Dirac Donor Statesin Graphene Controlled By Magnetic Field With Giant Rashba Splitting

With the boom of Dirac materials, like graphene and topological insulators, researches on relativistic quasiparticles have become an important part in condensed matter physics. The novel electronic properties give Dirac materials a great perspective in electronic and photonic applications, which makes the studies of Dirac-like quasiparticles’ quantum states or impurity states in extra electromagnetic fields very important. Traditional numerical methods for solving Schr?dinger equations could be adjusted to fit the new systems of Dirac-like equations.Furthermore, the discovery of giant Rashba effects induced by some kinds of transition metal substrates have promoted researches in graphene spintronic, as the intrinsic spin-orbit interactions in graphene is very small. The introduction of spin degree of freedom leads to an interesting modified quasiparticle effective Hamiltonian with both pseudospin and spin in it. Studies on quantum propertiesof these quasiparticles are meaningful.This thesis focus on the properties of donor states in a monolayer graphene with giant Rashba spin-orbit coupling and control effects of a perpendicular homogenous magnetic field, using a numerical method. Energy states and corresponding wave functions of quasiparticles have being calculated under different magnetic strength, SOI strength and effective coulomb strength. Competition of these parameters has been observed in controlling impurity states.Anti-cross of energy levels with same total angular momentum has been confirmed. By calculating the mean value of spin, the spin polarization has been found to exchange every time the energy states anti-cross.This discussion of controlling spin polarization of graphene donor states by magnetic fieldsmay be helpful in graphene spintronic.A numerical method for first order linear ODEs systems is used in this thesis based on the main ideas of a series expression method for second order ODEs of our research group. The method processes problems in all-matrices approach and is proper for many kinds of Dirac-like equations. In the thesis, the algorithm is showed in details, and floating-point errors is analyzed.