Spectral features due to inter-Landau-level transitions in the Raman spectrum of bilayer graphene

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 excitation of electron-hole pairs in bilayer graphene. In the absence of a magnetic field, due to the parabolic dispersion of the low-energy bands in a bilayer crystal, this contribution is constant and in doped structures has a threshold at twice the Fermi energy. In an external magnetic field, the dominant Raman-active modes are the n_{-} to n_{+} inter-Landau-level transitions with crossed polarisation of in/out photons. We estimate the quantum efficiency of a single n_{-} to n_{+} transition in the magnetic field of 10T as I_{n_{-} to n_{+}}~10^{-12}.Comment: 7 pages, 3 figures, expanded version published in PR

Valley-polarized tunneling currents in bilayer graphene tunneling transistors

We study theoretically the electron current across a monolayer graphene/hexagonal boron nitride/bilayer graphene tunneling junction in an external magnetic field perpendicular to the layers. We show that change in effective tunneling barrier width for electrons on different graphene layers of bilayer graphene, coupled with the fact that its Landau level wave functions are not equally distributed amongst the layers with a distribution that is reversed between the two valleys, lead to valley polarization of the tunneling current. We estimate that valley polarization ∼70% can be achieved in high quality devices at B=1 T. Moreover, we demonstrate that strong valley polarization can be obtained both in the limit of strong-momentum-conserving tunneling and in lower quality devices where this constraint is lifted

On spectral properties of bilayer graphene: the effect of an sic substrate and infrared magneto-spectroscopy

Abstract We investigate the effect of asymmetry in bilayer graphene induced by a diatomic substrate (such as SiC) and its influence on the bilayer spectrum in zero and strong magnetic fields. We also determine selection rules for inter-Landau level transitions, taking into account all four π bands. The discovery of self-standing graphene-planes of carbon atoms arranged in a honeycomb lattice [1]-stimulated intense studies of monolayer and bilayer graphene structures (see Also, interest in optical properties of graphene resulted in several experimental magneto-optics studies of graphene in FIR, IR and the visible range In this paper, we investigate the combined effect of intralayer and interlayer asymmetries caused by a substrate on the electronic spectra of bilayer graphene, both with and without applied magnetic field. We show that intralayer asymmetry leads to the opening of an indirect gap with a 'Mexican hat'-type feature in one of the bands (whether conduction or valence depends on the sign of the asymmetry) and to an asymmetric density of states (DOS). This is different to the DOS in 'biased' bilayer graphene A schematic view of bilayer graphene (marked with the hopping integrals considered throughout this paper) and the Brillouin zone of bilayer graphene are shown in , 0) (where ξ ∈ {+, −} and a is the lattice constant). We restrict ourselves to nearest neighbour inplane and A1(2) ↔ B2(1) interactions in the tight-binding approximation of π orbitals ψ μi (μ ∈ {A, B}, i ∈ {1, 2}) and parametrize hopping integrals and on-site asymmetries according to the Slonczewski-Weiss-McClure mode

The influence of interlayer asymmetry on the magnetospectroscopy of bilayer graphene.

We present a self-consistent calculation of the interlayer asymmetry in bilayer graphene caused by an applied electric field in magnetic fields. We show how this asymmetry influences the Landau level spectrum in bilayer graphene and the observable inter-Landau level transitions when they are studied as a function of high magnetic field at fixed filling factor as measured experimentally in Ref. [1]. We also analyze the magneto-optical spectra of bilayer flakes in the photon-energy range corresponding to transitions between degenerate and split bands of bilayers

The electronic properties of bilayer graphene

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energy. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.Comment: review, 31 pages, 15 figure

Edge states of graphene bilayer strip

The electronic structure of the zig-zag bilayer strip is analyzed. The electronic spectra of the bilayer strip is computed. The dependence of the edge state band flatness on the bilayer width is found. The density of states at the Fermi level is analytically computed. It is shown that it has the singularity which depends on the width of the bilayer strip. There is also asymmetry in the density of states below and above the Fermi energy.Comment: 9 page

Determination of interatomic coupling between two-dimensional crystals using angle-resolved photoemission spectroscopy

Lack of directional bonding between two-dimensional crystals like graphene or monolayer transition metal dichalcogenides provides unusual freedom in selection of components for vertical van der Waals heterostructures. However, even for identical layers, their stacking, in particular the relative angle between their crystallographic directions, modifies properties of the structure. We demonstrate that the interatomic coupling between two two-dimensional crystals can be determined from angle-resolved photoemission spectra of a trilayer structure with one aligned and one twisted interface. Each of the interfaces provides complementary information and together they enable self-consistent determination of the coupling. We parametrize interatomic coupling for carbon atoms by studying twisted trilayer graphene and show that the result can be applied to structures with different twists and number of layers. Our approach demonstrates how to extract fundamental information about interlayer coupling in a stack of two-dimensional crystals and can be applied to many other van der Waals interfaces.Comment: This is a post-peer-review, pre-copyedit version of an article published in Nature Communications. The final authenticated version is available online at: http://dx.doi.org/10.1038/s41467-020-17412-

Magneto-optical Selection Rules in Bilayer Bernal Graphene

The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with four most important interlayer interactions taken into account. Since the main features of the wave functions are well depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions

Strain-induced Evolution of Electronic Band Structures in a Twisted Graphene Bilayer

Here we study the evolution of local electronic properties of a twisted graphene bilayer induced by a strain and a high curvature. The strain and curvature strongly affect the local band structures of the twisted graphene bilayer; the energy difference of the two low-energy van Hove singularities decreases with increasing the lattice deformations and the states condensed into well-defined pseudo-Landau levels, which mimic the quantization of massive Dirac fermions in a magnetic field of about 100 T, along a graphene wrinkle. The joint effect of strain and out-of-plane distortion in the graphene wrinkle also results in a valley polarization with a significant gap, i.e., the eight-fold degenerate Landau level at the charge neutrality point is splitted into two four-fold degenerate quartets polarized on each layer. These results suggest that strained graphene bilayer could be an ideal platform to realize the high-temperature zero-field quantum valley Hall effect.Comment: 4 figure

Properties of Graphene: A Theoretical Perspective

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic