Linear photogalvanic effect in surface states of topological insulators

The theory of the linear photogalvanic effect is developed for direct optical transitions between surface states of three-dimensional topological insulators. The photocurrent governed by the orientation of the polarization plane of light and caused by the warping of the energy dispersion of two-dimensional carriers is calculated. It is shown that both the shift contribution caused by coordinate shifts of the particle wave packets during the optical transitions and the ballistic contribution caused by interference of the optical absorption and scattering by disorder have generally the same order of magnitude. The ballistic contribution is present owing to electron-hole asymmetry of topological surface states and has a frequency dependence in contrast to the shift photocurrent. In the nonlinear-in-the-light-intensity regime appearing due to saturation of the direct optical transitions, the ballistic contribution dominates. The nontrivial dependence of the photocurrent on the polarization plane orientation in the nonlinear regime appears solely due to the ballistic contribution. Our findings allow separating the ballistic and shift contributions to the Linear photogalvanic current in experiments.