Transmission in Graphene through Tilted Barrier in Laser Field

The transmission of Dirac fermions in graphene through a tilted barrier potential in the presence of a laser field of frequency ω is studied. By using Floquet theory, the Dirac equation is solved and then the energy spectrum is obtained. The boundary conditions together with the transfer matrix method allow to determine the transmission probabilities corresponding to all energy bands $E+l\hslash \omega$ $(l=0,\pm 1,\text{…})$. By limiting to the central band $l=0$ and the two first side bands $l=\pm 1$, it is shown that the transmissions are strongly affected by the laser field and barrier. Indeed, it is found that the Klein effect is still present, a variety of oscillations are inside the barrier, and there is essentially no transmission across all bands.