Large-scale and air-stable two-dimensional metal layers intercalated at the interface between epitaxial graphene and SiC offer an appealing material for quantum technology. The atomic and electronic details, as well as the control of the intercalated metals within the interface, however, remain very limited. In this Letter, we explored ultrathin indium confined between graphene and SiC using cryogenic scanning tunneling microscopy, complemented by first-principle density functional theory. Bias-dependent imaging and tunneling spectroscopy visualize a triangular superstructure with a periodicity of 14.7 ± 3 Å and an occupied state at about −1.6 eV, indicating proof of highly crystalline indium. The scanning tunneling microscopy tip was used to manipulate the number of indium layers below graphene, allowing to identify three monatomic In layers and to tune their corresponding electronic properties with atomic precision. This further allows us to attribute the observed triangular superstructure to be solely emerging from the In trilayer, tentatively explained by the lattice mismatch induced by lattice relaxation in the topmost In layer. Our findings provide a microscopic insight into the structure and electronic properties of intercalated metals within the graphene/SiC interface and a unique possibility to manipulate them with atomic precision using the scanning probe technique.
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Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) \emph{Non-uniqueness}: there are many different eigendecompositions of the same Laplacian, and (2) \emph{Instability}: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be a ``hard partition'' of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to ``softly partition'' eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods.more » « less
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The Pallas’s cat (Otocolobus manul) is one of the most understudied taxa in the Felidae family. The species is currently assessed as being of “Least Concern” in the IUCN Red List, but this assessment is based on incomplete data. Additional ecological and genetic information is necessary for the long-term in situ and ex situ conservation of this species. We identified 29 microsatellite loci with sufficient diversity to enable studies into the individual identification, population structure, and phylogeography of Pallas’s cats. These microsatellites were genotyped on six wild Pallas’s cats from the Tibet Autonomous Region and Mongolia and ten cats from a United States zoo-managed population that originated in Russia and Mongolia. Additionally, we examined diversity in a 91 bp segment of the mitochondrial 12S ribosomal RNA (MT-RNR1) locus and a hypoxia-related gene, endothelial PAS domain protein 1 (EPAS1). Based on the microsatellite and MT-RNR1 loci, we established that the Pallas’s cat displays moderate genetic diversity. Intriguingly, we found that the Pallas’s cats had one unique nonsynonymous substitution in EPAS1 not present in snow leopards (Panthera uncia) or domestic cats (Felis catus). The analysis of the zoo-managed population indicated reduced genetic diversity compared to wild individuals. The genetic information from this study is a valuable resource for future research into and the conservation of the Pallas’s cat.
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A scalable platform to synthesize ultrathin heavy metals may enable high efficiency charge-to-spin conversion for next-generation spintronics. Here we report the synthesis of air-stable, epitaxially registered monolayer Pb underneath graphene on SiC (0001) by confinement heteroepitaxy (CHet). Diffraction, spectroscopy, and microscopy reveal CHet-based Pb intercalation predominantly exhibits a mottled hexagonal superstructure due to an ordered network of Frenkel-Kontorova-like domain walls. The system’s air stability enables ex-situ spin torque ferromagnetic resonance (ST-FMR) measurements that demonstrate charge-to-spin conversion in graphene/Pb/ferromagnet heterostructures with a 1.5× increase in the effective field ratio compared to control samples.more » « lessFree, publicly-accessible full text available August 5, 2025