Related papers: WKB energy levels in gapped graphene under crossed…
First-principles density functional calculations for graphene and defected graphene are used to examine when the quasi-2D electrons near the Fermi energy in graphene could be represented by massless fermions obeying a Dirac-Weyl (DW)…
The present study explores the edge states in a finite-width graphene ribbon and a semi-infinite geometry subject to a perpendicular magnetic field and an in-plane electric field, applied perpendicular to a zigzag edge. To accomplish this,…
We consider massless Dirac fermions in a graphene monolayer subject to both a perpendicular magnetic field $B$ and a proximity-induced pairing gap $\Delta$. When the chemical potential is at the Dirac point, our exact solution of the…
We study the Landau level spectrum of bulk graphene monolayers beyond the Dirac Hamiltonian with linear dispersion. We consider an effective Wannier-like tight-binding model obtained from ab initio calculations, that includes long-range…
In this work we derive a WKB expansion for the electromagnetic fields solution of the time-harmonic Maxwell equations set in a domain with a thin layer. As a by-product of this expansion we obtain new second order asymptotic models with…
Graphene is a recently discovered carbon based material with unique physical properties. This is a monolayer of graphite, and the two-dimensional electrons and holes in it are described by the effective Dirac equation with a vanishing…
The nonlinear magneto-optic responses are investigated for gapped graphene and doped graphene in a perpendicular magnetic field. The electronic states are described by Landau levels, and the electron dynamics in an optical field is obtained…
The results of the development of an approximate approach, which can be considered as an analogue of the WKB method, are presented. This approach gives possibility to divide the electromagnetic field in structured waveguides into forward…
The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schr\"odinger…
We obtain analytical expressions for the eigenstates and the Landau level spectrum of biased graphene bilayers in a magnetic field. The calculations are performed in the context of a four-band continuum model and generalize previous…
In the presence of strong magnetic fields the electronic bandstructure of graphene drastically changes. The Dirac cone collapses into discrete non-equidistant Landau levels, which can be externally tuned by changing the magnetic field. In…
We study the problem of Dirac fermion confinement in graphene in the presence of a perpendicular magnetic field B. We show, analytically and numerically, that confinement leads to anomalies in the electronic spectrum and to a magnetic field…
The reflectance of graphene is investigated in the framework of the Dirac model with account of its realistic properties, such as nonzero chemical potential and band gap, at any temperature. For this purpose, the exact reflection…
Broken symmetry states in bilayer graphene in perpendicular electric $E_\perp$ and in-plane magnetic $B_\parallel$ fields are studied in the presence of the dynamically screened long-range Coulomb interaction and the symmetry-breaking…
In this paper, we will construct the coherent states for a Dirac electron in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene surface. First of all, we will identify the appropriate annihilation…
In the framework of the deformed quantum mechanics with minimal length, we consider the motion of a non-relativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function…
We show that the twisted graphene bilayer can reveal unusual topological properties at low energies, as a consequence of a Dirac-point splitting. These features rely on a symmetry analysis of the electron hopping between the two layers of…
In this work, we investigate the massive Kane-Mele model for graphene in the presence of disclination and an external magnetic field, where graphene behaviors as a topological insulator. In the low-energy limit, the effective field equation…
We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a…
A two-dimensional periodic array of scatterers has been introduced to a single layer of graphene in the presence of an external magnetic field perpendicular to the graphene layer. The eigenvalue equation for such a system has been solved…