Spin-orbit coupling (SOC) plays a central role in various physical phenomena that have been studied intensively in recent years. One major example is the emergence of topological insulators (TIs) and topological superconductors (TSCs). Especially, when SOC is present in conventional (s-wave) superconductors, the Cooper pairs can behave in a rather unconventional way. One consequence is that the original spin-zero Cooper pairs become spin-active. For this reason, as I will show in the first part of this talk, the Cooper pairs can contribute to spin density and spin current when time-reversal symmetry is broken by driving a supercurrent. We study in detail such superconducting magnetoelectric effect in a two-dimensional superconductor with arbitrary Rashba SOC and arbitrary chemical potential and find that the spin current generation becomes highly efficient as the Fermi level approaches the band bottom. Another ideal platform with strong SOC is the surface states of TIs. In the second part, I show our study of a three-layer heterostructure of a SC, a TI thin film and a ferromagnetic insulator (FMI), inspired by previous proposals for Majorana chiral modes based on TIs. I will show that the topological phase with single Majorana chiral mode in this system is readily accessible without requiring small magnetization compared to the SC gap. Also, we expect such a system to be much cleaner compared to the case of magnetic doping. Under the above two conditions, it may circumvent the issues arising from disorders or domain walls. We further propose a transport measurement to determine this phase making use of the phase coherence of a Josephson junction.
 James Jun He, Kanta Hiroki, Keita Hamamoto, Naoto Nagaosa, arXiv:1811.09057
 James Jun He, Tian Liang, Yukio Tanaka, Naoto Nagaosa, arXiv:1901.04635