Guided modes and quantum Goos–Hänchen shift in graphene waveguide: Influence of a velocity barrier

The influence of velocity on the guided modes, localized current density inside the channel and the Goos–Hänchen shift at the interface of graphene waveguide in the presence of a velocity barrier is investigated theoretically. It is found that each guided mode has a cutoff velocity determining the appearance of the oscillating wave mode and the velocity in the barrier regions can control the number of guided modes and the distribution of localized current density inside the channel. The number of guided modes and the conduction of graphene waveguide along the channel present a quantized feature for velocity. Finally, it is also indicated that the Goos–Hänchen shift at the interface of graphene waveguide can be well controlled by changing the velocity in barrier region.