The Theoretical Introduction And Comparitive Study Of The Anomalous Hall Effect And The Spin Hall Effect

As we all know, Hall effect which found in the ninth centry is a general Electromagnetics effect in the conductive system. In the experiment, Hall effect is the physics foundation to type the carrier and measure the density. The thesis will discuss the anomolous Hall effect and the spin Hall effect which are modern extensions of classical Hall effect. Due to the importance and complication of the phemonema, people have developed some new conception and metheds to study it. And we will study several methods, and present a theoretical work of our own in the mesoscopic transport theory. Our aim is to provide a basis of the progress of the theory, by reviewing the discovery and history of the anomalous Hall effect and the spin Hall effect, discussion the advantages and disadvantages, equivalence, complementary between the theories.At the beginning of the first part, we reviewed the history of the theory of the Hall effect, and the theory to explain the phenomenon of anomolous Hall effect and spin Hall effect, and existing problems. Then, in the chapter 2, the Boltzmamn equation was introduced which is based on the semiclassical wave packet theory. In this theory, the electron is described a wave packet, so we just need to consider how wave packets evolve. Then, we focused on the recent progress of the semiclassical theory, the relationship between the anomalous Hall conductivity and the Berry curvature of the Bloch states in momentum space. There are an anomalous speed unrelated the external magnetic field, it contribute to the intrinsic source of transverse conductivity. Then, we introduced the regorous theories based on the complete quantum mechanism, like Linear response theory and Kubo-Streda formula. The final of this chapter, we discussed the equivalence between the semiclassical Boltzmamn equation and the Kubo-Streda formula in the application of the anomalous Hall effect. And we have found that the two different theory can obtain the same conclusion. In the chapter 3, we introduced some theory to interpret the spin Hall effect. In some studies relating spin hall effect several years ago, people have used the method based on keldysh nonequivalent Green function and the method based on Landauer-Buttikers scattering wave function separately to study the spin transport problems in the semiconductor system. But, we found there are no one compare the differences and similarities of the both theory. So, we compared the transport theories of the mesoscopic system. We provided a method that can deduce the non-equilibrium Green's function from Landauer-Buttiker's scattering wave function approach in non-interacting mesoscopic systems. We show that for non-interacting problems, these two equivalent tools are based on very different physical picture but can be complementary to each other in theoretical applications. Then, Finally, we summary the whole work, and give an outlook of some problem in the future study.