We report the exact solution of spectral problem for a graphene sheet framed by two armchair- and two zigzag-shaped boundaries. The solution is found for the $π$ electron Hamiltonian and gives, in particular, a closed analytic expression of edge-state energies in graphene. It is shown that the lower symmetry of graphene, in comparison with $C_{6h}$ of 2D graphite, has a profound effect on the graphene band structure. This and other obtained results have far going implications for the understanding of graphene electronics. Some of them are briefly discussed.
We revisit the model of graphene as a $π$-conjugated macromolecule \cite{PRL} and show that it allows to understand the origin and describe, in many cases explicitly, the electronic structure of graphene sheets, achiral graphene ribbons and carbon tubes of any size, and also graphene tori on the basis of the exact solution to the eigenvalue problem for the respective structures. The exact expressions of dispersion relations and detectable observables for these structures are compared with the predictions of other related models demonstrating that the revisited model either suggests the exact v…
We study one dimensional (1D) carbon ribbons with the armchair edges and the zigzag carbon nanotubes and their counterparts with finite length (0D) in the framework of the Hückel model. We prove that a 1D carbon ribbon is metallic if its width (the number of carbon rings) is equal to $2+3n$. We show that the dispersion law (electron band energy) of a 1D metallic ribbon or a 1D metallic carbon nanotube has a universal {\it sin-}like dependence at the Fermi energy which is independent of its width. We find that in case of metallic graphene ribbons of finite length (rectangular graphene macromole…
An exact description of $π$ electrons based on the tight-binding model of graphene as an alternant, plane macromolecule is presented. The model molecule can contain an arbitrary number of benzene rings and has armchair- and zigzag-shaped edges. This suggests an instructive alternative to the most commonly used approach, where the reference is made to the honeycomb lattice periodic in its A and B sublattices. Several advantages of the macromolecule model are demonstrated. The newly derived analytical relations detail our understanding of $π$ electron nature in achiral graphene ribbons and carbo…
Explicit expressions of the band spectrum near the neutrality point for armchair and zigzag graphene ribbons and carbon nanotubes were derived based on a tight-binding macromolecule model of graphene. The obtained dispersion relations are used to determine and compare the conductance ladders of these structures and are beneficial for many other applications. Our results are different in many respects from previously reported data. This new information forms a solid reliable basis for evaluation of the potential of graphene nanoelectronic devices.
Origin of the spectrum of $π$ electrons that results from coupling of $N$ $\cal N$-long acenes via C-C covalent bonding have been traced with the use of the Green function formalism. Exact expressions of acene and graphene Green's functions, which are useful for analysis of electronic properties of these macromolecules, are obtained and advanced to the form suitable for instructive applications.
As a particular application of the earlier proposed model of graphene as a macromolecule, we found the exact analytical expression of dispersion relation for the band of edge states in graphene zigzag ribbons. This band is often referred to as "dispersionless band" or "zero mode". The obtained result contrasts description of edge states given in the referenced paper, showing that the earlier given explanation is valid only for a very narrow region of values of the electron/hole wave vector, but for the rest, it is not correct.
Molecular dynamics simulations show that a graphene nanoribbon with alternating regions which are one and three hexagons wide can transform into a hybrid 1D nanoobject with alternating double chains and polycyclic regions under electron irradiation in HRTEM. A scheme of synthesis of such a nanoribbon using Ullmann coupling and dehydrogenation reactions is proposed. The reactive REBO-1990EVC potential is adapted for simulations of carbon-hydrogen systems and is used in combination with the CompuTEM algorithm for modeling of electron irradiation effects. The atomistic mechanism of formation of t…
In recent work by Schnez et al. [PRB 78, 195427 (2008)], they studied the analytical model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field. In this comment we first point out that the results Eqs.(5), (6) and (11) presented by them in [1] are not reliable and then give our results.
In a recent comment (arXiv:1607.06081), Falaye et al. claim that there are certain flaws in our publication (Phys. Rev. B, 78, 195427 (2008)). We point out that our results, in particular the analytic derivation of the energy spectrum of a circular graphene quantum dot exposed to a perpendicular magnetic field, are correct and equivalent to the result of Falaye et al. A misleading notation error is corrected.
