Related papers: Why Dirac points in graphene are where they are?
Dirac points are found to emerge due to the crossing of bands in the electronic structure of bilayer graphene for configurations in which the alignment between two hexagonal lattices preserves the parallelism of the armchair/zigzag lines…
We present the results of the symmetry classification of the electron energy bands in graphene and silicene using group theory algebra and the tight--binding approximation. The analysis is performed both in the absence and in the presence…
We study the band structure of graphene's Dirac-Weyl quasi-particles in a one-dimensional magnetic superlattice formed by a periodic sequence of alternating magnetic barriers. The spectrum and the nature of the states strongly depend on the…
When two graphene layers are rotated from AA or AB configuration by a small angle, the band structure changes dramatically. Numerical calculations have shown that, at certain discrete angles called magic angles, the low energy bands become…
The energy spectra for the tight-binding models on the Lieb and kagom\'e lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band…
We analyze the energy spectrum of graphene in the presence of spin-orbit coupling and a unidirectionally periodic Zeeman field, focusing on the stability and location of Dirac points it may support. It is found that the Dirac points at the…
General properties of long wavelength triangular graphene superlattice are studied. It is shown that Dirac points with and without gaps can arise at a number of high symmetry points of the Brillouin Zone. The existence of gaps can lead to…
We develop a diagrammatic perturbation theory to account for the emergence of moir\'e bands in the continuum model of twisted bilayer graphene. Our framework is build upon treating the moir\'e potential as a perturbation that transfers…
Energy band structure of the bilayer graphene superlattices with $\delta$-function magnetic barriers and zero average magnetic flux is studied within the four-band continuum model, using the transfer matrix method. The periodic magnetic…
We study characteristic band structures of the fermions on a square kagome lattice, one of the two-dimensional lattices hosting a corner-sharing network of triangles. We show that the band structures of the nearest-neighbor tight-binding…
By means of atomistic tight-binding calculations, we investigate the transport properties of vertical devices made of two incommensurately misoriented graphene layers. With a chosen transport direction (Ox-axis), we define two classes of…
In this article, we show that, in the dissociation regime and under a non-degeneracy assumption, the reduced Hartree-Fock theory of graphene presents Dirac points at the vertices of the first Brillouin zone and that the Fermi level is…
We propose that the strain induced effective pseudo-magnetic field in graphene can also be explained by a curl movement of the Dirac points, if the Dirac points can be regarded as a slowly varying function of position. We also prove that…
In the present work, we give a phenomenological theory of the monolayer graphene where two worlds quantum and classical meet together and complete each other in the most natural way. It appears that the graphene is the unique material where…
We study the electronic structure of two Dirac electron gazes coupled by a periodic Hamiltonian such as it appears in rotated graphene bilayers. Ab initio and tight-binding approaches are combined and show that the spatially periodic…
We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical…
The tight-binding model of electrons in graphene is reviewed. We derive low-energy Hamiltonians supporting massless Dirac-like chiral fermions and massive chiral fermions in monolayer and bilayer graphene, respectively, and we describe how…
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…
We emphasize that there exist four Dirac-type points in the electron-energy spectrum of a graphite bilayer near the point K of its Brillouin zone. One of the Dirac points is at the point K, and three Dirac points lie nearby. Each of these…
We present a symmetry analysis of the trigonal band structure in graphene, elucidating the transformational properties of the underlying basis functions and the crucial role of time-reversal invariance. Group theory is used to derive an…