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 opto-electronic 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 Bi$_{\mathrm{2}}$X$_{\mathrm{3}}$ (X: Te, Se), we find that Dirac surface states with a hexagonal warping term support shift current by linearly polarized light. Moreover, we study ``shift spin current'' that arises in Dirac surface states by introducing time-reversal symmetry breaking perturbation. The estimate for the magnitudes of the shift charge and spin current densities are 0.13 I$_{\mathrm{0}}$ and 0.40 I$_{\mathrm{0\thinspace }}$(nA/m) for Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$ with the intensity of light I$_{\mathrm{0}}$ measured in (W/m$^{\mathrm{2}})$, respectively, which can offer a useful method to generate these currents efficiently.