Quantum resonant tunneling behaviors of double-barrier structures on graphene are investigated under the tightbinding approximation. The Klein tunneling and resonant tunneling are demonstrated for the quasiparticles with energy close to the Dirac points. The Klein tunneling vanishes by increasing the height of the potential barriers to more than 300 meV. The Dirac transport properties continuously change to the Schro¨dinger ones. It is found that the peaks of resonant tunneling approximate to the eigen-levels of graphene nanoribbons under appropriate boundary conditions. A comparison between the zigzag- and armchair-edge barriers is given.
Based on the scattering matrix approach.we systematically investigate the anharmonic effect of the pumped current in double-barrier strructures with adiabatic time-modulation of two sinusoidal AC driven potential heights. The pumped currem as a functionof the pha.se difference bet ween the two driven potentials looks like to be sinusoidal, but actually it contains sine functions of double and more phase difference, it is found that this kind of anharmonic effect of the pumped current is determined combinedly by the Berry curvature and parameter va.riation loop trajectory. Therefore small ratio of the driving amplitude and the static amplitude is not necessary for harmonic pattern in the pmnped era＇rent, to dominate for smooth Berry curvatureon the surface within the parameter variation loop.
In the adiabatic and weak-modulation quantum pump, net electron flow is driven from one reservoir to another by absorbing or emitting an energy quantum nω from or to the reservoirs. This paper considers high-order dependence of the scattering matrix on the time. Non-sinusoidal behaviour of strong pumping is revealed. The relation between the pumped current and the ac driving amplitude varies from power of 2, 1 to 1/2 when stronger modulation is exerted. Open experimental observation can be interpreted by multi-energy-quantum-related processes.
