The Hartman effect in graphene systems

The present paper investigates that the tunneling time for bilayer graphene potential barrier with monolayer graphene leads to all range of energy. Numerical results reveal that parameters such as the incident energy and angle plays a significant role in inducing of the Hartman effect. In contrast to single-layer graphene, in the bilayer graphene, due to the chirality of quasi-particles induction of Klein and Hartman effects occur in the normal incidence case. Moreover, it is demonstrated that even for energy levels above barrier, the Hartman effect is present.