Abstract:
Using the quasiclassical theory, we analyze the vortex structure of strong-paramagnetic superconductors.There, induced paramagnetic moments are accumulated exclusively around the vortex core. We quantitatively evaluate the significant paramagnetic effect in the H-dependence of various quantities, such as low temperature specific heat, Knight shift, magnetization and the flux line lattice (FLL) form factor. The anomalous H-dependence of the FLL form factor observed by the small angle neutron scattering in CeCoIn_5 is attributable to the large paramagnetic contribution.

Abstract:
We estimate the effect of the superconducting gap anisotropy in the dispersive gap mode of phonons, which is observed by the neutron scattering on borocarbide superconductors. We numerically analyze the phonon spectrum considering the electron-phonon coupling, and examine contributions coming from the gap suppression and the sign change of the pairing function on the Fermi surface. When the sign of the pairing function is changed by the nesting translation, the gap mode does not appear. We also discuss the suppression of the phonon softening of the Kohn anomaly due to the onset of superconductivity. We demonstrate that observation of the gap dispersive mode is useful for sorting out the underlying superconducting pairing function.

Abstract:
We show that the lightly doped La_{2-x}Sr_{x}CuO_{4} can be described in terms of a stripe magnetic structure or soliton picture. The internal relationship between the recent neutron observation of the diagonal (x=0.05) to vertical (x >= 0.06) stripe transition, which was predicted, and the concomitant metal-insulator transition is clarified by this solitonic physics. The phase diagram with the unidentified transition lines between antiferromagnetic to stripe phases, the doping dependence of the modulation period, the origin of the mid-infrared optical absorption are investigated comparatively with other single layer systems: La_{2-x}Sr_{x}NiO_{4} and (La,Nd)_{2-x}Sr_{x}CuO_{4}. The novel type of quasi-particles and holes is fully responsible for metallic conduction and ultimately superconductivity.

Abstract:
Motivated by recent stimulative observations in halogen (X)-bridged binuclear transition-metal (M) complexes, which are referred to as MMX chains, we study solitons in a one-dimensional three-quarter-filled charge-density-wave system with both intrasite and intersite electron-lattice couplings. Two distinct ground states of MMX chains are reproduced and the soliton excitations on them are compared. In the weak-coupling region, all the solitons are degenerate to each other and are uniquely scaled by the band gap, whereas in the strong-coupling region, they behave differently deviating from the scenario in the continuum limit. The soliton masses are calculated and compared with those for conventional mononuclear MX chains.

Abstract:
Focusing on La_{2-x}Sr_{x}CuO_{4}, we study the stripe structure by the self-consistent mean-field theory of the Hubbard model. By introducing the realistic Fermi surface topology, the SDW-gapped insulator is changed to metallic. The solitonic features of the stripe structure and the contribution of the mid-gap states are presented. We consider the band dispersion, the local density of states, the spectral weight, and the optical conductivity, associated with the solitonic structure. These results may provide important information for the experimental research of the stripe structure, such as the angle-resolved photoemission experiments. The ``Fermi surface'' shape is changed depending on the ratio of the incommensurability delta and the hole density n_h. In real space, only the stripe region is metallic when delta/n_h is large.

Abstract:
To investigate the different vortex structure between two chiral pairing p_x +(-) i p_y, we calculate the pair potential, the internal field, the local density of states, and free energy in the vortex lattice state based on the quasiclassical Eilenberger theory, and analyze the magnetic field dependence. The induced opposite chiral component of the pair potential plays an important role in the vortex structure. It also produces H^{1/2}-behavior of the zero-energy density of states at higher field. These results are helpful when we understand the vortex states in Sr2RuO4.

Abstract:
The superconducting gap modulation is investigated in the presence of a weak stripe structure, using the Bogoliubov-de Gennes theory on the two-dimensional Hubbard model with nearest-neighbor site pairing interaction. We calculate the local density of states and discuss the recently observed scanning tunneling spectroscopy spectra with four lattice periodicity on Bi_2 Sr_2 Ca Cu_2 O_{8+delta} We also consider the spectral weight in the reciprocal space, where the Fermi surface and the superconducting gap are modulated by the band folding effect of the stripe structure.

Abstract:
We study the vortex structure and its field dependence within the framework of the quasi-classical Eilenberger theory to find the difference between the d_{x^2-y^2}- and s-wave pairings. We clarify the effect of the d_{x^2-y^2}-wave nature and the vortex lattice effect on the vortex structure of the pair potential, the internal field and the local density of states. The d_{x^2-y^2}-wave pairing introduces a fourfold-symmetric structure around each vortex core. With increasing field, their contribution becomes significant to the whole structure of the vortex lattice state, depending on the vortex lattice's configuration. It is reflected in the form factor of the internal field, which may be detected by small angle neutron scattering, or the resonance line shape of mu-SR and NMR experiments. We also study the induced s- and d_{xy}-wave components around the vortex in d_{x^2-y^2}-wave superconductors.

Abstract:
Superconducting double transition in PrOs_4_Sb_12 is investigated by analyzing the anisotropy of the upper critical field H_c2 in the ab-plane, and the possible pairing state is discussed. When mixing due to gradient coupling is active, the twofold-symmetric component is necessarily induced in the fourfold symmetric phase, leading to the twofold oscillation of H_c2, contrary to the experimental result. To avoid the mixing effect, the weak spin-orbit coupling triplet pairing state is considered as a likely pairing function, where time-reversal symmetry is broken.

Abstract:
The Ginzburg Landau theory for d_{x^2-y^2}-wave superconductors is constructed, by starting from the Gor'kov equation with including correction terms up to the next order of ln(T_c/T). Some of the non-local correction terms are found to break the cylindrical symmetry and lead to the fourfold symmetric core structure, reflecting the internal degree of freedom in the pair potential. Using this extended Ginzburg Landau theory, we investigate the fourfold symmetric structure of the pair potential, current and magnetic field around an isolated single vortex, and clarify concretely how the vortex core structure deviates from the cylindrical symmetry in the d_{x^2-y^2}-wave superconductors.