Transport in three-dimensional topological insulators: Theory and experiment

This paper reviews recent theoretical and experimental work on transport due to the surface states of three-dimensional topological insulators. The theoretical focus is on longitudinal transport in the presence of an electric field, including Boltzmann transport, quantum corrections and weak localization, as well as longitudinal and Hall transport in the presence of both electric and magnetic fields and/or magnetizations. Special attention is paid to transport at finite doping, and to the π-Berry phase, which leads to the absence of backscattering, Klein tunneling and half-quantized Hall response. Signatures of surface states in ordinary transport and magnetotransport are identified. The review also covers transport experiments of the past years, tracing its evolution from the initial obscuring of surface transport by bulk transport to the increasing success of experimental work in identifying transport due to the surface states. Current and likely future experimental challenges are given prominence and the present status of the field is assessed.