 90 Gg yr−1), with its contribution to stratospheric chlorine increasing from 8.2 (± 1.5) to ∼ 12.9 (± 2.4) ppt Cl (where ppt denotes parts per trillion) over this period. DCE's relatively short overall tropospheric lifetime (∼ 83 d) limits, although does not preclude, its transport to the stratosphere, and we show that its impact on ozone is small at present. Annually averaged, DCE is estimated to have decreased ozone in the lower stratosphere by up to several parts per billion (< 1 %) in 2020, although a larger effect in the springtime Southern Hemisphere polar lower stratosphere is apparent (decreases of up to ∼ 1.3 %). Given strong potential for growth in DCE production tied to demand for PVC, ongoing measurements would be of benefit to monitor potential future increases in its atmospheric abundance and its contribution to ozone depletion. 

Transition metal dichalcogenide (TMD) moiré superlattices have emerged as a significant area of study in condensed matter physics. Thanks to their superior optical properties, tunable electronic band structure, strong Coulomb interactions, and quenched electron kinetic energy, they offer exciting avenues to explore correlated quantum phenomena, topological properties, and light–matter interactions. In recent years, scanning tunneling microscopy (STM) has made significant impacts on the study of these fields by enabling intrinsic surface visualization and spectroscopic measurements with unprecedented atomic scale detail. Here, we spotlight the key findings and innovative developments in imaging and characterization of TMD heterostructures via STM, from its initial implementation on the in situ grown sample to the latest photocurrent tunneling microscopy. The evolution in sample design, progressing from a conductive to an insulating substrate, has not only expanded our control over TMD moiré superlattices but also promoted an understanding of their structures and strongly correlated properties, such as the structural reconstruction and formation of generalized two-dimensional Wigner crystal states. In addition to highlighting recent advancements, we outline upcoming challenges, suggest the direction of future research, and advocate for the versatile use of STM to further comprehend and manipulate the quantum dynamics in TMD moiré superlattices.