Photo-galvanic effect in Bi$_{2}$Se$_{3}$ thin films with ionic liquid gating*

A key challenge in three dimensional (3D) topological insulators (TIs) is to reveal the helical spin-polarized surface states via electrical transport measurements. A recent study [Nature Nanotech. {\bf 7}, 96 (2012)] showed that circularly polarized light can be used to generate and control photocurrents in the 3D TI Bi$_2$Se$_3$, even at photon energies that are well above the bulk band gap. Symmetry considerations suggest that this ``photo-galvanic effect'' arises purely from photo-currents induced in the surface Dirac states. To gain insights into this phenomenon, we have carried out systematic measurements of the photo-galvanic effect in electrically gated MBE-grown Bi$_2$Se$_3$ thin films of varying thickness. By using an ionic liquid as an optically transparent gate, we map out the behavior of the photo-galvanic effect as a function of Fermi energy over a temperature range 5 K $\leq T \leq$ 300 K.