In the previous publications (E. Kogan and V. U. Nazarov, Phys. Rev. B {\bf 85}, 115418 (2012) and E. Kogan, Graphene {\bf 2}, 74 (2013)) we presented point group symmetry classification of energy bands in graphene. In the present note we generalize classification by considering the space group symmetry. Also in the framework of group theory we describe destruction of the Dirac points in graphene by a supercell potential.
We analyze in the framework of the space group theory the change of the dispersion law in grapenein the vicinity of the (former) Dirac points due to application of supercell potential with the $\sqrt{3}\times\sqrt{3}$ space periodicity and the same point symmetry as graphene.
Energy versus magnetic field (Hofstadter butterfly diagram) in twisted bilayer graphene is studied theoretically. If we take the usual Landau gauge, we cannot take a finite periodicity even when the magnetic flux through a supercell is a rational number. We show that the \textit{periodic} Landau gauge, which has the periodicity in one direction, makes it possible to obtain the Hofstadter butterfly diagram. Since a supercell can be large, magnetic flux through a supercell normalized by the flux quantum can be a fractional number with a small denominator, even when a magnetic field is not extrem…
We present first-principles calculations of the electronic band structure and spin-orbit effects in graphene functionalized with methyl molecules in dense and dilute limits. The dense limit is represented by a 2$\times$2 graphene supercell functionalized with one methyl admolecule. The calculated spin-orbit splittings are up to $0.6$ meV. The dilute limit is deduced by investigating a large, 7$\times$7, supercell with one methyl admolecule. The electronic band structure of this supercell is fitted to a symmetry-derived effective Hamiltonian, allowing us to extract specific hopping parameters i…
Here, we report the performance of vacancy affected supercell of a hybrid Graphene-Boron Nitride embedded armchair nanoribbon (a-GNR-BN) based n-MOSFET at its ballistic transport limit using Non Equilibrium Green's Function (NEGF) methodology. A supercell is made of the 3p configuration of armchair nanoribbon that is doped on the either side with 6 BN atoms and is also H-passivated. The type of vacancies studied are mono (B removal), di (B and N atom removal) and hole (removal of 6 atoms) formed all at the interface of carbon and BN atoms. Density Functional Theory (DFT) is employed to evaluat…
We demonstrate theoretically and experimentally a topological transition of classical light in "photonic graphene": an array of waveguides arranged in the honeycomb geometry. As the system is uniaxially strained (compressed), the two unique Dirac points (present in the spectrum of conventional graphene) merge and annihilate each other, and a band gap forms. As a result, edge states are created on the zig-zag edge and destroyed on the bearded edge. These results are applicable for any 2D honeycomb-type structure, from carbon-based graphene to photonic lattices and crystals.
We study the stability and electronic structure of magic-angle twisted bilayer graphene on the hexagonal boron nitride (TBG/BN). Full relaxation has been performed for commensurate supercells of the heterostructures with different twist angles ($θ'$) and stackings between TBG and BN. We find that the slightly misaligned configuration with $θ' = 0.54^\circ$ and the AA/AA stacking has the globally lowest total energy due to the constructive interference of the moiré interlayer potentials and thus the greatly enhanced relaxation in its $1 \times 1$ commensurate supercell. Gaps are opened at the F…
The supercell approach enables us to treat the electronic structure of defective crystals, but the calculated energy bands are too complicated to understand or to compare with angle-resolved photoemission spectra because of inevitable zone folding. We discuss how to visualize supercell band structures more effectively by incorporating in them unfolded spectral weights and orbital decompositions. We then apply these ideas to gain a better understanding of the band structure of graphene containing various types of points defects, including nitrogen impurity, hydrogen adsorbate, and vacancy defec…
Photo-induced transition probabilities in graphene are studied theoretically from the viewpoint of Floquet theory. Conduction band populations are computed for a strongly, periodically driven graphene sheet under linear, circular, and elliptic polarization. Features of the momentum spectrum of excited quasi-particles can be directly related to the avoided crossing of the Floquet quasi-energy levels. In particular, the impact of the ellipticity and the strength of the laser excitation on the avoided crossing structure -- and on the resulting transition probabilities -- is studied. It is shown t…