We present the collective excitations spectrum (magnetoplasmon spectrum) of Dirac electrons in a weakly modulated single graphene layer in the presence of a uniform magnetic field. We consider electric modulation in one-dimension and the magnetic field applied perpendicular to graphene.We derive analytical results for the intra-Landau band plasmon spectrum within the self-consistent-field approach. We find Weiss oscillations in the magnetoplasmon spectrum which is the primary focus of this work. Results are presented for the intra-Landau band magnetoplasmon spectrum as a function of inverse ma…
We have studied the electronic excitation spectrum in periodically rippled graphene on Ru(0001) and flat, commensurate graphene on Ni(111) by means of high-resolution electron energy loss spectroscopy and a combination of density functional theory and tight-binding approaches. We show that the periodic moiré superlattice originated by the lattice mismatch in graphene/Ru(0001) induces the emergence of an extra mode, which is not present in graphene/Ni(111). Contrary to the ordinary intra-band plasmon of doped graphene, the extra mode is robust in charge-neutral graphene/metal contacts, having i…
We present an analytical description of pi electrons of a finite size bilayer graphene within a framework of the tight-binding model. The bilayered structures considered here are characterized by a rectangular geometry and have a finite size in one or both directions with armchair- and zigzag-shaped edges. We provide an exact analytical description of the spectrum of pi electrons in the zigzag and armchair bilayer graphene nanoribbons and nanotubes. We analyze the dispersion relations, the density of states, and the conductance quantization.
Collective excitations spectrum of Dirac electrons in mono and bilayer graphene in the presence of a uniform magnetic field is investigated. Analytical results for inter-Landau band plasmon spectrum within the self-consistent-field approach are obtained. SdH type oscillations that are a monotonic function of the magnetic field are observed in the plasmon spectrum of both mono- and bi-layer graphene systems. The results presented are also compared with those obtained in conventional 2DEG. The chiral nature of the quasiparticles in mono and bilayer graphene system results in the observation of $…
In this work, we determine the effects of temperature on the magnetoplasmon spectrum of an electrically modulated graphene monolayer as well as the two-dimensional electron gas (2DEG). The intra-Landau-band magnetoplasmon spectrum within the Self Consistent Field (SCF) approach is investigated for both the aforementioned systems. Results obtained not only exhibit Shubnikov-de Hass (SdH) oscillations but also commensurability oscillations (Weiss oscillations). These oscillations are periodic as a function of inverse magnetic field. We find that both the magnetic oscillations, SdH and Weiss, hav…
We study the magneto-optical conductivity of a number of Van der Waals heterostructures, namely, twisted bilayer graphene, AB-AB and AB-BA stacked twisted double bilayer graphene and monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride. As magnetic field increases, the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. Whilst twisted bilayer graphene displays only weak circular dichroism, monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride show specifically strong circular dichro…
Using the continuum model, we investigate theoretically contribution of the low-energy electronic excitations to the Raman spectrum of superconducting monolayer graphene. We consider superconducting phases characterised by an isotropic order parameter in a single valley and find a Raman peak at a shift set by the size of the superconducting gap. The height of this peak is proportional to the square root of the gap and the third power of the Fermi level, and we estimate its quantum efficiency as $I\sim10^{-14}$.
The nematic phase transition in electronic liquids, driven by Coulomb interactions, represents a new class of strongly correlated electronic ground states. We studied suspended samples of bilayer graphene, annealed so that it achieves very high quasiparticle mobilities. Bilayer graphene is a truly two-dimensional material with complex chiral electronic spectra and the high quality of our samples allowed us to observe strong spectrum reconstructions and electron topological transitions that can be attributed to a nematic phase transition and a decrease in rotational symmetry. These results are …
We show that topology of the low-energy band structure in bilayer graphene critically depends on mechanical deformations of the crystal which may easily develop in suspended graphene flakes. We describe the Lifshitz transition that takes place in strained bilayers upon splitting the parabollic bands at intermediate energies into several Dirac cones at the energy scale of few meV. Then, we show how this affects the electron Landau level spectra and the quantum Hall effect.
The magneto-optical absorption properties of graphene multilayers are theoretically studied. It is shown that the spectrum can be decomposed into sub-components effectively identical to the monolayer or bilayer graphene, allowing us to understand the spectrum systematically as a function of the layer number. Odd-layered graphenes always exhibit absorption peaks which shifts in proportion to sqrt(B), with B being the magnetic field, due to the existence of an effective monolayer-like subband. We propose a possibility of observing the monolayer-like spectrum even in a mixture of multilayer graph…
The particle-hole excitation spectrum for doped graphene is calculated from the dynamical polarizability. We study the zero and finite magnetic field cases and compare them to the standard two-dimensional electron gas. The effects of electron-electron interaction are included within the random phase approximation. From the obtained polarizability, we study the screening effects and the collective excitations (plasmon, magneto-excitons, upper-hybrid mode and linear magneto-plasmons). We stress the differences with the usual 2DEG.
