Electronic State And Quantum Transport In Graphene

This dissertation consists of three parts.(1) Based on the tight-binding model, we analytically investigate the electronic state andenergy band of graphene, such as the zigzag nanoribbons, armchair nanoribbons, semi-infinitenanoribbons and the limited graphene. To the zigzag nanoribbons, we deduce the accurateranges of infinite direction wave vector and energy of the edge state, and we discuss thetransition point between the edge state and the standing wave state. To the limited graphene, itis found that there are only two kinds of electronic states, i.e., the standing wave state andedge state. For the standing wave state, the wave function is in the form of sine function intwo directions; for the edge state, the wave function is in the form of hyperbolic sine functionin the direction of armchair boundary and in the form of sine function in the direction ofzigzag boundary. When the width of two restricted boundary goes into infinity, the result ofthe limited graphene tends to that in the infinity case.(2) Quantum resonant tunneling behaviors of double-barrier structures on graphene areinvestigated under the tight-binding approximation. The Klein tunneling and resonanttunneling are demonstrated for the quasiparticles with energy close to the Dirac points. TheKlein tunneling vanishes by increasing the height of the potential barriers to more than300meV. The Dirac transport properties continuously change to the Schrodinger ones. It is foundthat the peaks of resonant tunneling approximate to the eigen-levels of graphene nanoribbonsunder appropriate boundary conditions. Compared to the low barriers, the conductance withhigh-barrier can be significantly increased due to the contribution from more resonant levels.(3) Based on the scattering matrix approach, we systematically investigate theanharmonic effect of the pumped current in double-barrier structures with adiabatictime-modulation of two sinusoidal AC driven potential heights. The pumped current as afunction of the phase difference between the two driven potentials looks like to be sinusoidal,but actually it contains sine functions of double and more phase difference. It is found thatthis kind of anharmonic effect of the pumped current is determined combinedly by the Berry curvature and parameter variation loop trajectory. So the harmonic pattern is dominated bysmooth Berry curvature on the surface within the parameter variation loop.