Related papers: Magnetic field barriers in graphene: an analytical…
Electronic properties of the graphene layer sandwiched between two hexagonal boron nitride sheets have been studied using the first-principles calculations and the minimal tight-binding model. It is shown that for the ABC-stacked structure…
We derive semiclassical quantization equations for graphene mono- and bilayer systems where the excitations are confined by the applied inhomogeneous magnetic field. The importance of a semiclassical phase, a consequence of the spinor…
In this review we focus on the effect of the Dirac nature of graphene quasiparticles on two separate aspects. The first of these involves transport across superconducting graphene junctions with barriers of thickness $d_0$ and arbitrary…
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…
Undistorted monolayer graphene has energy bands which cross at protected Dirac points. It elastically deforms and much research has assumed the Dirac description persists, now in a curved space and coupled to a gauge field related to…
Much attention has been focused on ways of rendering graphene semiconducting. We study periodically gated graphene in a tight-binding model and find that, contrary to predictions based on the Dirac equation, it is possible to open a band…
In this paper, we study a theoretical method to calculate the conductance across a square barrier potential in monolayer graphene. We have obtained an analytical expression for the transmission coefficient across a potential barrier for…
We analyze spectral properties of a quantum graph in the form of a ring chain with a $\delta$ coupling in the vertices exposed to a homogeneous magnetic field perpendicular to the graph plane. We find the band spectrum in the case when the…
The spurious states found in numerical implementations of envelope function models for semiconductor heterostructures and nanostructures have been shown to be readily removed by employing a first-order difference scheme. This approach is…
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…
Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional electron systems and, ultimately, create materials with tailored electronic properties. Previously, it proved difficult to…
Single-layer graphenes subject to periodic lateral strains are artificial crystals that can support boundary spectra with an intrinsic polarity. These are analyzed by comparing the effects of periodic magnetic fields and strain-induced…
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 $\pi$ electron Hamiltonian and gives, in particular, a closed analytic expression…
The unusual transport properties of graphene are the direct consequence of a peculiar bandstructure near the Dirac point. We determine the shape of the pi bands and their characteristic splitting, and the transition from a pure 2D to…
Magnetic fields are often used for characterizing transport in nanoscale materials. Recent magnetotransport experiments have demonstrated that ballistic transport is possible in graphene antidot lattices (GALs). These experiments have…
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…
We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively…
The presence of periodic modulation in graphene leads to a reconstruction of the band structure and formation of minibands. In an external uniform magnetic field, a fractal energy spectrum called Hofstadter butterfly is formed. Particularly…
Transmission of Dirac fermions through a chip of graphene under the effect of magnetic field and a time vibrating double barrier with frequency $w$ is investigated. Quantum interference within the oscillating barrier has an important effect…
The spectrum of magnetic edge states and their transport properties in the presence of a perpendicular non-homogeneous magnetic field in a quantum wire formed by a parabolic confining potential are obtained. Systems are studied where the…