We show that the transmission through single and double δ-function potential barriers of strength P in bilayer graphene is periodic in P with period π. For a certain range of P values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behaviour is found for the conductance. The spectrum of a periodic succession of δ-function barriers (Kronig-Penney model) in bilayer graphene is periodic in P with period 2π. For P smaller than a critical value, the spectrum exhibits two Dirac points while for P larger than this value an energy gap o…
We compute the optical conductivity of graphene beyond the usual Dirac cone approximation, giving results that are valid in the visible region of the conductivity spectrum. The effect of next nearest neighbor hoping is also discussed. Using the full expression for the optical conductivity, the transmission and reflection coefficients are given. We find that even in the optical regime the corrections to the Dirac cone approximation are surprisingly small (a few percent). Our results help in the interpretation of the experimental results reported by Nair {\it et al.} [Science {\bf 320}, 1308 (20…
We have theoretically studied the collective response properties of the two-dimensional chiral electron gas in bilayer graphene within the random phase approximation. The cooperation of external controlling factors like perpendicular electric bias, temperature, doping, and substrate background provides great freedom to manipulate the dynamic dielectric function and the low-energy plasmon dispersion of the system. Intriguing situations with potential application are systematically explored and discussed. Extra undamped plasmon modes might emerge under electric bias. They have almost zero group …
We study the orbital effect of a strong magnetic field parallel to the layers on the energy spectrum of the Bernal-stacked graphene bilayer and multilayers, including graphite. We consider the minimal model with the electron tunneling between the nearest sites in the plane and out of the plane. Using the semiclassical analytical approximation and exact numerical diagonalization, we find that the energy spectrum consists of two domains. In the low- and high-energy domains, the semiclassical electron orbits are closed and open, so the spectra are discrete and continuous, correspondingly. The dis…
We analytically calculate the energy spectrum of a circular graphene quantum dot with radius R subjected to a perpendicular magnetic field B by applying the infinite-mass boundary condition. We can retrieve well-known limits for the cases R, B going to infinity and B going to zero. Our model is capable of capturing the essential details of recent experiments. Quantitative agreement between theory and experiment is limited due to the fact that a circular dot is not close enough to the experimental geometry, that disorder plays a significant role, and that interaction effects may be relevant.
Inelastic light scattering from Dirac-type electrons in graphene is shown to be dominated by the generation of the inter-band electronic modes which are odd in terms of time-inversion symmetry and belong to the irreducible representation A$_2$ of the point group C$_{6v}$ of the honeycomb crystal. At high magnetic fields, these electron-hole excitations appear as peculiar $n^- \to n^+$ inter-Landau-level modes with energies $ω_n=2\sqrt{2n} \hbar v/λ_B$ and characteristically crossed polarisation of in/out photons.
Twisted bilayer graphene with tiny rotation angles have drawn significant attention due to the observation of the unconventional superconducting and correlated insulating behaviors. In this paper, we employ a full tight-binding model to investigate collective excitations in twisted bilayer graphene near magic angle. The polarization function is obtained from the tight-binding propagation method without diagonalization of the Hamiltonian matrix. With the atomic relaxation considered in the simulation, damped and undamped interband plasmon modes are discovered near magic angle under both room te…
The buffer layer has been analysed by combined micro-Raman and micro-transmission experiments. The epitaxial graphene growth on the (0001) Si face of 6H-SiC substrates was tuned to get a mixed surface at the early stage of graphitization with i) bare SiC, ii) buffer layer and iii) in some localized areas small monolayers flakes on top of the buffer layer. These unique samples enabled to measure the Raman spectrum of the buffer layer (close to the Raman spectrum of a carbon layer with a significant percentage of sp3 bonds) and its corresponding relative extinction at 514.5 nm. The Raman spectru…
The interaction between electrons and plasmons in trilayer graphene is investigated within the Overhauser approach resulting in the 'plasmaron' quasi-particle. This interaction is cast into a field theoretical problem, nd its effect on the energy spectrum is calculated using improved Wigner-Brillouin perturbation theory. The plasmaron spectrum is shifted with respect to the bare electron spectrum by $ΔE(\mathbf{k})\sim 50\div200\,{\rm meV}$ for ABC stacked trilayer graphene and for ABA trilayer graphene by $ΔE(\mathbf{k})\sim 30\div150\,{\rm meV}$ ($ΔE(\mathbf{k})\sim 1\div5\,{\rm meV}$) for t…
