Zero, positive and negative quantum Goos-Hänchen shifts in graphene barrier with vertical magnetic field

We have explored the zero, positive and negative quantum Goos-Hänchen (GH) shifts of the transmitted Dirac carriers in graphene through a potential barrier with vertical magnetic field. Numerical results show that only one energy position at the zero GH shift exists and is highly dependent on the y-directional wave vector, the energy gap, the magnetic field and the potential. The positive and negative GH shifts happen when the incident energy is more and less than the energy position at the zero GH shift, respectively. In addition, we found that there are two values of potential at the zero GH shifts, where a potential window can always keep the positive GH shifts. These results may be useful in designing a graphene-based valley or spin splitter as well as manipulating the electrons and holes in graphene nanostructure.