In this paper we propose an analytical method to calculate the band structures of graphene-like nanoribbons of the armchair type with arbitrary line defects or uniaxial strains. The model is based on the tight-binding model and the standing wave assumption for the armchair nanoribbons. It gives accurate band results for large supercell systems. Within this method, we analyze different local states near the line defect in the graphene and boron-nitride nanoribbons. We also derive the analytical expression for the local states in a semi-infinite graphene nanoribbon by this method and the transfe…
We study the energetic stability and the local electronic structure of the general twisted trilayer graphene (TTG) with the top and bottom layers rotated with respect to the middle layer respectively by $θ$ and $θ'$. Approximate supercells of the moiré-of-moiré superlattices with $θ$ and $θ^{\prime}$ within $1^{\circ}\sim 2^{\circ}$ are established to describe the structural and electronic properties of relaxed TTG with the periodic boundary condition. Full relaxation demonstrates that the commensurate TTG with $θ=θ^{\prime}$ has the local minimum total energy ($E_{tol}$) at a fixed $θ$, while…
In a recent paper [Phys. Rev. B 89, 125418 (2014)], the authors argue that it is possible to map the electronic properties of twisted bilayer graphene to those of bilayer graphene in an in-plane magnetic field. However, their description of the low-energy dynamics of twisted bilayer graphene is restricted to the extended zone scheme and therefore neglects the effects of the superperiodic structure. If the energy spectrum is studied in the supercell Brillouin zone, we find that the comparison with an in-plane magnetic field fails because (i) the energy spectra of the two situations exhibit diff…
In this work, we perform ab initio calculations, based on the density functional theory, of the effects on the graphene bilayer when we intercalate carbon atoms between the layers. We use the unit cell of the bilayer to construct larger unit cells (supercells), positioning a single carbon atom in the hollow position between the monolayers and periodically replicating the supercell. By increasing the size of the unit cell and consequently, the periodicity of the inserted atoms, we are able to minimize the carbon-carbon interaction and therefore infer the changes in the electronic, vibrational a…
Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moiré potential resulting from the van der Waals interaction with the substrate. The slight lattice mismatch gives rise to a periodic supercell potential. Zone folding is expected to create replica of the original Dirac cone and Hofstadter butterflies. Our large-scale tight binding simulation reveals an unexpected coexistence of a relativistic and non-relativistic Landau level structure. The presence of the zeroth Landau level and its associated butter…
First-principles calculations of the spin-orbit coupling in graphene with hydrogen adatoms in dense and dilute limits are presented. The chemisorbed hydrogen induces a giant local enhancement of spin-orbit coupling due to $sp^3$ hybridization which depends strongly on the local lattice distortion. Guided by the reduced symmetry and the local structure of the induced dipole moments we use group theory to propose realistic minimal Hamiltonians that reproduce the relevant spin-orbit effects for both single-side semihydrogenated graphene (graphone) and for a single hydrogen adatom in a large super…
We present a theoretical study of resonance characteristics in graphene from adatoms with $s$ or $p_z$ character binding in top, bridge, and hollow positions. The adatoms are described by two tight-binding parameters: onsite energy and hybridization strength. We explore a wide range of different magnitudes of these parameters by employing T-matrix calculations in the single adatom limit and by tight-binding supercell calculations for dilute adatom coverage. We calculate the density of states and the momentum relaxation rate and extract the resonance level and resonance width. Top position with…
We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are different from the original massless Dirac fermions. The quasiparticle wavevector (measured from the new Dirac point), the generalized pseudospin vector, and the group velocity are not collinear. We further show that with an appropriate periodic potential of triangular symmetry, there exists an energy window over which the only available states are these quasipart…
Pristine graphene is not suitable for hydrogen storage at ambient conditions since it binds the hydrogen molecules only by van der Waals interactions. However, the adsorption energy of the hydrogen molecules can be improved by doping or decorating metal atoms on the graphene monolayer. The doping and decoration processes are challenging due to the oxygen interference in hydrogen adsorption and the clustering issue of metal atoms. To improve the hydrogen adsorption energy in pristine graphene, we have explored the hydrogen storage capabilities of graphene monolayer in the presence of compressiv…
