Infrared/terahertz spectra of the photogalvanic effect in (Bi,Sb)Te based three-dimensional topological insulators

We report on the systematic study of infrared/terahertz spectra of photocurrents in (Bi,Sb)Te based three-dimensional topological insulators. We demonstrate that in a wide range of frequencies, ranging from fractions up to tens of terahertz, the photocurrent is caused by the linear photogalvanic effect (LPGE) excited in the surface states. The photocurrent spectra reveal that at low frequencies the LPGE emerges due to free carrier Drude-like absorption. The spectra allow us to determine the room temperature carrier mobilities in the surface states despite the presence of thermally activated residual impurities in the material bulk. In a number of samples we observed an enhancement of the linear photogalvanic effect at frequencies between 30 and 60 THz, which is attributed to the excitation of electrons from helical surface to bulk conduction band states. Under this condition and applying oblique incidence we also observed the circular photogalvanic effect driven by the radiation helicity.

Figure 1

Photocurrent $J_{x,y}$ measured along $x$ and $y$ directions and normalized on the radiation intensity $I$ in (a) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, (b) $\left({\mathrm{Bi}}_{0.06}{\mathrm{Sb}}_{0.94}\right){}_2{\mathrm{Te}}_3$, (c) $\left({\mathrm{Bi}}_{0.57}{\mathrm{Sb}}_{0.43}\right){}_2{\mathrm{Te}}_3$, and (d) ${\mathrm{Bi}}_2{\mathrm{Te}}_3/{\mathrm{Sb}}_2{\mathrm{Te}}_3$ heterostructure with ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thickness of 15 nm. Solid lines show fit after Eq. (1), see also Eq. (4) and discussion. Note that the polarization independent offset $D\left(D^{\prime }\right)$, being much smaller than the amplitude $A\left(f\right)$, is subtracted in these plots. The insets in panels (a) and (b) define the angle $\alpha$ and show the experimental setup. Arrows on top illustrate the polarization plane orientation for several angles $\alpha$.

Figure 2

Frequency dependence of the coefficient $A$ for (a) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, (b) $\left({\mathrm{Bi}}_{0.06}{\mathrm{Sb}}_{0.94}\right){}_2{\mathrm{Te}}_3$, (c) $\left({\mathrm{Bi}}_{0.57}{\mathrm{Sb}}_{0.43}\right){}_2{\mathrm{Te}}_3$, and (d) ${\mathrm{Bi}}_2{\mathrm{Te}}_3/{\mathrm{Sb}}_2{\mathrm{Te}}_3$ heterostructure with ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thickness of 15 nm. Solid line shows fit after Eq. (2), see also Eq. (6) and discussion. Dashed lines are guide for eye, demonstrating deviation of photocurrent amplitude from the Drude-like behavior.

Figure 3

(a) Frequency dependence of coefficient $A$ of a ${\mathrm{Sb}}_2{\mathrm{Te}}_3/{\mathrm{Bi}}_2{\mathrm{Te}}_3$ heterostructure with $d_{\mathrm{ST}}=7.5$ nm. Solid line shows fit after Eq. (2), see also Eq. (6) and discussion. Dashed line is guide for eye, demonstrating deviation of photocurrent amplitude from the Drude-like behavior. (b) Azimuthal angle dependence of the photocurrent $J_y/I$ measured at frequency $f=53$ THz. Solid lines show fit after Eq. (1), see also Eq. (4) and discussion. Inset shows experimental setup.

Figure 4

(a) Dependence of the normalized photocurrent $J_x/I$ on the angle $\phi$ measured in a ${\mathrm{Sb}}_2{\mathrm{Te}}_3/{\mathrm{Bi}}_2{\mathrm{Te}}_3$ heterostructure with $d_{\mathrm{ST}}=7.5$ nm. Data are shown for the $\left(yz\right)$ plane of incidence and angle of incidence $\theta ={40}^{\circ }$. Solid line shows fit after Eq. (3), see also Eq. (7) and discussion. Horizontal lines and downwards pointing arrows indicate photocurrent for circularly polarized radiation. (b) Dependence of the circular coefficient $C$ on the angle of incidence. Solid line shows fit after Eq. (3), see also Eq. (7) and discussion. Inset shows experimental setup.