The Study Of Quantum Topological Phase Transitions And Transport Properties Of Graphene Nanoribbon-Monolayer-bilayer Graphene Under A Perpendicular Magnetic Field

Graphene is a kind of two-dimensional materials of carbon honeycomb lattice. Graphene is important in condensed matter physics field due to it is the first truly two-dimensional materials which have many novel properties and wildly applications.In this thesis, first we introduce discovery of the graphene and then explain two important topological phases which includes Quantum Hall and Quantum spin Hall effect in graphene. Second we introduce the numerical method and use the tight-binding model to obtain the energy spectrum of the graphene nanoribbon, derive the definition of Green’s function.We focus on the of monolayer-bilayer graphene in a perpendicular magnetic field.Due to the unique structure of monolayer-bilayer graphene, the edge and interface states could be controlled by both interlayer potential and exchange field. We find that the Hall conductance in monolayer-bilayer graphene is not antisymmetric at the zero energy.When there is exchange field, monolayer region is in Quantum spin Hall phase and the weak-Quantum spin Hall phase is in bilayer region. However when there are the interlayer potential and the exchange field in the system, the system has a phase transition,in monolayer region the Quantum spin Hall phase translate into Quantum Hall phase,weak-Quantum spin Hall phase in bilayer region translate into Quantum spin Hall phase.There is a spin-polarized current at the interface when Quantum spin Hall and Quantum Hall phase coexist. We also justify that the Quantum spin Hall phase is still robust against the weak disorder even the time reversal symmetry is broken. In addition, via the local density of states we obtain the edge and interface state distribution.