Density functional calculations of optimized geometries for the migration of single hydrogen and hydroxyl groups on graphene are performed. It is shown that the migration energy barrier for the hydroxyl group is three times larger than for hydrogen. Crucial role of supercell size for the values of the migration barriers are discussed. The paired migration of hydrogen and hydroxyl groups has also been examined. It could be concluded that hydroxyl groups based magnetism is rather stable in contrast with unstable hydrogen based magnetism of functionalized graphene. The role of water in the migrat…
The fractal spectrum of magnetic minibands (Hofstadter butterfly), induced by the moiré super- lattice of graphene on an hexagonal crystal substrate, is known to exhibit gapped Dirac cones. We show that the gap can be closed by slightly misaligning the substrate, producing a hierarchy of conical singularities (Dirac points) in the band structure at rational values Phi = (p/q)(h/e) of the magnetic flux per supercell. Each Dirac point signals a switch of the topological quantum number in the connected component of the quantum Hall phase diagram. Model calculations reveal the scale invariant cond…
In this Letter, we put forward a resolution to the prolonged ambiguity in energy band gaps between theory and experiments of fabricated graphene nanoribbons (GNRs). Band structure calculations using density functional theory are performed on oxygen passivated GNRs supercells of customized edge configurations without disturbing the inherent sp2 hybridization of carbon atoms. Direct band gaps are observed for both zigzag and armchair GNRs, consistent with the experimental reports. In addition, band gap values of GNRs scattered about an average value curve for a given crystallographic orientation…
We present a computationally efficient method to incorporate density-functional theory into the calculation of reflectivity in low-energy electron microscopy. The reflectivity is determined by matching plane waves representing the electron beams to the Kohn-Sham wave functions calculated for a finite slab in a supercell. We show that the observed quantum interference effects in the reflectivity spectra of a few layers of graphene on a substrate can be reproduced well by the calculations using a moderate slab thickness.
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 $Γ$ point for the large moiré 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 …
We have investigated the way in which the concentration and distribution of adatoms affect the geometric and electronic properties of graphene. Our calculations were based on the use of first principle under the density functional theory which reveal various types of $π$-bonding. The energy band structure of this doped graphene material may be explored experimentally by employing angle-resolved photo-emission spectroscopy (ARPES) for electronic band structure measurements and scanning tunneling spectroscopy (STS) for the density-of-states (DOS) both of which have been calculated and reported i…
The moiré potential of graphene on hexagonal boron nitride (hBN) generates a supercell sufficiently large as to thread a full magnetic flux quantum $Φ_0$ for experimentally accessible magnetic field strengths. Close to rational fractions of $Φ_0$, $p/q \cdotΦ_0$, magnetotranslation invariance is restored giving rise to Brown-Zak fermions featuring the same dispersion relation as in the absence of the field. Employing a highly efficient numerical approach we have performed the first realistic simulation of the magnetoconductance for a 250 nm wide graphene ribbon on hexagonal boron nitride using…
Hydrogen adsorption on graphene in commensurate periodic arrangements leads to bandgap opening at the Dirac point and the emergence of dispersionless midgap bands. We study these bandgap effects and their dependence on periodicity for a single hydrogen adsorbate on periodic graphene supercells using spin-polarized density-functional theory calculations. Our results show that for certain periodicities, marked by a scale factor of three, the bandgap is suppressed to a great extent, and has a special level structure around the neutrality point. We present explanations for the origin of the change…
We numerically study the interplay of band structure, topological invariant and disorder effect in two-dimensional electron system of graphene in a magnetic field. Two \emph{distinct} quantum Hall effect (QHE) regimes exist in the energy band with the unconventional "half-integer" QHE appearing near the band center, consistent with the experimental observation. The latter is more robust against disorder scattering than the conventional QHE states near the band edges. The phase diagram for the unconventional QHE is obtained where the destruction of the Hall plateaus at strong disorder is throug…
Low-energy moiré flat bands in magic-angle twisted bilayer graphene (tBG) have demonstrated incredible potentials to exhibit rich exotic quantum phenomena. Theoretically, the moiré flat bands of tBG are based on the extended structures, i.e., the moiré patterns with periodic boundary conditions. However, a fundamental question of whether the flat bands can exist in the graphene moiré patterns with a reduced structure symmetry, such as sample edges, remains unanswered. Here, via scanning tunneling microscopy and spectroscopy, we study the local electronic properties of a magic-angle tBG near th…
