Transmission in graphene through tilted barrier in laser field

We study the transmission of Dirac fermions in graphene through a tilted barrier potential in the presence of a laser field of frequency $\omega$. By using Floquet theory, we solve the Dirac equation and then obtain the energy spectrum. The boundary conditions together with the transfer matrix method allow us to determine the transmission probabilities corresponding to all energy bands $E+l\hbar\omega$ $(l=0,\pm1, \cdots)$. By limiting to the central band $l=0$ and the two first side bands $l=\pm 1$, we show 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.