Josephson effect in spin-singlet superconductor/ferromagnetic insulator/spin-triplet superconductor junctions with helical pp-wave states

We study the Josephson effect in spin-singlet superconductor/helical $p$-wave superconductor junctions with a ferromagnetic barrier using the quasiclassical Green function method. It is found that both $\sin{\phi}$-type and $\cos{\phi}$-type current-phase relations always exist, irrespective of the gap symmetries in superconductors. The indispensable condition for the $\sin{\phi}$-type and $\cos{\phi}$-type current is that the magnetization must have a component parallel to the crystallographic $a$ or $b$ axis, which is distinct from the case of $p$-wave superconductor described by a \vect{d}-vector with a uniform direction. The relation between the condition and the symmetries of the gap functions is analysed. We investigate in detail the symmetries and the sign reversal of the Josephson current when the magnetization is rotated.Comment: 9 pages,7 figure

Exotic orbits due to spin-spin coupling around Kerr black holes

We report exotic orbital phenomena of spinning test particles orbiting around a Kerr black hole, i.e., some orbits of spinning particles are asymmetrical about the equatorial plane. When a nonspinning test particle orbits around a Kerr black hole in a strong field region, due to relativistic orbital precessions, the pattern of trajectories is symmetrical about the equatorial plane of the Kerr black hole. However, the patterns of the spinning particles' orbit are no longer symmetrical about the equatorial plane for some orbital configurations and large spins. We argue that these asymmetrical patterns come from the spin-spin interactions between spinning particles and Kerr black holes, because the directions of spin-spin forces can be arbitrary, and distribute asymmetrically about the equatorial plane.Comment: 15 pages, 20 figure