We study the Raman signature of stripe domains in monolayer W x Mo1-x S2 alloys, characterized using experimental techniques and density functional theory (DFT) calculations. These stripe domains were found in star-shaped monolayer WS2 exhibiting a high concentration of molybdenum (Mo) atoms in its central region, and unique Raman peaks that were not previously reported. We attribute these peaks to the splitting of the original doubly degenerate E2g modes, arising from the lower symmetry of the W-Mo stripe domains. We confirm the stripe presence and location using high-resolution scanning transmission electron microscopy (STEM) imaging and use DFT to elucidate the structural, electronic, and vibrational properties of the stripes when the stoichiometry corresponds to W0.5Mo0.5S2. The findings provide insight into the evolution of the Raman spectra as stripe domains arise in TMD alloys, thus contributing to a broader understanding of the influence of atomic-level structural modifications on material properties.

We study the Raman signature of stripe domains in monolayer WxMo1-xS2 alloys, characterized using experimental techniques and density functional theory (DFT) calculations. These stripe domains were found in star-shaped monolayer WS2 exhibiting a high concentration of molybdenum (Mo) atoms in its central region, and unique Raman peaks that were not previously reported. We attribute these peaks to the splitting of the original doubly degenerate E2g modes, arising from the lower symmetry of the W-Mo stripe domains. We confirm the stripe presence and location using high-resolution scanning transmission electron microscopy (STEM) imaging and use DFT to elucidate the structural, electronic, and vibrational properties of the stripes when the stoichiometry corresponds to W0.5Mo0.5S2. The findings provide insight into the evolution of the Raman spectra as stripe domains arise in TMD alloys, thus contributing to a broader understanding of the influence of atomic-level structural modifications on material properties.

Resonant Raman spectra of armchair graphene nanoribbons (AGNRs) are computed using Density Functional Theory (DFT) and third-order perturbation theory. Results are benchmarked against available experimental data and compared to previously used theoretical approaches based on the Placzek approximation. Comparable agreement with experiments is found for both previously and presently used methods. In addition, a numerical analysis is carried out to provide a justification for the resonant modeling method based on the use of the frequency-dependent dielectric tensor in the Placzek approximation. This work also provides additional predictions and references for wide AGNRs that might be investigated with Raman scattering experiments in the future.

Many computational models have been developed to predict the rates of atomic displacements in two-dimensional (2D) materials under electron beam irradiation. However, these models often drastically underestimate the displacement rates in 2D insulators, in which beam-induced electronic excitations can reduce the binding energies of the irradiated atoms. This bond softening leads to a qualitative disagreement between theory and experiment, in that substantial sputtering is experimentally observed at beam energies deemed far too small to drive atomic dislocation by many current models. To address these theoretical shortcomings, this paper develops a first-principles method to calculate the probability of beam-induced electronic excitations by coupling quantum electrodynamics (QED) scattering amplitudes to density functional theory (DFT) single-particle orbitals. The presented theory then explicitly considers the effect of these electronic excitations on the sputtering cross section. Applying this method to 2D hexagonal BN and MoS2 significantly increases their calculated sputtering cross sections and correctly yields appreciable sputtering rates at beam energies previously predicted to leave the crystals intact. The proposed QED-DFT approach can be easily extended to describe a rich variety of beam-driven phenomena in any crystalline material.

Structural relaxation in slightly misaligned bilayer graphene leads to the formation of domains separated by topological solitons. The influence of such a soliton lattice on phonons is investigated in the framework of the Frenkel-Kontorova model, where a solution is derived in the continuum limit. A nearly free phonon model is developed to explain the characteristic features in the phonon band structure derived from the Frenkel-Kontorova model. Its 2D extension is discussed and applied on the specific case of twisted bilayer graphene. This model explains a number of computational results reported until now and can be used directly to investigate other misaligned two-dimensional networks as found in van der Waals heterostructures.

The electronic, optical, and magnetic properties of graphene nanoribbons (GNRs) can be engineered by controlling their edge structure and width with atomic precision through bottom-up fabrication based on molecular precursors. This approach offers a unique platform for all-carbon electronic devices but requires careful optimization of the growth conditions to match structural requirements for successful device integration, with GNR length being the most critical parameter. In this work, the growth, characterization, and device integration of 5-atom wide armchair GNRs (5-AGNRs) are studied, which are expected to have an optimal bandgap as active material in switching devices. 5-AGNRs are obtained via on-surface synthesis under ultrahigh vacuum conditions from Br- and I-substituted precursors. It is shown that the use of I-substituted precursors and the optimization of the initial precursor coverage quintupled the average 5-AGNR length. This significant length increase allowed the integration of 5-AGNRs into devices and the realization of the first field-effect transistor based on narrow bandgap AGNRs that shows switching behavior at room temperature. The study highlights that the optimized growth protocols can successfully bridge between the sub-nanometer scale, where atomic precision is needed to control the electronic properties, and the scale of tens of nanometers relevant for successful device integration of GNRs.

