This article reviews experimental work on the ultrafast electron dynamics in the topological surface state (TSS) of three-dimensional (3D) topological insulators (TIs) observed with time- and angle-resolved two-photon photoemission (2PPE). The focus is laid on the generation of ultrafast photocurrents and the time-resolved observation of their decay. 2PPE not only allow to unambiguously relate the photocurrents to the spin-polarized electronic surface states. Probing of the asymmetric momentum distribution of the electrons carrying the current makes it possible to study the microscopic scattering processes that governs the unusual electron transport in the time domain. Ultrashort mid-infrared pump pulses permit not only a direct optical excitation of the TSS in Sb$_2$Te$_3$ but also lead to a strong asymmetry of the TSS population in momentum space. Two-dimensional band mapping of the TSS shows that this asymmetry is in fact representative for a macroscopic photocurrent while the helicity-dependence of the photocurrent is found to be small. The time-resolved observation of the photocurrent decay reveals a huge mean free path of the electrons in the TSS.
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