Local Density Of States And Spin Orbit Coupling Effects On Iron-based Superconductor Properties

Since the discovery of the high-temperature superconductivity in copper oxides, despite enormous unprecedented efforts by researchers all over the world, the physicalnature of high-temperature superconductivity in cuprates is still not completely understood. Recent discovery of high-temperature superconductivity in iron-based compounds has ignited a worldwide burst of activity. This is a new type of compounds with the critical temperature higher than McMillan limit besides the cuprates. There are important similarities between Fe-pnictides and cuprates. Both are layered systems, and both feature close proximity of antiferromagnetic order and superconductivity in their respective phase diagrams. But there are crucial differences as well. Fe-pnictide layers demand a multiband description from the start and the parent Fe-pnictides are semimetals with several electron and hole pockets on the Fermi surface.To understand the superconductivity of these materials it is essential to determine the superconducting pairing symmetry. Though extensive study have been carried out, experimental results on the pairing symmetry in Fe-based superconductors are still controversial. In this paper, we will consider the interband Coulomb repulsion influence on the AFM spin fluctuations, and explore the effect of the LDOS on the gap symmetry. Because the phonon linewidth is pro-portional to the imaginary part of the density-density response function, we propose a third possible phase sensitive method to detect the sign-reversal pairing in the Fe-based superconductors. As the spin fluctuations may play a major role in the superconductivity, it is essential to explore how these AFM orders develop in these materials. With this purpose, we also investigated effects of the spin-orbit coupling on magnetic and superconducting properties in iron-based superconductors.This thesis is consist of four parts as follows:In the first part, we reviewed the history of discovery of the iron-based superconductor at first, and then introduced the iron-based high-temperature superconducting materials and the results of experiments.In the second part, we gived the four structions of the recent discoveried iron-based superconductor:"1111" type system."122" type system,"111" type system,"11" type system, and at the same time we simply introduced the phase diagram, electron structure and magnetic structure of the iron-based superconductor.In the third part, we gived an advance to study the electron-electron couplings mediated by antiferromagnetic(AFM) spin fluctuation in Hubbard model.We first study the symmetry of the superconducting gap induced by the AFM fluctuation in the Fe-based compounds using two-gap model. We found that the superconducting gap symmetry shows an obvious different with different Fermi surface sheets nesting, and the gap node emergence is dependent on the local density of states(LDOS) of quasiparticles. This mechanism explains the controversial experiments results observed in the ARPES and some transport experiments. Secondly, to determinate the relative phase of the gap between different points on the Fermi surface, we propoused a new method to measure the phonon linewidth.In the forth part, we studied the SOC on the various magnetic orders observed in pnictides and the pairing symmetry in the iron-based superconductors. We found that our results can provide a self-consistent account of the diverse magnetic orders and different pairing symmetry which are discovered by experiments. We also calculate the LDOS of the vortex state. A remarkable resonant peak appears when the SOC interactions are considered. However, this resonant peak is absent without considering the SOC interaction. These results may be helpful to consistently understand the different experiment results.