The importance of phonons in the strong correlation phenomena observed in twisted-bilayer graphene (TBG) at the so-called magic-angle is under debate. Here we apply gate-dependent micro-Raman spectroscopy to monitor the G band line width in TBG devices of twist angles θ = 0° (Bernal), ∼1.1° (magic-angle), and ∼7° (large-angle). The results show a broad and p-/n-asymmetric doping behavior at the magic angle, in clear contrast to the behavior observed in twist angles above and below this point. Atomistic modeling reproduces the experimental observations in close connection with the joint density of electronic states in the electron-phonon scattering process, revealing how the unique electronic structure of magic-angle TBGs influences the electron-phonon coupling and, consequently, the G band line width. Overall, the value of the G band line width in magic-angle TBG is larger when compared to that of the other samples, in qualitative agreement with our calculations.

Many computational models have been developed to predict the rates of atomic displacements in two-dimensional (2D) materials under electron beam irradiation. However, these models often drastically underestimate the displacement rates in 2D insulators, in which beam-induced electronic excitations can reduce the binding energies of the irradiated atoms. This bond softening leads to a qualitative disagreement between theory and experiment, in that substantial sputtering is experimentally observed at beam energies deemed far to small to drive atomic dislocation by many current models. To address these theoretical shortcomings, this paper develops a first-principles method to calculate the probability of beam-induced electronic excitations by coupling quantum electrodynamics (QED) scattering amplitudes to density functional theory (DFT) single-particle orbitals. The presented theory then explicitly considers the effect of these electronic excitations on the sputtering cross section. Applying this method to 2D hexagonal BN and MoS$_2$ significantly increases their calculated sputtering cross sections and correctly yields appreciable sputtering rates at beam energies previously predicted to leave the crystals intact. The proposed QED-DFT approach can be easily extended to describe a rich variety of beam-driven phenomena in any crystalline material.

This repository contains the experimental data related to the article "Localization of lattice dynamics in low-angle twisted bilayer graphene" and is provided to the reader under the “data availability” directive. the files have been organized on a per-figure basis.

A low twist angle between the two stacked crystal networks in bilayer graphene enables self-organized lattice reconstruction with the formation of a periodic domain. This superlattice modulates the vibrational and electronic structures, imposing new rules for electron-phonon coupling and the eventual observation of strong correlation and superconductivity. Direct optical images of the crystal superlattice in reconstructed twisted bilayer graphene are reported here, generated by the inelastic scattering of light in a nano-Raman spectroscope. The observation of the crystallographic structure with visible light is made possible due to lattice dynamics localization, the images resembling spectral variations caused by the presence of strain solitons and topological points. The results are rationalized by a nearly-free-phonon model and electronic calculations that highlight the relevance of solitons and topological points, particularly pronounced for structures with small twist angles. We anticipate our discovery to play a role in understanding Jahn-Teller effects and electronic Cooper pairing, among many other important phonon-related effects, and it may be useful for characterizing devices in the most prominent platform for the field of twistronics.

The phonon spectra of twisted bilayer graphene (tBLG) are analyzed for a series of 692 twisting angle values in the $[0,30{\degree}]$ range. The evolution of the phonon bandstructure as a function of twist angle is examined using a band unfolding scheme where the large number of phonon modes computed at the $\Gamma$ point for the large moir\'e tBLG supercells are unfolded onto the Brillouin Zone (BZ) of one of the two constituent layers. In addition to changes to the low-frequency breathing and shear modes, a series of well-defined side-bands around high-symmetry points of the extended BZ emerge due to the twist angle-dependent structural relaxation. The results are rationalized by introducing a nearly-free-phonon model that highlights the central role played by solitons in the description of the new phonon branches, which are particularly pronounced for structures with small twist angles, below a buckling angle $\theta_{\rm B}\sim {3.75}{\degree}$.

Selective two-electron oxygen reduction reaction (ORR) offers a promising route for hydrogen peroxide synthesis, and defective sp2 carbon-based materials are attractive, low-cost electrocatalysts for this process. However, due to a wide range of possible defect structures formed during material synthesis, identification and fabrication of precise active sites remain a challenge. Here, we report a graphene edgebased electrocatalyst for two-electron ORR - nanowire-templated three-dimensional fuzzy graphene (NT3DFG). NT-3DFG exhibits excellent efficiency (onset potential of 0.79 $\pm$ 0.01 V versus RHE), selectivity (93 $\pm$ 3 % H2O2), and tunable ORR activity as a function of graphene edge site density. Using spectroscopic surface characterization and density functional theory calculations, we find that NT-3DFG edge sites are readily functionalized by carbonyl (C=O) and hydroxyl (C-OH) groups under alkaline ORR conditions. Our calculations indicate that multiple site configurations at both armchair and zigzag edges may achieve a local coordination environment that allows selective, two-electron ORR. We derive a general geometric descriptor based on the local coordination environment that provides activity predictions of graphene surface sites within ~0.1 V of computed values. Herein we combine synthesis, spectroscopy, and simulations to improve active site characterization and accelerate carbon-based electrocatalyst discovery.

