Related papers: Electronic states in a bilayer graphene quantum ri…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed…
We consider the quantum mechanics of a spinless charged particle on a 2-dimensional sphere. When threaded with a magnetic monopole field, this is the well-known Haldane sphere that furnishes a translationally-invariant, incompressible…
Electronic localization is numerically studied in disordered bilayer graphene with an electric-field induced energy gap. Bilayer graphene is a zero-gap semiconductor, in which an energy gap can be opened and controlled by an external…
We study the properties of a two-dimensional non-relativistic electron gas (TDEG) constrained on wires along a M\"{o}bius strip. We considered wires around the strip and along the transverse direction, across the width of the strip. For…
The evolution of $N$ spin-$1/2$ system with all-range Ising-type interaction is considered. For this system we study the entanglement of one spin with the rest spins. It is shown that the entanglement depends on the amount of spins and the…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
A parabolic quantum dot (QD) as realized by biasing nanostructured gates on bilayer graphene is investigated in the presence of electron-electron interaction. The energy spectrum and the phase diagram reveal unexpected transitions as…
Symmetry breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the…
We show that characteristics of the electron's form factor in two-dimensional materials are observable in quasiparticle interference (QPI) spectrum. We study QPI in twisted bilayer graphene using real-space tight-binding calculations…
It is shown that the quantum ground state energy of particle of mass m and electric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E_0=eB/2m. Remarkably, this formula is…
Electronic properties of triangular and hexagonal nano-scale quantum dots (QDs) of Silicene and bilayer graphene are studied. It is shown that the low-energy edge-localized electronic states, existing within the size-quantized gap are…
Rotated graphene bilayers form an exotic class of nanomaterials with fascinating electronic properties governed by the rotation angle theta. For large rotation angles, the electron eigenstates are restricted to one layer and the bilayer…
Dirac fermions interacting with a cylindrically symmetric quantum dot potential created in single and bilayer graphene are not confined but form quasi-bound states. The broadening of these quasi-bound states (i. e. the inverse of their…
In a Bernal-stacked graphene bilayer, an electronic state in Landau level $% N=0$ is described by its guiding-center index $X$ (in the Landau gauge) and by its valley, spin, and orbital indices $\xi =\pm K,\sigma =\pm 1,$ and $% n=0,1.$…
Topological properties of electronic states in multivalley two-dimensional materials, such as mono- and bilayer graphene, or thin films of rhombohedral graphite, give rise to various unusual magneto-transport regimes. Here, we investigate…
In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we…
Metal/graphene interfaces generated by electrode deposition induce barriers or potential modulations influencing the electronic transport properties of graphene based devices. However, their impact on the local mechanical properties of…
The tunability of binding energies is explored by modulating a finite dielectric slab width in a planar, three dielectric system. After verifying the equivalence of the field method and method of images, three different configurations are…
We propose a model of spin-polarized-current state for electrons in bilayer graphene. The model resolves the puzzles as revealed by experiments that (a) the energy gap $E_{\rm gap}$ of the insulating ground state at the charge neutrality…