We study the energy levels of graphene magnetic circular quantum dot surrounded by an infinite graphene sheet in the presence of an electrostatic potential. We solve Dirac equation to derive the solutions of energy spectrum associated with different regions composing our system. Using the continuum model and applying boundary conditions at the interface, we obtain analytical results for the energy levels. The dependence of the energy levels on the quantum dot radius, magnetic field and electrostatic potential is analyzed for the two valleys K and ¢ K . We show that the energy levels exhibit characteristics of interface states and have an energy gap.

We study the Goos-Hänchen (GH) shifts for transmitted Dirac fermions in gapped graphene through a single barrier structure having a time periodic oscillating component. Our analysis shows that the GH shifts in transmission for central band l = 0 and two first sidebands l = ±1 change sign at the Dirac points E = V + l ω. In particular the GH shifts in transmission exhibit enhanced peaks at each bound state associated with the single barrier when the incident angle is less than the critical angle associated with total reflection.

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We study the propagation of electrons in a circular quantum dot of gapped graphene subject to the magnetic flux ϕ. We present analytical expressions for the eigenstates, scattering coefficients, scattering efficiency and radial component of the reflected current. We identify different scattering regimes as a function of the physical parameters such as the incident electronic energy, potential barrier, radius of quantum dot, gap and ϕ. We choose two values of the flux ϕ = 1/2, 3/2 and show that for low energy of the incident electron, the scattering resonances appear and the far-field scattered current presents distinct preferred scattering directions.

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