Quantum transport in topological matters under magnetic fields

Topological matters include topological insulator, topological semimetal and topological superconductor. The topological semimetals are three-dimensional topological states of matter with gapless electronic excitations. They are simply divided into Weyl, Dirac, and nodal-line semimetals according to the touch type of the conduction band and the valence band. Their characteristic electronic structures lead to topologically protected surface states at certain surfaces, corresponding to the novel transport properties. We review our recent works on quantum transport mainly in topological semimetals. The main theories describing the transport behavior of topological matters are given in different magnetic regions.