We derive an effective Hamiltonian at low energies for bilayer graphene when Fermi velocity manufactured on each layer is different of the velocity measured in pristine graphene. Based on the effective Hamiltonian, we investigate the influence of Fermi velocity asymmetry on the band structure of trigonally warped bilayer graphene in the presence of interlayer applied bias. In this case, the Fermi line at low energies is still preserved its threefold rotational symmetry appearing as the three pockets. Furthermore, the interlayer asymmetry in Fermi velocities leads to an indirect band gap which …
We study the Bloch spectrum and spin physics of 2D massless Dirac electrons in single layer graphene subject to a one dimensional periodic Kronig-Penney potential and Rashba spin-orbit coupling. The Klein paradox exposes novel features in the band dispersion and in graphene spintronics. In particular it is shown that: (1) The Bloch energy dispersion $\veps(p)$ has unusual structure: There are {\it two Dirac points} at Bloch momenta $\pm p \ne 0$ and a narrow band emerges between the wide valence and conduction bands. (2) The charge current and the spin density vector vanish. (3) Yet, all the n…
Employing tight-binding model we investigate the effects of a uniform Y-shaped Kekule lattice distortion on the electronic spectrum and optical conductivity of graphene. We derive a low-energy effective Hamiltonian which is found to be in excellent agreement with one calculated from a diagonalization of the full tight-binding Hamiltonian. Then using the low-energy Hamiltonian and Kubo formula we obtain an analytical expression for the real part of the optical conductivity used to explore the effects of chemical potential, temperature and on-site and hopping energy deviations in details. In par…
There are several growing methods for graphene. In this study, the growth of graphene-like clusters on the SiC wafers is done by annealing the wafers in a vacuum evaporation system equipped with a heating source accessory. For evaluating the quality of the growth method, the Raman spectra and infrared intensities of graphene-like clusters are studied theoretically and experimentally. For doing the theoretical study, three types of graphene clusters are considered and their Raman spectrum and infrared intensities are found using the Hartree-Fock method. The results show that the geometry of the…
Gapless spectrum of graphene allows easy spatial separation of electrons and holes with an external in-plane electric field. Guided collective plasmon modes can propagate along the separation line, whose amplitude decays with the distance to it. Their spectrum and direction of propagation can be controlled with the strength and direction of in-plane electric field. In case of a bilayer graphene additional control is possible by the perpendicular electric field that opens a gap in the band spectrum of electrons. We investigate guided plasmon spectra in bilayer p-n junctions using hydrodynamics …
In this paper we investigate the influence of the next-nearest-neighbor coupling of tight-binding model of graphene on the spectrum of plasmon excitations. The nearest-neighbor tight-binding model was previously used to calculate plasmon spectrum in the next paper [1]. We expand the previous results of the paper by the next-nearest-neighbor tight-binding model. Both methods are based on the numerical calculation of the dielectric function of graphene and loss function. Here we compare plasmon spectrum of the next-nearest and nearest-neighbor tight-binding models and find differences between pl…
We investigate the fine structure in the energy spectrum of bilayer graphene in the presence of various stacking defaults, such as a translational or rotational mismatch. This fine structure consists of four Dirac points that move away from their original positions as a consequence of the mismatch and eventually merge in various manners. The different types of merging are described in terms of topological invariants (winding numbers) that determine the Landau-level spectrum in the presence of a magnetic field as well as the degeneracy of the levels. The Landau-level spectrum is, within a wide …
Recently, atomically well-defined cove-shaped graphene nanoribbons have been obtained using bottom-up synthesis. These nanoribbons have an optical gap in the visible range of the spectrum which make them candidates for donor materials in photovoltaic devices. From the atomistic point of view, their electronic and optical properties are not clearly understood. Therefore, in this work we carry out ab-initio density functional theory calculations combine with many-body perturbation formalism to study their electronic and optical properties. Through the comparison with experimental measurements, w…
The electronic spectrum of three coupled graphene layers (graphene trilayers) is investigated in the presence of an external magnetic field. We obtain analytical expressions for the Landau level spectrum for both the ABA and ABC - type of stacking, which exhibit very different dependence on the magnetic field. The effect of layer asymmetry and of external gate voltages can strongly influence the properties of the system.
