Quantum Tunneling Transport Properties Of An Electron In Graphene

Recently, graphene as a promising material for electron device has received great attentions. The electron in graphene has special energy band structure, which can lead to unique transport properties. In this thesis, we study the quantum tunneling time of electron transport in2-dimensional graphene. We first consider the system of monolayer grapheme covered by a rectangular potential barrier and imposed a small perpendicular magnetic field on the barrier region. With the help of electron-spin coherent state, we use its Larmor precession in magnetic barrier as a clock to define a tunneling Lamor time passing through a rectangular barrier. It is shown that this tunneling time is equal to the dwell time. With the increasing of incident angle of electron, the wave functiong in barrier changes from oscillating mode to evanescent mode. When the wave function in barrier is an oscillating mode, the curve of tunneling-time against the barrier-width oscillates around an increasing average-line. While for the wave function of an evanescent mode, the tunneling time is independent of the barrier width and the Hartman effect occurs. In particular, the tunneling time for Klein tunneling just equals the potential barrier width divided by the Fermi velocity. Then we investigate the quantum tunneling time of a Dirac electron through double rectangular potential-barriers in monolayer graphene and discuss the tunneling time varies with the width of the potential barrier and the potential well. It is shown that the changes of the larmor time with the barrier width is almost consistent with the case through the single barrier except the each peak tunneling time for oscilating mode is split into two parts due to the interference of wave function in potential well. The tunneling time against the well-width shows the form of periodic oscillation. The period becomes long with the increasing the incident angle. When the Klein tunneling occurs, the tunneling time just equals the two barrier width divided by the Fermi velocity but is independent on the the width of potential well. Finally, we consider the influence of the vector potential A of magnetic field on the tunneling process. It is found that regardless of the incident angle the wave function still is the evanescent mode in potential berrier region and Klein tunneling does not occur. The tunneling time is independent of the barrier width showing the Hartman effect.