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  1. 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. 
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    Free, publicly-accessible full text available May 5, 2025
  2. 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. 
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    Free, publicly-accessible full text available March 26, 2025
  3. The interface between two different materials can show unexpected quantum phenomena. In this study, we used molecular beam epitaxy to synthesize heterostructures formed by stacking together two magnetic materials, a ferromagnetic topological insulator (TI) and an antiferromagnetic iron chalcogenide (FeTe). We observed emergent interface-induced superconductivity in these heterostructures and demonstrated the co-occurrence of superconductivity, ferromagnetism, and topological band structure in the magnetic TI layer—the three essential ingredients of chiral topological superconductivity (TSC). The unusual coexistence of ferromagnetism and superconductivity is accompanied by a high upper critical magnetic field that exceeds the Pauli paramagnetic limit for conventional superconductors at low temperatures. These magnetic TI/FeTe heterostructures with robust superconductivity and atomically sharp interfaces provide an ideal wafer-scale platform for the exploration of chiral TSC and Majorana physics. 
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    Free, publicly-accessible full text available February 9, 2025
  4. Abstract

    Over the last decade, the possibility of realizing topological superconductivity (TSC) has generated much excitement. TSC can be created in electronic systems where the topological and superconducting orders coexist, motivating the continued exploration of candidate material platforms to this end. Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures that host emergent interfacial superconductivity when a non-superconducting antiferromagnet (FeTe) is interfaced with a topological insulator (TI) (Bi, Sb)2Te3. By performing in-vacuo angle-resolved photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find that the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point. We provide evidence to show that the observed interfacial superconductivity and its chemical potential dependence is the result of the competition between the Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling mediated by Dirac surface states and antiferromagnetic exchange couplings that generate the bicollinear antiferromagnetic order in the FeTe layer.

     
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  5. null (Ed.)