Electronic Transport In Mesoscopic Systems And Raman Dynamic Properties In The Spin 1/2 XXZ Model

In recent years,topological insulator,spin current and the transport properties of related materials been fully studied and developed,provide theoretical support for the manufacture of related electronic devices.In turn,it provides experimental support for these theories.We define some fundamental physical quantites in the mesoscopic sys-tem,and give the microscopic explanation of conductance of two-dimensional nanode-vices,finally generalize to the tight-binding model through the scattering matrix.The passage is divided into three parts.First,in the case of considering the next-nearest neighbor hopping energy,we employ the concept of the bond charge current and give the local current profile,qualitatively explain the oscillation of conductance curve.Sec-ond,the geometric nature of Berry phase is expounded in detail,and prove Berry phase is a local gauge invariant quantity.We calculate the electron anomalous velocity related to the Berry curvature,and discuss spin quantum Hall effect and irregular quantum Hall effect in graphene and silicene.The staggered potential in silicene destroy the valley symmetry where the electrons can move from a conduction band at K to a valence band at K',that is the valley polarized metal phase in silicene.The inhomogeneity of spin or-bit coupling in Rashba produces spin current,especially in the interval where it changes drastically spin vortex appears.Third,we connect the solvable lattice model in statistical mechanics with the theory of quantum affine algebra.The one dimensional Heisenberg spin 1/2 XXZ model is equivalent to the six vertex angle model,a rigorous solution is also given,and solve the zero frequency and non-zero frequency Raman dynamic properties.