Ultrafast electron dynamics in a topological surface state observed in two-dimensional momentum space

We study ultrafast population dynamics in the topological surface state of Sb$_2$Te$_3$ in two-dimensional momentum space with time- and angle-resolved two-photon photoemission. Linear polarized mid-infrared pump pulses are used to permit a direct optical excitation across the Dirac point. We show that this resonant excitation is strongly enhanced within the Dirac cone along three of the six $\bar{\Gamma}$-$\bar{M}$ directions and results in a macroscopic photocurrent when the plane of incidence is aligned along a $\bar{\Gamma}$-$\bar{K}$ direction. Our experimental approach makes it possible to disentangle the decay of transiently excited population and photocurent by elastic and inelastic electron scattering within the full Dirac cone in unprecedented detail. This is utilized to show that doping of Sb$_2$Te$_3$ by vanadium atoms strongly enhances inelastic electron scattering to lower energies, but only scarcely affects elastic scattering around the Dirac cone.