Quantum Manipulation Of Topological Phase In Monolayer And Bilayer Graphene

Graphene has unusual honeycomb geometry and electron transport property,where the electrons in the vicinity of zero energy exhibit a linear dispersion relation and gapless band structure.In this paper,we introduce the geometry of graphene,the physical properties,preparation method and application prospects.We also introduce the model and the research method.Based on the tight-binding model and Green function method,we systematically investigate the the energy structure and the electronic transport properties of graphene under external fields.We investigate the electronic states of a zigzag graphene nanoribbon in the presence of mutually perpendicular electric and magnetic fields.We find that both edge and bulk states are localized in the vicinity of zero energy,leading to spin-polarized states and quantized transport in the system.A quantum spin Hall(QSH)phase is characterized by helical edge and tilted bulk states.By tuning Fermi energy and in-plane electric field,a topological phase transition is also realized.The electronic states support the transport of spin and charge,and the corresponding spin and charge Hall conductivities are calculated in a four-terminal geometry.We further study electronic properties of zigzag-edged graphene nanoribbons engineered by the edge potential.The system exhibits both quantum valley Hall phase(QVH)and single-edge QVH phase due to spatial-inversion symmetry breaking driven by staggered sublattice potential and edge potential.Considering the spin-orbit interaction,we find that these edge modes are helical with respect to their valley and spin indexes,thus the system can host both the QVH phase and the QSH phase.We expect that these results may have important application in spintronic and valleytronic devices.