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Unlike conventional two-dimensional (2D) semiconductor superlattices, moir\'{e} patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a continuous+atomistic theory treating 2D materials as crystalline elastic membranes, we abandon the flat-membrane scenario usually assumed for these materials and address out-of-plane deformations. We confront our predictions to experimental analyses on model systems, epitaxial graphene, and MoS$_2$ on metals and reveal that compression/expansion and bending energies stored in the membrane can compete with adhesion energy, leading to a subtle moir\'{e} wavelength selection and the formation of wrinkles., Comment: 7 pages, 3 figures

We report the observation of an intense anomalous peak at 1608 cm$^{-1}$ in the Raman spectrum of graphene associated to the presence of chromium nanoparticles in contact with graphene. Bombardment with an electron beam demonstrates that this peak is distinct from the well studied D$'$ peak appearing as defects are created in graphene; the new peak is found non dispersive. We argue that the bonding of chromium atoms with carbon atoms softens the out-of-plane optical (ZO) phonon mode, in such a way that the frequency of its overtone decreases to $2\omega_{\rm ZO}\sim\omega_{\rm G}$, where $\omega_{\rm G}$=1585~cm$^{-1}$ is the frequency of the Raman-active E$_{\rm 2g}$ mode. Thus, the observed new peak is attributed to the 2ZO mode which becomes Raman-active following a mechanism known as Fermi resonance. First-principles calculations on vibrational and anharmonic properties of the graphene/Cr interface support this scenario., Comment: 12 pages, 10 figures

Transition metal surfaces catalyse a broad range of thermally-activated reactions involving carbon-containing-species -- from atomic carbon to small hydrocarbons or organic molecules, and polymers. These reactions yield well-separated phases, for instance graphene and the metal surface, or, on the contrary, alloyed phases, such as metal carbides. Here, we investigate carbon phases on a rhenium (0001) surface, where the former kind of phase can transform into the latter. We find that this transformation occurs with increasing annealing time, which is hence not suitable to increase the quality of graphene. Our scanning tunneling spectroscopy and reflection high-energy electron diffraction analysis reveal that repeated short annealing cycles are best suited to increase the lateral extension of the structurally coherent graphene domains. Using the same techniques and with the support of density functional theory calculations, we next unveil, in real space, the symmetry of the many variants (two six-fold families) of a rhenium surface carbide observed with diffraction since the 1970s, and finally propose models of the atomic details. One of these models, which nicely matches the microscopy observations, consists of parallel rows of eight aligned carbon trimers with a so-called $(7\times\sqrt{\mathrm{19}})$ unit cell with respect to Re(0001)., Comment: 12 pages, 6 figures

Graphene holds promises for exploring exotic superconductivity with Dirac-like fermions. Making graphene a superconductor at large scales is however a long-lasting challenge. A possible solution relies on epitaxially-grown graphene, using a superconducting substrate. Such substrates are scarce, and usually destroy the Dirac character of the electronic band structure. Using electron diffraction (reflection high-energy, and low-energy), scanning tunneling microscopy and spectroscopy, atomic force microscopy, angle-resolved photoemission spectroscopy, Raman spectroscopy, and density functional theory calculations, we introduce a strategy to induce superconductivity in epitaxial graphene $via$ a remote proximity effect, from the rhenium substrate through an intercalated gold layer. Weak graphene-Au interaction, contrasting with the strong undesired graphene-Re interaction, is demonstrated by a reduced graphene corrugation, an increased distance between graphene and the underlying metal, a linear electronic dispersion and a characteristic vibrational signature, both latter features revealing also a slight $p$ doping of graphene. We also reveal that the main shortcoming of the intercalation approach to proximity superconductivity is the creation of a high density of point defects in graphene (10$^{14}$~cm$^{-2}$). Finally, we demonstrate remote proximity superconductivity in graphene/Au/Re(0001), at low temperature., Comment: 13 pages, 6 figures, to appear in 2D Materials

A broad variety of defects has been observed in two-dimensional materials. Many of these defects can be created by top-down methods such as electron irradiation or chemical etching, while a few of them are created along bottom-up processes, in particular during the growth of the material, in which case avoiding their formation can be challenging. This occurs e.g. with dislocations, Stone-Wales defects, or atomic vacancies in graphene. Here we address a defect that has been observed repeatedly since 2007 in epitaxial graphene on metal surfaces like Ru(0001) and Re(0001), but whose nature has remained elusive thus far. This defect has the appearance of a vacant hill in the periodically nanorippled topography of graphene, which comes together with a moir{\'e} pattern. Based on atomistic simulations and scanning tunneling microscopy/spectroscopy measurements, we argue that such defects are topological in nature and that their core is a stacking fault patch, either in graphene, surrounded by loops of non-hexagonal carbon rings, or in the underlying metal. We discuss the possible origin of these defects in relation with recent reports of metastable polycyclic carbon molecules forming upon graphene growth. Like other defects, the vacant hills may be considered as deleterious in the perspective of producing high quality graphene. However, provided they can be organized in graphene, they might allow novel optical, spin, or electronic properties to be engineered.

In crystal growth, surfactants are additive molecules used in dilute amount or as dense, permeable layers to control surface morphologies. Here, we investigate the properties of a strikingly different surfactant: a two-dimensional and covalent layer with close atomic packing, graphene. Using in situ, real time electron microscopy, scanning tunneling microscopy, kinetic Monte Carlo simulations, and continuum mechanics calculations, we reveal why metallic atomic layers can grow in a two-dimensional manner below an impermeable graphene membrane. Upon metal growth, graphene dynamically opens nanochannels called wrinkles, facilitating mass transport, while at the same time storing and releasing elastic energy via lattice distortions. Graphene thus behaves as a mechanically active, deformable surfactant. The wrinkle-driven mass transport of the metallic layer intercalated between graphene and the substrate is observed for two graphene-based systems, characterized by different physico-chemical interactions, between graphene and the substrate, and between the intercalated material and graphene. The deformable surfactant character of graphene that we unveil should then apply to a broad variety of species, opening new avenues for using graphene as a two-dimensional surfactant forcing the growth of flat films, nanostructures and unconventional crystalline phases.

Moir\'e superlattices in graphene supported on various substrates have opened a new avenue to engineer graphene's electronic properties. Yet, the exact crystallographic structure on which their band structure depends remains highly debated. In this scanning tunneling microscopy and density functional theory study, we have analysed graphene samples grown on multilayer graphene prepared onto SiC and on the close-packed surfaces of Re and Ir with ultra-high precision. We resolve small-angle twists and shears in graphene, and identify large unit cells comprising more than 1,000 carbon atoms and exhibiting non-trivial nanopatterns for moir\'e superlattices, which are commensurate to the graphene lattice. Finally, a general formalism applicable to any hexagonal moir\'e is presented to classify all reported structures., Comment: 14 pages, 6 figures