A mechanism leading to the spin-triplet superconductivity is proposed based on the antiferromagnetic spin-fluctuation. The effects of anisotropy in spin-fluctuation on the Cooper pairing and on the direction of $\mathit{d}$ vector are examined in the one-band Hubbard model with random-phase approximation. The gap equations for the anisotropic case are derived and applied to ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. It is found that a nesting property of the Fermi surface together with the anisotropy leads to the triplet superconductivity with the $\mathit{d}=\mathit{ẑ}(\sin k_x\pm i\sin k_y)$, which is consistent with experiments.

Spatial dependencies of the pair potential and the local density of states near the surfaces of $d_{x^{2}-y^{2}}$-wave superconductors are studied theoretically. The calculation is based on the t-J model within a mean-field theory with Gutzwiller approximation. Various types of surface geometries are considered. Similar to our result in the extended Hubbard model, it is found that the formation of zero-energy states strongly depends on the surface geometry. In addition to this feature, the zero-energy states give peak splitting for the (110) surfaces when the super-exchange interaction $J$ is large. This is due to the induced s-wave component near the surface. The present result explains the microscopic origin of the spontaneous time- reversal symmetry breaking at the surfaces of high-$T_{c}$ superconductors.Comment: 8 pages, 3 figures, to appear in Journal of the Physical Society of Japan Vol.67 No.

Using a microscopic theory for the magnetoconductivity at low magnetic fields, we show how all components of the conductivity tensor can be calculated in the low scattering rate limit. In the lowest order of the scattering rate, we recover the result of the semiclassical Boltzmann transport theory. At higher order, we get corrections containing the Berry curvature and the orbital magnetic moment. We use this formalism to study the linear longitudinal magnetoconductivity in tilted Weyl semimetals. We discuss how our result is related to the semiclassical Boltzmann approach and show the differences that arise compared to previous studies related to the orbital magnetic moment.