Perfect transmission of the ultrarelativistic quasielectrons in pristine graphene

Abstract

Within the framework of the Landauer-Buttiker formalism, the conductivity of one- and two-barrier graphene structures is calculated. The conditions for formation of the maximum value of the conductivity depending on the energy of ultrarelativistic quasielectrons as well as on the parameters of these structures (the values of Fermi velocity in different regions and the potential barriers height) are analyzed. It is believed that there is an electrostatic barrier and also the Fermi velocity barrier due to the fact that this quantity may aсquire different values in the barrier and out-of-barrier regions of the considered structures. The obtained expression for the transmission rates accounts for the π phase change of the transmitted wave function (which was not taken into consideration in the known formulae for the transmission rates of some papers). Consideration of this phase change leads to some new important features which characterize the transmission process in the graphene structures. We are the first to show that the effect of the supertunnelling manifests itself in graphene and it is observed both in the dependences of the transmission rates and of the conductivity on the quasielectron energy. This effect consists in the fact that, under certain conditions, the transmission through the structure is perfect (transmission rates T = 1) for the arbitrary angle of incidence of quasielectrons on the barrier. The expression іs given that determines the specified conditions for the supertunneling. The analysis of the transmission dependence on the problem parameters is also provided. • All-angled perfect tunneling can be observed in the graphene-based single barrier resonant-tunneling structure. • This type of tunneling significantly affects the conductivity of the given structure. • The analogous effect manifests itself also in the graphene based double barrier resonant-tunneling structure.