Goos-Hänchen Shifts in Gapped Graphene subject to External Fields

We study Dirac fermions in gapped graphene that are subjected to a magnetic field and a potential barrier harmonically oscillating in time. The tunneling modes inside the gap and the associated Goos-Hänchen (GH) shifts are analytically investigated. We show that the GH shifts in transmission for the central band and the first two sidebands change sign at the Dirac points $ε+l\hbar\tildeω$ $(l=0,\pm 1)$. We also find that the GH shifts can be either negative or positive and becomes zero at transmission resonances.

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