Transmissions in Graphene through Double Barriers and Periodic Potential

Abstract: 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 on quasi-particles tunneling. A combination of both a time dependent potential and a magnetic field generate physical states whose energy is double quantified by the pair of integers $(n, l)$ with high degeneracy. The large number of modes that exist in the energy spectrum presents a colossal difficulty in numerical computations. Thus we were obliged to make a truncation and limit ourselves to the central $(n = 0)$ and two adjacent side band ($n=\pm 1$).