Shift charge and spin photocurrents in Dirac surface states of topological insulator

The generation of photocurrent in condensed matter is of main interest for photovoltaic and optoelectronic applications. Shift current, a nonlinear photoresponse, has attracted recent intensive attention as a dominant player of bulk photovoltaic effect in ferroelectric materials. In three dimensional topological insulators $\text{Bi}_2\text{X}_3$ (X: Te, Se), we find that Dirac surface states with a hexagonal warping term carry shift current by linearly polarized light. In addition, shift spin-current is introduced with the time-reversal symmetry breaking perturbation. The estimate for the magnitudes of the shift charge- and spin-currents are 0.13$I_0$ and 0.21$I_0$(nA/m) with the intensity of light $I_0$ measured in $(\text{W}/\text{m}^2)$, respectively, which can offer a useful method to generate these currents efficiently.