Localized Magnetic States In Two-dimensional Semi-dirac Systems

Dirac point is a very important character in the newly discovered materials,and plays a role in the various properties.By changing the band parameters,the Dirac points can move,and even merge into single one,which leads to a number of unusual properties.Recently,such a merging transition has been realized in organic conductors?-(BEDT-TTF)2I3 and artificial cold-atom lattices,as well as in artificially assembled nanostructures.In this thesis,we study the localized magnetic states across the merging transition of Dirac points in two dimensions.The main results are summarized as follows:1.We incorporate an effective Hamiltonian,which describes the merging transition of Dirac points.By means of the diagonalization of Hamiltonian,we obtain the dispersion relation being linear along one direction and parabolic along the other.On this basis,we introduce an impurity in the system,which can be described by the Anderson localization theory.2.In order to study the localized magnetic states of adsorbed impurities,the retarded Green's functions are introduced.By using the equation of motion method,the Green's function can be derived,which imaginary part gives the density of states for the impurity energy level.By making the integral for the density of state,we get the occupation number of the spin sates of the impurity.It is found that when the merging parameter ?=0,where the two Dirac points merge into single one,the boundary between the magnetic and nonmagnetic impurity states is unsymmetric about the parameter y=0.5,which is in consistent with the previous results.For ??0,the merging transition of Dirac points brings about a significant modification for the impurity self-energy,thus has an important effect on the magnetic state of the impurity.At ?<0,the two Dirac points remain separated from each other.With decreasing the impurity level ?0 from ?0>|?|,the impurity magnetization region shrinks,and reaches minimum at ?0=|?|.Continuing to diminish ?0,the impurity magnetization region will grow.In contrast,at ?>0,the impurity magnetization region exhibits a different behavior,i.e.,the impurity magnetization region always decay with decreasing the impurity level ?0.These phenomena can be understood from the change on density of state across the merging transition of Dirac points.The magnetic moment and the corresponding magnetic transition of the impurity in this system are also investigated.