Theoretical Investigations Of The FFLO State, The Spin Excitations And The Superconducting Pairing In Unconventional Superconductors

This paper is organized as follows:In section I, we introduce the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) un-conventional superconductors firstly. Because an unambiguous experimental demon-stration of the FFLO state is hindered by the stringent requirements for its realization. Based on the theories of the mean-field by self-consistently solving Bogoliubov-de Gennes(BdG) equations, we study theoretically the relationship between the magnetic frustration and the emergence of the FFLO state on a triangular lattice. We find that the required lower critical magnetic field to enter the FFLO state decreases with the increase of both the anisotropic ratio and the on-site Coulomb repulsive interaction and at the effect of impurities, the FFLO state is stable at a large anisotropic ratio. These results demonstrate that it is easier to enter the FFLO state on the structurally frustrated triangular lattice in comparison with the square lattice, and suggest that the layered or-ganic superconductors with a triangular lattice and/or under an appropriate hydrostatic pressure may be good candidates for exploring the FFLO state.In section II, the effects of magnetic vortices and nonmagnetic impurities on the low energy quasiparticle excitations and the spin-lattice relaxation rate are examined in the iron-based superconductors for the s±-, s-and d-wave pairing symmetries, respec-tively. The main effect of the vortices is to enhance the quasiparticle excitations and the spin-lattice relaxation rate for all symmetries, and leads to a T3dependence of the re-laxation rate followed by a nearly T-linearity at lower temperatures. This enhancement can only be seen for the s±-and d-wave symmetries in the presence of nonmagnetic impurities. These results suggest that the s±-wave and d-wave pairing states behave similarly in response to the magnetic field and nonmagnetic impurities, therefore it may be impossible to distinguish them on the basis of the measurements of spin-lattice relaxation rates when a magnetic field and/or impurity scatterings are present.In section Ⅲ, we investigate the band renormalization, FS reconstruction and the symmetry of the superconducting gap in KyFe2-xSe2iron-based superconductors using a five-orbital model. We have found that the most favorable superconducting pairing symmetry mediated by the spin fluctuations is the dx2-y2-wave. By using the t-J1-J2-J3model, we have studied the distribution of the magnetic order in this system in the presence of the Fe vacancies. We have also analyzed the magnetic phase diagram and find a blocked checkerboard antiferromagnetic order in agreement with the experimental measurements.