Pseudo-magnetic field distribution and pseudo-Landau levels in suspended graphene flakes

Combining the tight-binding approximation and linear elasticity theory for a planar membrane, we investigate stretching of a graphene flake assuming that two opposite edges of the sample are clamped by the contacts. We show that, depending on the aspect ratio of the flake and its orientation, gapped states may form in the membrane in the vicinity of the contacts. This gap in the pre-contact region should be biggest for the armchair orientation of the flake and width to length ratio of around 1.Comment: 7 pages + 3 figure

Landau levels in deformed bilayer graphene at low magnetic fields

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ff=+-4 being the most stable in the quantum Hall effect measurement, instead of ff=+-8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ff=+-4 is, down to very low fields, weakly dependent on the strength of the magnetic field.Comment: 14 single-column pages, 5 figures, more details on material presented in arXiv:1104.502

Spectroscopic Signatures of Electronic Excitations in Raman Scattering in Thin Films of Rhombohedral Graphite

Rhombohedral graphite features peculiar electronic properties, including persistence of low-energy surface bands of a topological nature. Here, we study the contribution of electron-hole excitations towards inelastic light scattering in thin films of rhombohedral graphite. We show that, in contrast to the featureless electron-hole contribution towards Raman spectrum of graphitic films with Bernal stacking, the inelastic light scattering accompanied by electron-hole excitations in crystals with rhombohedral stacking produces distinct features in the Raman signal which can be used both to identify the stacking and to determine the number of layers in the film.Comment: 15 pages in preprint format, 4 figures, accepted versio

Electronic Raman Scattering in Twistronic Few-Layer Graphene

We study electronic contribution to the Raman scattering signals of two-, three- and four-layer graphene with layers at one of the interfaces twisted by a small angle with respect to each other. We find that the Raman spectra of these systems feature two peaks produced by van Hove singularities in moir\'{e} minibands of twistronic graphene, one related to direct hybridization of Dirac states, and the other resulting from band folding caused by moir\'{e} superlattice. The positions of both peaks strongly depend on the twist angle, so that their detection can be used for non-invasive characterization of the twist, even in hBN-encapsulated structures.Comment: 7 pages (including 4 figures) + 10 pages (3 figures) supplemen

Using in-plane anisotropy to engineer Janus monolayers of rhenium dichalcogenides

The new class of Janus two-dimensional (2D) transition-metal dichalcogenides with two different interfaces are currently gaining increasing attention due to their distinct properties different from the typical 2D materials. Here, we show that in-plane anisotropy of a 2D atomic crystal, like ReS$_{2}$ or ReSe$_{2}$, allows formation of a large number of inequivalent Janus monolayers. We use first-principles calculations to investigate the structural stability of 29 distinct ReX$_{2-x}$Y$_{x}$ ($\mathrm{X,Y \in \{S,Se\}}$) structures, which can be obtained by selective exchange of exposed chalcogens in a ReX$_{2}$ monolayer. We also examine the electronic properties and work function of the most stable Janus monolayers and show that the large number of inequivalent structures provides a way to engineer spin-orbit splitting of the electronic bands. We find that the breaking of inversion symmetry leads to sizable spin splittings and spontaneous diople moments than are larger than those in other Janus dichalcogenides. Moreover, our caluclations suggest that the work function of the Janus monolayers can be tuned by varying the content of the substituting chalcogen. Our work demonstrates that in-plane anisotropy provides additional flexibility in sub-layer engineering of 2D atomic crystals

Moiré band model and band gaps of graphene on hexagonal boron nitride

Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Hamiltonian perturbed by smoothly varying moir\'e pattern pseudospin fields. Here, we present the moir\'e-band model of G/BN for arbitrary small twist angles under a framework that combines symmetry considerations with input from ab-initio calculations. Our analysis of the band gaps at the primary and secondary Dirac points highlights the role of inversion symmetry breaking contributions of the moir\'e patterns, leading to primary Dirac point gaps when the moir\'e strains give rise to a finite average mass, and to secondary gaps when the moir\'e pseudospin components are mixed appropriately. The pseudomagnetic strain fields which can reach values of up to $\sim$40 Tesla near symmetry points in the moir\'e cell stem almost entirely from virtual hopping and dominate over the contributions arising from bond length distortions due to the moir\'e strains.Comment: 14 pages, 8 figures, 3 table

