Quantum Chaotic Scattering In Bilayer Graphene

Quantum transport of open mesoscopic system is one of the most active areas in the past few decades. Recent experiments found that graphene exhibits many unusual electronic transport properties, for example the low energy electron or hole around the Dirac point can be described by the Dirac equation. Because of its high electron mobility at the room temperature, graphene has attracted much attention and is expected to lead an information technology revolution.Because the bilayer graphene(BLG) and single layer graphene(SLG) have wide application prospects in micro-nano-electronics and spintronics devices, there has extensive focus on electronic and spin transport properties. This dissertation carries research along this line and investigates SLG and BLG’s electronic and spin transport properties in various physical applications’ s aspects.In the ?rst chapter, we introduce the lattice structure and electronic properties of SLG and BLG. And we give an introduction about the unique physical properties in SLG and BLG, such as quantum hall effect, chiral tunneling, and the minimal conductivity. The dissertation mainly concerns that how the unique properties of SLG and BLG affect its transport properties.In the second chapter, we give a detailed introduction of the method used in this work: nonequilibrium Green’s function theory(NEGF) and LandauerBüttiker formula. Particularly, we introduce the method of how to utilize NEGF dealing with the mesoscopic transport problems. In accordance with our system,the matrix form of Green’s function is provided. These are our main methods used to investigate on SLG and BLG’s electronic and spin transport properties.In the third chapter, we investigate the transport ?uctuations in both nonrelativistic quantum dots and BLG dots with mixed, chaotic, and intermediate scattering dynamics in the classical limit. The main purpose of the work is to determine whether ?nite mass effect in BLG dots can eliminate the sharp conductance ?uctuations, as compared with previous results on SLG. We have still observed sharp conductance ?uctuations in the BLG chaotic quantum dots’ s conductance spectrum. The signatures of abrupt conductance variations indicating that the mass has little effect on relativistic quantum transport. An interesting phenomenon is that, when traveling along the classical ballistic orbit,the quasi-particle tends to hop back and forth between the two layers, exhibiting a Zitterbewegung-like effect. This means that conductance ?uctuations are characteristically greatly enhanced in relativistic quantum systems, regardless of whether the quasi-particle is massless or massive.In the fourth chapter, we investigate the quantum tunneling of electron in an AB-stacked BLG in?uenced by external potential for simulating quantum point contacts, which is an indispensable component in mesoscopic physics. The calculations show that chiral tunneling of an electron in bilayer graphene under con?nement potential tends to go through an elevated potential path, that have absolutely no counterpart in non-relativistic quantum systems. Due to BLG’s symmetry of the group D3 dof lattice structure, the patterns of the local density of states and the local electron current also demonstrate symmetry in the spatial distribution. Chiral tunneling of an electron can lead to an extreme type of fractal-like conductance ?uctuations, not seen previously in 2D electron gas(2DEG). The results in this chapter may play an instructive role for designing quantum point contracts based on BLG.In the ?fth chapter, we study the charge conduction and transport of spin polarization in the ferromagnetic single layer graphene junction in the presence Rashba’s and intrinsic spin orbit coupling, respectively. We ?nd that as the strength of the spin orbit coupling increases, an obvious degradation occurs in spin polarization, regardless of whether the spin orbit coupling is Rashba’s or intrinsic. The spin polarization and spin resolved conductances show oscillation with Rashba’s spin orbit coupling in the ferromagnetic single layer graphene junction. These phenomena indicate that ferromagnetic exchange ?eld and spin orbit coupling are a pair of competitive factors in spin polarization. This result implies the development of ferromagnetic single layer graphene based spin ?lter which require stable spin polarization properties.The last chapter gives a conclusion of this dissertation and some prospects for the future works in this ?eld.