Laser Assisted Dirac Electron in a Magnetized Annulus

We study the behaviour of a charge bound on a graphene annulus under the assump- tion that the particle can be treated as a massless Dirac electron. The eigenstates and relative en- ergy are found in closed analytical form. Subsequently, we consider a large annulus with radius ρ ∈ [5000, 10,000]a0 in the presence of a static magnetic field orthogonal to its plane and again the eigenstates and eigenenergies of the Dirac electron are found in both analytical and numerical form. The possibility of designing filiform currents by controlling the orbital angular momentum and the magnetic field is shown. The currents can be of interest in optoelectronic devices that are controlled by electromagnetic radiation. Moreover, a small radial force acts upon the annulus with a stretching effect. A linearly polarized electromagnetic field propagating in the orthogonal direction is added; the time evolution of the operators show that the acceleration of the electron is proportional to the rate of change of the spin of the particle.