Interaction-driven charge textures and unconventional superconductivity in strained monolayer graphene
Posgrado en Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM)（墨西哥国立自治大学物理科学研究生院）；Department of Physics, University of Arkansas（阿肯色大学物理系）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IMDEA Nanoscience（马德里IMDEA纳米科学研究所）；Center for Theoretical Physics, Hainan University（海南大学理论物理中心）；Department of Physics, Colorado State University（科罗拉多州立大学物理系）；Depto. de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México (UNAM)（墨西哥国立自治大学物理学院复杂系统系）
Rotated graphene multilayers form a new class of graphene related systems with electronic properties that drastically depend on the rotation angles. It has been shown that bilayers behave like two isolated graphene planes for large rotation angles. For smaller angles, states in the Dirac cones belonging to the two layers interact resulting in the appearance of two van Hove singularities. States become localised as the rotation angle decreases and the two van Hove singularities merge into one peak at the Dirac energy. Here we go further and consider bilayers with very small rotation angles. In …
Graphene ripples possess peculiar essential properties owing to the strong chemical bonds, as an investigation using first principle calculations clearly revealed. Various charge distributions, bond lengths, energy bands, and densities of states strongly depend on the corrugation structures, ripple curvatures and periods. Armchair ripples belonging to a zero-gap semiconductor display split middle-energy states, while the zigzag ripples exhibit highly anisotropic energy bands, semi-metallic behavior implicated by the destruction of the Dirac cone, and the newly created critical points. Their de…
An unconventional insulating phase and a superconducting phase were recently discovered in the twisted bilayer graphene [Y. Cao et al, Nature {\bf 556}, 80; {\bf 556}, 43 (2018)], but the relevant low-energy electronic states have not been clearly identified yet. In this work, I show that the interlayer hopping induces a spatially modulated Dirac mass term in the continuum Hamiltonian, and leads to a low-energy band formed by Dirac zero modes in the moiré superlattice. This moiré band becomes extremely flat and thus strongly correlated as the Dirac velocity vanishes at the magic angle, and ent…
Triple point fermions are elusive electronic excitations that generalize Dirac and Weyl modes beyond the conventional high energy paradigm. Yet, finding real materials naturally hosting these excitations at the Fermi energy has remained challenging. Here we show that twisted bilayer graphene is a versatile platform to realize robust triple point fermions in two dimensions. In particular, we establish that the introduction of localized impurities lifts one of the two degenerate Dirac cones, yielding triple point fermions at charge neutrality. Furthermore, we show that the valley polarization is…
We derive a material-realistic real-space many-body Hamiltonian for twisted bilayer graphene from first principles, including both single-particle hopping terms for $p_z$ electrons and long-range Coulomb interactions. By disentangling low- and high-energy subspaces of the electronic dispersion, we are able to utilize state-of-the-art constrained Random Phase Approximation calculations to reliably describe the non-local background screening from the high-energy $s$, $p_x$, and $p_y$ electron states for arbitrary twist angles. The twist-dependent low-energy screening from $p_z$ states is subsequ…
We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at $σ_{xy} = \pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at $σ_{xy} = \pm n(4e^2/h)$ starting from the edges of the band center regime towards the band center with an increasing ac field. Beyond a critical field strength, a Hall plateau with $σ_{xy} = 0$ can be realized at the band center, hence restoring fully a conventional integer QHE with particle-ho…
Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the two-dimensional material, enhance electron correlations, and give rise to novel condensed-matter phases such as superconductors, Mott insulators, Wigner crystals and quantum anomalous Hall insulators. Previous works predominantly focus on the flat band dispersion of coupled Dirac states from different graphene layers. In this work, we propose a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates. We take…
The layer-based random-phase approximation is further developed to investigate electronic excitations in tri-layer ABC-stacked graphene. All the layer-dependent atomic interactions and Coulomb interactions are included in the dynamic charge screening. There exist rich and unique (momentum, frequency)-excitation phase diagrams, in which the complex single-particle excitations and five kinds of plasmon modes, are dominated by the unusual energy bands and doping carrier densities. The latter frequently experience the significant Landau damping due to the former, leading to the coexistence/destruc…
