The energy spectrum of a graphene sheet subject to a single barrier potential having a time periodic oscillating height and subject to a magnetic field is analyzed. The corresponding transmission is studied as function of the incident energy and potential parameters. Quantum interference within the oscillating barrier has an important effect on quasiparticles tunneling. In particular the timeperiodic electrostatic potential generates additional sidebands at energies ǫ + l ω (l = 0, ±1, · · · ) in the transmission probability originating from the photon absorption or emission within the oscillating barrier. Due to numerical difficulties in truncating the resulting coupled channel equations we limited ourselves to low quantum channels, i.e. l = 0, ±1.

We study the tunneling of Dirac fermions in graphene through a double barrier potential. This is allowing the carriers to have an effective mass inside the barrier as generated by a lattice missmatch with the boron nitride substrate. The consequences of this gap opening on the transmission are investigated and the realization of resonant tunneling conditions is analyzed.

Transmission probabilities of Dirac fermions in graphene under linear barrier potential oscillating in time are investigated. Solving Dirac equation we end up with the solutions of the energy spectrum depending on several modes coming from the oscillations. These will be used to obtain a transfer matrix that allows to determine transmission amplitudes of all modes. Due to numerical difficulties in truncating the resulting coupled channel equations, we limit ourselves to low quantum channels, i.e. l = 0, ±1, and study the three corresponding transmission probabilities.

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Using the energy spectrum of a system made of graphene subjected to a linear barrier potential, we study the Goos-Hänshen shifts. The calculation is done by first determining the corresponding phase shifts via the transmission and reflection probabilities. Numerical analysis shows that the Goos-Hänshen shifts depend strongly on the incident energy, barrier height and width, and vary positively or negatively under suitable conditions.

We study the effect of a magnetic field on Goos-Hänchen shifts in gaped graphene subjected to a double triangular barrier. Solving the wave equation separately in each region composing our system and using the required boundary conditions, we then compute explicitly the transmission probability for scattered fermions. These wavefunctions are then used to derive the Goos-Hänchen shifts in terms of different physical parameters such as energy, electrostatic potential strength and magnetic field. Our numerical results show that the Goos-Hänchen shifts are affected by the presence of the magnetic field and depend on the geometrical structure of the triangular barrier.

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.

We study the Goos-Hänchen shifts for Dirac fermions in graphene scattered by a triangular double barrier potential. The massless Dirac-like equation was used to describe the scattered fermions by such potential configuration. Our results show that the GHL shifts is affected by the geometrical structure of the double barrier. In particular the GHL shifts change sign at the transmission zero energies and exhibit enhanced peaks at each bound state associated with the double barrier when the incident angle is less than the critical angle associated with the total reflection.