ARPES signatures of few-layer twistronic graphenes

Diverse emergent correlated electron phenomena have been observed in twisted graphene layers due to electronic interactions with the moir\'e superlattice potential. Many electronic structure predictions have been reported exploring this new field, but with few momentum-resolved electronic structure measurements to test them. Here we use angle-resolved photoemission spectroscopy (ARPES) to study the twist-dependent ($1^\circ < \theta < 8^\circ$) electronic band structure of few-layer graphenes, including twisted bilayer, monolayer-on-bilayer, and double-bilayer graphene (tDBG). Direct comparison is made between experiment and theory, using a hybrid $\textbf{k}\cdot\textbf{p}$ model for interlayer coupling and implementing photon-energy-dependent phase shifts for photo-electrons from consecutive layers to simulate ARPES spectra. Quantitative agreement between experiment and theory is found across twist angles, stacking geometries, and back-gate voltages, validating the models and revealing displacement field induced gap openings in twisted graphenes. However, for tDBG at $\theta=1.5\pm0.2^\circ$, close to the predicted magic-angle of $\theta=1.3^\circ$, a flat band is found near the Fermi-level with measured bandwidth of $E_w = 31\pm5$ meV. Analysis of the gap between the flat band and the next valence band shows significant deviations between experiment ($\Delta_h=46\pm5$meV) and the theoretical model ($\Delta_h=5$meV), indicative of the importance of lattice relaxation in this regime

Band dispersion in the deep 1s core level of graphene

Chemical bonding in molecules and solids arises from the overlap of valence electron wave functions, forming extended molecular orbitals and dispersing Bloch states, respectively. Core electrons with high binding energies, on the other hand, are localized to their respective atoms and their wave functions do not overlap significantly. Here we report the observation of band formation and considerable dispersion (up to 60 meV) in the $1s$ core level of the carbon atoms forming graphene, despite the high C $1s$ binding energy of $\approx$ 284 eV. Due to a Young's double slit-like interference effect, a situation arises in which only the bonding or only the anti-bonding states is observed for a given photoemission geometry.Comment: 12 pages, 3 figures, including supplementary materia

Visualizing Orbital Content of Electronic Bands in Anisotropic 2D Semiconducting ReSe2

Many properties of layered materials change as they are thinned from their bulk forms down to single layers, with examples including indirect-to-direct band gap transition in 2H semiconducting transition metal dichalcogenides as well as thickness-dependent changes in the valence band structure in post-transition metal monochalcogenides and black phosphorus. Here, we use angle-resolved photoemission spectroscopy to study the electronic band structure of monolayer ReSe$_{2}$, a semiconductor with a distorted 1T structure and in-plane anisotropy. By changing the polarization of incoming photons, we demonstrate that for ReSe$_{2}$, in contrast to the 2H materials, the out-of-plane transition metal $d_{z^{2}}$ and chalcogen $p_{z}$ orbitals do not contribute significantly to the top of the valence band which explains the reported weak changes in the electronic structure of this compound as a function of layer number. We estimate a band gap of 1.7 eV in pristine ReSe$_{2}$ using scanning tunneling spectroscopy and explore the implications on the gap following surface-doping with potassium. A lower bound of 1.4 eV is estimated for the gap in the fully doped case, suggesting that doping-dependent many-body effects significantly affect the electronic properties of ReSe$_{2}$. Our results, supported by density functional theory calculations, provide insight into the mechanisms behind polarization-dependent optical properties of rhenium dichalcogenides and highlight their place amongst two-dimensional crystals.Comment: 37 pages (including Supporting Information), 7 figures in the main tex