We investigate the magnetic minibands of a heterostructure consisting of bilayer graphene (BLG) and hexagonal boron nitride (hBN) by numerically diagonalizing a two-band Hamiltonian that describes electrons in BLG in the presence of a moire potential. Due to inversion-symmetry breaking characteristic for the moire potential, the valley symmetry of the spectrum is broken, but despite this, the zero-energy Landau level in BLG survives, albeit with reduced degeneracy. In addition, we derive effective models for the low-energy features in the magnetic minibands and demonstrate the appearance of se…
The theoretical results are presented showing that strain-induced anisotropy of graphene spectrum gives rise to the valley currents under the illumination by normally incident light. The currents of the two graphene valleys are mutually compensated providing zero net electric current. The magnitude and direction of the valley currents are determined by the parameters of strain and light polarization. For not too high photon energy strain-induced valley current exceed that due to intrinsic warping of the graphene spectrum which suggests feasibility of strain-mediated valleytronics.
We present the solutions of the energy spectrum of charge carriers confined in quantum ring in ABA-stacked trilayer graphene subjected to a perpendicular magnetic field. The calculations were performed in the context of the continuum model by solving the Dirac equation for a zero width ring geometry, i.e. freezing out the carrier radial motion. We show that the obtained energy spectrum exhibits different symmetries with respect to the magnetic field and other parameters. The application of a potential shift the energy spectrum vertically while the application of a magnetic field breaks all sym…
A single graphene layer exhibits an anomalous Landau level spectrum. A massless Dirac like low energy electronic spectrum underlies this anomaly. We study, analytically and numerically, the effect of a uniform electric field $(E)$ on the anomalous Landau levels. We solve the problem exactly within the Dirac cone approximation and find an interesting scaling of the spectrum, leading to the collapse of the Landau levels at a critical $E_c(B)$, for a given magnetic field $B$. We offer a physical interpretation of our result, which uses `graphene relativity' and the boost operation. Electric field…
We present a theoretical study of the bandstructure and Landau levels in bilayer graphene at low energies in the presence of a transverse magnetic field and Rashba spin-orbit interaction in the regime of negligible trigonal distortion. Within an effective low energy approach (Löwdin partitioning theory) we derive an effective Hamiltonian for bilayer graphene that incorporates the influence of the Zeeman effect, the Rashba spin-orbit interaction, and inclusively, the role of the intrinsic spin-orbit interaction on the same footing. Particular attention is spent to the energy spectrum and Landau…
We theoretically investigate the electronic structures of moiré superlattices arising in monolayer / bilayer graphene stacked on hexagonal boron nitride (hBN) in presence and absence of magnetic field. We develop an effective continuum model from a microscopic tight-binding lattice Hamiltonian, and calculate the electronic structures of graphene-hBN systems with different rotation angles. Using the effective model, we explain the characteristic band properties such as the gap opening at the corners of the superlattice Brillouin zone (mini-Dirac point). We also investigate the energy spectrum a…
The spectrum of two-dimensional (2D) plasma waves in graphene has been recently studied in the Dirac fermion model. We take into account the whole dispersion relation for graphene electrons in the tight binding approximation and the local field effects in the electrodynamic response. Near the wavevectors close to the corners of the hexagon-shaped Brillouin zone we found new low-frequency 2D plasmon modes with a linear spectrum. These "inter-valley" plasmon modes are related to the transitions between the two nearest Dirac cones.
We investigate the gap in the single-electron spectrum of twisted bilayer graphene. In a perfect infinite lattice of a twisted bilayer, the gap varies exponentially in response to weak changes of the twist angle. Such a large sensitivity makes theoretical predictions of the gap nearly impossible, since experimentally the twist angle is always known with finite accuracy. To address this issue, we numerically study finite clusters of twisted bilayer graphene. For finite systems, changing the twist angle causes a gradual crossover between gapless and gapped regimes. The crossover occurs when the …
The effects of second-neighbor interactions in Kekule patterned graphene electronic properties are studied starting from a tight-binding Hamiltonian. Thereafter, a low-energy effective Hamiltonian is obtained by projecting the high energy bands at the Gamma point into the subspace defined by the Kekule wave vector. The spectrum of the low energy Hamiltonian is in excellent agreement with the one obtained from a numerical diagonalization of the full tight-binding Hamiltonian. The main effect of the second-neighbour interaction is that a set of bands gains an effective mass and a shift in energy…
Graphene subject to a spatially uniform, circularly-polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator, including non-vanishing Chern numbers associated with bulk bands and current-carrying edge states. Transport properties of this system however are complicated by the non-equilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge stat…
We investigate the emergence of extra Dirac points in the electronic structure of a periodically spaced barrier system, i.e., a superlattice, on single-layer graphene, using a Dirac-type Hamiltonian. Using square barriers allows us to find analytic expressions for the occurrence and location of these new Dirac points in k-space and for the renormalization of the electron velocity near them in the low-energy range. In the general case of unequal barrier and well widths the new Dirac points move away from the Fermi level and for given heights of the potential barriers there is a minimum and maxi…
We have investigated the Coulomb screening properties and plasmon spectrum in a bilayer graphene under a perpendicular electric bias. The bias voltage applied between the two graphene layers opens a gap in the single particle energy spectrum and modifies the many-body correlations and collective excitations. The energy gap can soften the plasmon modes and lead to a crossover of the plasmons from a Landau damped mode to being undamped. Plasmon modes of long lifetime may be observable in experiments and may have potentials for device applications.