Magic-angle twisted bilayer graphene (TBG) has attracted significant interest recently due to the discoveries of diverse correlated and topological states in this system. Despite the extensive research on the electron-electron interaction effects and topological properties of the electrons, the phonons of magic-angle TBG are relatively less explored. In this work, we study the phonon properties in magic-angle TBG based on \textit{ab} \textit{initio} deep potential molecular dynamics. We have calculated phonon band structures and density of states at the magic angle, and have systematically ana…
Enhancement of the chemical activity of graphene is evidenced by first-principles modelling of chemisorption of the hydrogen, fluorine, oxygen and hydroxyl groups on strained graphene. For the case of negative strain or compression, chemisorption of the single hydrogen, fluorine or hydroxyl group is energetically more favourable than those of their pairs on different sublattices. This behaviour stabilizes the magnetism caused by the chemisorption being against its destruction by the pair formations. Initially flat, compressed graphene is shown to buckle spontaneously right after chemisorption …
Analysis of the electronic structure of an ordinary two-dimensional electron gas (2DEG) under an appropriate external periodic potential of hexagonal symmetry reveals that massless Dirac fermions are generated near the corners of the supercell Brillouin zone. The required potential parameters are found to be achievable under or close to laboratory conditions. Moreover, the group velocity is tunable by changing either the effective mass of the 2DEG or the lattice parameter of the external potential, and it is insensitive to the potential amplitude. The finding should provide a new class of syst…
We study the electronic structure of graphene with a single substitutional vacancy using a combination of the density-functional, tight-binding, and impurity Green's function approaches. Density functional studies are performed with the all-electron spin-polarized linear augmented plane wave (LAPW) method. The three $sp^2 σ$ dangling bonds adjacent to the vacancy introduce localized states (V$σ$) in the mid-gap region, which split due to the crystal field and a Jahn-Teller distortion, while the $p_z π$ states introduce a sharp resonance state (V$π$) in the band structure. For a planar structur…
The honeycomb lattice sets the basic arena for numerous ideas to implement electronic, photonic, or phononic topological bands in (meta-)materials. Novel opportunities to manipulate Dirac electrons in graphene through band engineering arise from superlattice potentials as induced by a substrate such as hexagonal boron-nitride. Making use of the general form of a weak substrate potential as dictated by symmetry, we analytically derive the low-energy minibands of the superstructure, including a characteristic 1.5 Dirac cone deriving from a three-band crossing at the Brillouin zone edge. Assuming…
In the vicinity of the magic angle in twisted bilayer graphene (TBG), the two low-energy van Hove singularities (VHSs) become exceedingly narrow1-10 and many exotic correlated states, such as superconductivity, ferromagnetism, and topological phases, are observed11-16. Heterostrain, which is almost unavoidable in the TBG, can modify its single-particle band structure and lead to novel properties of the TBG that have never been considered so far. Here, we show that heterostrain in a TBG near the magic angle generates a new zero-energy flat band between the two VHSs. Doping the TBG to partially …
IMDEA Nanoscience（IMDEA纳米科学研究所）；Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院人工微纳结构教育部重点实验室）；School of Artificial Intelligence, Wuhan University（武汉大学人工智能学院）；Wuhan Institute of Quantum Technology（武汉量子技术研究院）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
This work reports an electronic and micro-structural study of an appealing system for optoelectronics: tungsten disulphide WS$_2$ on epitaxial graphene (EG) on SiC(0001). The WS$_2$ is grown via chemical vapor deposition (CVD) onto the EG. Low-energy electron diffraction (LEED) measurements assign the zero-degree orientation as the preferential azimuthal alignment for WS$_2$/EG. The valence-band (VB) structure emerging from this alignment is investigated by means of photoelectron spectroscopy measurements, with both high space and energy resolution. We find that the spin-orbit splitting of mon…
The dominance of Coulomb interactions over kinetic energy of electrons in narrow, non-trivial moiré bands of magic-angle twisted bilayer graphene (TBG) gives rise to a variety of correlated phases such as correlated insulators, superconductivity, orbital ferromagnetism, Chern insulators and nematicity. Most of these phases occur at or near an integer number of carriers per moiré unit cell. Experimental demonstration of ordered states at fractional moiré band-fillings at zero applied magnetic field $B$, is a challenging pursuit. In this letter, we report the observation of states near half-inte…
