Time-dependent Goos-H\"anchen Shifts in Gapped Graphene

Abstract

We study the Goos-H\"anchen (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 $l=\pm1$ change sign at the Dirac points $E=V+l\hbar\omega$. In particular the GH shifts inbtransmission 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. Klein tunneling, reflected by perfect transmission at normal incidence, is also preserved in the presence of an oscillating barrier.