Magnetotransport measurements are performed in ultraclean (lithographically patterned) graphene nanoribbons down to 70 nm. At high magnetic fields, a fragmentation of the electronic spectrum into a Landau levels pattern with unusual features is unveiled. The singular Landau spectrum reveals large magneto-oscillations of the Fermi energy and valley degeneracy lifting. Quantum simulations suggest some disorder threshold at the origin of mixing between opposite chiral magnetic edge states and disappearance of quantum Hall effect.
An efficient method with no numerical diagonalization of a huge Hamiltonian matrix and calculation of a tedious Green's function is proposed to acquire the exact energy spectrum and dynamical conductivity in a gated AA-stacking $N$-layer Graphene (AANLG) with the intrinsic spin-orbital coupling (SOC). $2N \times 2N$ tight-binding Hamiltonian matrix, velocity operator and Green's function representation of an AANLG are simultaneously reduced to $N$ $2\times 2$ diagonal block matrices through a proper transformation matrix. A gated AANLG with intrinsic SOC is reduced to $N$ graphene-like layers.…
In a recent publication [Phys. Rev. B $\textbf{89}$, 155403 (2014)], the authors investigated the spectrum of a Coulomb impurity in graphene in the presence of magnetic and electric fields using the coupled series expansion approach. In the first part of their publication they investigated how Coulomb impurity states collapse in the presence of a perpendicular magnetic field. We argue that the obtained spectrum does not give information about the atomic collapse and that their interpretation of the spectrum regarding atomic collapse is not correct. We also argue that the obtained results are o…
Using the Landau-Zener-Stückelberg-Majorana-type (LZSM) semiclassical approach, we study both graphene and a thin film of a Weyl semimetal subjected to a strong AC electromagnetic field. The spectrum of quasi energies in the Weyl semimetal turns out to be similar to that of a graphene sheet. Earlier it has been predicted qualitatively that the transport properties of strongly-irradiated graphene oscillate as a function of the radiation intensity [S.V. Syzranov et al., Phys. Rev. B 88, 241112 (2013)]. Here we obtain rigorous quantitative results for a driven linear conductance of graphene and a…
The fine structure of the Dirac energy spectrum in graphene induced by electron-optical phonon coupling is investigated in the portion of the spectrum near the phonon emission threshold. The derived new dispersion equation in the immediate neighborhood below the phonon threshold corresponds to an electron-phonon bound state. We find that the singular vertex corrections beyond perturbation theory increase strongly the electron-phonon binding energy. The predicted enhancement of the effective electron-phonon coupling can be measured using angle-resolved spectroscopy.
We investigate the contribution of the low-energy electronic excitations towards the Raman spectrum of bilayer graphene for the incoming photon energy Omega >> 1eV. Starting with the four-band tight-binding model, we derive an effective scattering amplitude that can be incorporated into the commonly used two-band approximation. Due to the influence of the high-energy bands, this effective scattering amplitude is different from the contact interaction amplitude obtained within the two-band model alone. We then calculate the spectral density of the inelastic light scattering accompanied by the e…
The recent Quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice, and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered th…
We study theoretically the coherent electron focusing in graphene nanoribbons. Using semiclassical and numerical tight binding calculations we show that perfect armchair edges give rise to equidistant peaks in the focusing spectrum. In the case of zigzag edges at low magnetic fields one can also observe focusing peaks but with increasing magnetic field a more complex interference structure emerges in the spectrum. This difference in the spectra can be observed even if the zigzag edge undergoes structural reconstruction. Therefore transverse electron focusing can help in the identification and …
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 …
