Narrow Results

Density functional theory is adopted for the electronic structure and phonon calculation of Ca-doped bilayer graphene. The AA and AB stacking configurations are simulated, and the atoms are relaxed so that the atomic forces working on them are close to zero ($5.0\times 10^{-3}$ eV/Å). In the final relaxation, the symmetry of $C_{8}Ca{C}_8$ is $D_{2h}$ for AA stacking and $C_S$ for AB stacking. The formation energy of AA stacking (1.72 eV) is much lower than that of AB stacking ($8.07$ eV). According to the electronic structure calculations, the Dirac point shifts down from the Fermi level, indicating that the Ca atom behaves as an n-type dopant. The calculated Fermi velocities for pristine bilayer graphene are $7.69\times 10^5$ (AA stacking) and $7.75\times 10^5$ m/s (AB stacking). Those for Ca-doped bilayer graphene are $7.29\times 10^5$ (AA stacking) and $7.22\times 10^5$ m/s (AB stacking). Phonon calculations revealed that considering the vibrational effect, the defect concentration is $1.4\times 10^{16}$ cm${}^{-3}$ in the AA stacking system. Meanwhile, concentration is deficient in the AB stacking system due to the asymmetric defect configuration.

We consider a model of half-filled bilayer graphene, in which the three dominant Slonczewski–Weiss–McClure hopping parameters are retained, in the presence of short-range interactions. Under a smallness assumption on the interaction strength $U$ as well as on the inter-layer hopping $ϵ$, we construct the ground state in the thermodynamic limit, and prove that the pressure and two-point Schwinger function, away from its singularities, are analytic in $U$, uniformly in $ϵ$. The interacting Fermi surface is degenerate, and consists of eight Fermi points, two of which are protected by symmetries, while the locations of the other six are renormalized by the interaction, and the effective dispersion relation at the Fermi points is conical. The construction reveals the presence of different energy regimes, where the effective behavior of correlation functions changes qualitatively. The analysis of the crossover between regimes plays an important role in the proof of analyticity and in the uniform control of the radius of convergence. The proof is based on a rigorous implementation of fermionic renormalization group methods, including determinant estimates for the renormalized expansion.

We review recent work on superlattices in monolayer and bilayer graphene. We highlight the role of the quasiparticle chirality in generating new Dirac fermion modes with tunable anisotropic velocities in one dimensional (1D) superlattices in both monolayer and bilayer graphene. We discuss the structure of the Landau levels and magnetotransport in such superlattices over a wide range of perpendicular (orbital) magnetic fields. In monolayer graphene, we show that an orbital magnetic field can reverse the anisotropy of the transport imposed by the superlattice potential, suggesting possible switching-type device applications. We also consider topological modes localized at a kink in an electric field applied perpendicular to bilayer graphene, and show how interactions convert these modes into a two-band Luttinger liquid with tunable Luttinger parameters. The band structures of electric field superlattices in bilayer graphene (with or without a magnetic field) are shown to arise naturally from a coupled array of such topological modes. We briefly review some bandstructure results for 2D superlattices. We conclude with a discussion of recent tunneling and transport experiments and point out open issues.

We have investigated electronic transport of charge carriers in a gapped bilayer graphene superlattice (GBGS), based on transfer matrix method. We have found that conductivity of the system has an oscillatory behavior respect to the gap value. As the gap value is simply changeable by external voltage in bilayer graphene, the conductivity can be controlled by gate voltage. It also has been shown that transmission probability for normal incident angle depends on barrier width in presence of band gap within barrier region. As a result, a GBGS behaves very differently compared to a gapless bilayer graphene superlattice.

We use quantum Monte Carlo method to study a magnetic impurity located next to a vacancy in Bernal stacked bilayer graphene. Due to the broken symmetry between two sublattices in bilayer system, there exist two different types of vacancy induced localized state. We find that the magnetic property of the adatom located on the adjacent site of the vacancy depends on whether the vacancy belongs to A or B sublattice. In general, local moment is more strongly suppressed if the vacancy belongs to the sublattice A near the zero-energy. We switch the values of the chemical potential and study the basic thermodynamic quantities and the correlation functions between the magnetic adatom and carbon sites.

In bilayer graphene, the A and B sites in each layer have different local electronic structures due to the presence of the second layer. In this work, using first-principles calculations, we examine the effect of sublattice inequivalence on various properties of hydrogen defects in bilayer graphene. Density functional calculations show that induced magnetic moments by H adsorption on A and B sites of bilayer graphene are both equal to $1{\mu }_B$ at zero temperature, but change slightly and develop a mismatch at finite temperature. We show how this variation follows from the fact that H on A site remains gapless but H on B site opens an energy gap. We also use a tight-binding model to explain the differences in band structures for H adsorption on A and B sites. The results obtained in this work suggest that there are important differences in electronic and magnetic properties between H adsorption on monolayer and bilayer graphene.

