Klein tunneling through the trapezoidal potential barrier in graphene: conductance and shot noise

When a single-layer graphene sheet is contacted with metallic electrodes, tunnel barriers are formed as a result of the doping of graphene by the metal in the contact region. If the Fermi energy level is modulated by a gate voltage, the phenomenon of Klein tunneling results in specific features in the conductance and noise. Here we obtain analytically exact solutions for the transmission and reflection probability amplitudes using a trapezoidal potential barrier, allowing us to calculate the differential conductance and the Fano factor for a graphene sheet in the ballistic regime. We put in evidence an unexpected global symmetry—the transmission probability is the same for energies symmetric with respect to half of the barrier height. We outline a proposal for the experimental verification of these ideas using realistic sample parameters. (paper)