The Hartman effect in graphene

We investigate theoretically the Hartman effect in quantum tunneling through single and double barriers in a single graphene layer. The numerical results indicate that the Hartman effect in graphene depends heavily on the incident angle and the energy of the carrier in the tunneling process through single and double barriers. We find that the Hartman effect disappears for normal incidence and appears when the incident angle and energy are larger than some critical values.