Transport in two-dimensional topological materials: recent developments in experiment and theory

We review theoretical and experimental highlights in transport in two-dimensional topological materials over the last five years. Topological materials comprise topological insulators, Weyl semimetals and topological superconductors. This review focuses on key developments in the understanding of transport phenomena involving surfaces and interfaces of two-dimensional topological materials that have not been covered elsewhere. The review is structured around the following general topics: (i) topological insulators are finding applications in magnetic devices, while controversy continues to surround Hall transport in doped samples and the general issue of topological protection; (ii) state-of-the-art experiments on transition metal dichalcogenides have revealed new valley-dependent electrical and optical phenomena which have spin-dependent counterparts in topological insulators; (iii) in Weyl semimetals the manifestations of Fermi arcs in transport are actively investigated as well as controversial; (iv) a new and growing field centres on the non-linear electrical and optical responses of topological materials, where fundamental questions emerge about the interplay of the Berry curvature and disorder scattering; and (v) topological superconductor research is dominated by the quest for chiral superconductivity, Majorana fermions and topological quantum computing. Prospects for future research in this vast field are outlined in the closing section. (topical review)