The vibrational properties of twisted bilayer graphene (tBLG) show complex features, due to the intricate energy landscape of its low-symmetry configurations. A machine learning-based approach is developed to provide a continuous model between the twist angle and the simulated Raman spectra of tBLGs. Extracting the structural information of the twist angle from Raman spectra corresponds to solving a complicated inverse problem. Once trained, the machine learning regressors (MLRs) quickly provide predictions without human bias and with an average 98% of the data variance being explained by the model. The significant spectral features learned by MLRs are analyzed revealing the intensity profile near the calculated G-band to be the most important feature. The trained models are tested on noise-containing test data demonstrating their robustness. The transferability of the present models to experimental Raman spectra is discussed in the context of validation of the level of theory used for construction of the analyzed database. This work serves as a proof of concept that machine-learning analysis is a potentially powerful tool for interpretation of Raman spectra of tBLG and other 2D materials.

Electron beam irradiation by transmission electron microscopy (TEM) is a common and effective method for post-synthesis defect engineering in two-dimensional transition metal dichalcogenides (TMDs). Combining density functional theory (DFT) with relativistic scattering theory, we simulate the generation of such defects in monolayer group-VI TMDs, MoS2, WS2, MoSe2, and WSe2, focusing on two fundamental TEM-induced atomic displacement processes: chalcogen sputtering and chalcogen vacancy migration. Our calculations show that the activation energies of chalcogen sputtering depend primarily on the chalcogen species, and are smaller in selenides than in sulfides. Meanwhile, chalcogen vacancy migration activation energies hinge on the transition metal species, being smaller in TMDs containing Mo. Incorporating these energies into a relativistic, temperature-dependent cross section, we predict that, with appropriate TEM energies and temperatures, one can induce migrations in all four group-VI TMDs without simultaneously producing vacancies at a significant rate. This can allow for the formation of complicated defects and extended patterns, and thus, for the controlled manipulation of TMD crystals for targeted functionality, without the risk of substantial collateral damage.

Graphene, a honeycomb sp2 hybridized carbon lattice, is a promising building block for hybrid-nanomaterials due to its electrical, mechanical, and optical properties. Graphene can be readily obtained through mechanical exfoliation, solution-based deposition of reduced graphene oxide (rGO), and chemical vapor deposition (CVD). The resulting graphene films' topology is two-dimensional (2D) surface. Recently, synthesis of three-dimensional (3D) graphitic networks supported or templated by nanoparticles, foams, and hydrogels was reported. However, the resulting graphene films lay flat on the surface, exposing 2D surface topology. Out-of-plane grown carbon nanostructures, such as vertically aligned graphene sheets (VAGS) and vertical carbon nanowalls (CNWs), are still tethered to 2D surface. 3D morphology of out-of-plane growth of graphene hybrid-nanomaterials which leverages graphene's outstanding surface-to-volume ratio has not been achieved to date. Here we demonstrate highly controlled synthesis of 3D out-of-plane single- to few-layer fuzzy graphene (3DFG) on a Si nanowire (SiNW) mesh template. By varying graphene growth conditions (CH4 partial pressure and process time), we control the size, density, and electrical properties of the NW templated 3DFG (NT-3DFG). 3DFG growth can be described by a diffusion-limited-aggregation (DLA) model. The porous NT-3DFG meshes exhibited high electrical conductivity of ca. 2350 S m-1. NT-3DFG demonstrated exceptional electrochemical functionality, with calculated specific electrochemical surface area as high as ca. 1017 m2 g-1 for a ca. 7 μm thick mesh. This flexible synthesis will inspire formation of complex hybrid-nanomaterials with tailored optical and electrical properties to be used in future applications such as sensing, and energy conversion and storage.

We report how the presence of electron-beam-induced sulfur vacancies affects first-order Raman modes and correlate the effects with the evolution of the in situ transmission-electron microscopy two-terminal conductivity of monolayer MoS2 under electron irradiation. We observe a red-shift in the E' Raman peak and a less pronounced blue-shift in the A'1 peak with increasing electron dose. Using energy-dispersive X-ray spectroscopy and selected-area electron diffraction, we show that irradiation causes partial removal of sulfur and correlate the dependence of the Raman peak shifts with S vacancy density (a few %). This allows us to quantitatively correlate the frequency shifts with vacancy concentration, as rationalized by first-principles density functional theory calculations. In situ device current measurements show an exponential decrease in channel current upon irradiation. Our analysis demonstrates that the observed frequency shifts are intrinsic properties of the defective systems and that Raman spectroscopy can be used as a quantitative diagnostic tool to characterize MoS2-based transport channels.