The present paper investigates that the tunneling time for bilayer graphene potential barrier with monolayer graphene leads to all range of energy. Numerical results reveal that parameters such as the incident energy and angle plays a significant role in inducing of the Hartman effect. In contrast to single-layer graphene, in the bilayer graphene, due to the chirality of quasi-particles induction of Klein and Hartman effects occur in the normal incidence case. Moreover, it is demonstrated that even for energy levels above barrier, the Hartman effect is present.

We investigate the dispersion relation and decay rate of plasmon modes in a double-layer system made of bilayer graphene (BLG) and infinite GaAs quantum well at zero-temperature within the generalized random-phase-approximation and taking into account the 2DEG layer-thickness and inhomogeneity of the background dielectric. We illustrate that the acoustic plasmon dispersion curve of the considered system differs significantly from that of monolayer graphene (MLG)–GaAs heterostructure and BLG–GaAs without layer-thickness. Calculations also demonstrate that meanwhile the optical plasmon curve is affected slightly by spacer width and exchange-correlation, the acoustic one depends remarkably on the interlayer distance, inhomogeneity of the background dielectric, carrier densities, spacer dielectric constant, quantum well width and exchange-correlations.

We theoretically study the spin-dependent group delay time through ferromagnetic bilayer graphene superlattice in the absence and presence of the bandgap. It is found that the group delay time depends on the spin degree of freedom and exhibits an oscillatory behavior with respect to the Fermi energy and barrier width. Furthermore, in the absence of the bandgap, the superluminal or Hartman effect exists only for the normal angle of incidence. Moreover, when bandgap value is large enough $(\mathrm{\Delta }\ge 60\mathrm{\text{meV}})$, the Hartman effect can be observed for all angles of incidence. These results are contrary to the observed behavior for monolayer graphene superlattice.

We consider a double-layer system made of two parallel bilayer graphene sheets separated by a dielectric medium. We calculate the finite-temperature electrical conductivity of the first layer due to charged impurities located in two layers. We study the effects of temperature, interlayer distance, dielectric constants and impurity concentration, carrier concentration on the electrical conductivity. We show the importance of charged impurities located in layer II in determining electrical conductivity of the first layer for small interlayer distance. The results in this paper give us more understanding about the long-range charged impurity scattering in bilayer graphene under the effect of the second one.

This article is a review of our work related to Raman studies of single layer and bilayer graphenes as a function Fermi level shift achieved by electrochemically top gating a field effect transistor. Combining the transport and in situ Raman studies of the field effect devices, a quantitative understanding is obtained of the phonon renormalization due to doping of graphene. Results are discussed in the light of time dependent perturbation theory, with electron phonon coupling parameter as an input from the density functional theory. It is seen that phonons near Γ and K points of the Brillouin zone are renormalized very differently by doping. Further, Γ-phonon renormalization is different in bilayer graphene as compared to single layer, originating from their different electronic band structures near the zone boundary K-point. Thus Raman spectroscopy is not only a powerful probe to characterize the number of layers and their quality in a graphene sample, but also to quantitatively evaluate electron phonon coupling required to understand the performance of graphene devices.

In this paper, our focus is on ABA trilayer graphene nanoribbon (TGN), in which the middle layer is horizontally shifted from the top and bottom layers. The conductance model of TGN as a FET channel is presented based on Landauer formula. Besides the good reported agreement with experimental study lending support to our model, the presented model demonstrates that minimum conductivity increases dramatically by temperature. It also draws parallels between TGN and bilayer graphene nanoribbon, in which similar thermal behavior is observed. Maxwell–Boltzmann approximation is employed to form the conductance of TGN near the neutrality point. Analytical model in degenerate regime in comparison with reported data proves that TGN-based transistor will operate in degenerate regime like what we expect in conventional semiconductors. Moreover, our model confirms that in similar condition, the conductivity of TGN is less than bilayer graphene nanoribbon as reported in some experiments.

A model of twisted bilayer graphene has been offered on the base of developed quasi-relativistic approach with high energy $k\cdot p$-Hamiltonian. Monolayer-graphene twist is accounted as a perturbation of monolayer-graphene Hamiltonian in such a way that at a given point of the Brillouin zone there exists an external non-Abelian gauge field of another monolayer. Majorana-like resonances have been revealed in the band structure of model at a magic rotation angle ${𝜃}_M=1.05^{\circ }$. The simulations have also shown that a superlattice energy gap existing at a rotation angle $1.08^{\circ }$ vanishes at a rotation angle $1.0^{\circ }$.