Transport theory of metallic B20 helimagnets

B20 compounds are a class of cubic helimagnets harboring nontrivial spin textures such as spin helices and skyrmions. It has been well understood that the Dzyaloshinskii-Moriya (DM) interaction is the origin of these textures, and the physics behind the DM interaction is the spin-orbit coupling (SOC). However, the SOC shows its effect not only on the spins but also on the electrons. In this paper, we will discuss the effects of the SOC on the electron and spin transports in B20 compounds. An effective Hamiltonian is presented from symmetry analysis, and the spin-orbit coupling therein shows anomalous behaviors in anisotropic magnetoresistance and helical resistance. New effects such as an inverse spin-galvanic effect are proposed, and the origin of the DM interaction is discussed.