Far-infrared cyclotron resonance and Faraday effect in ${\text{Bi}}_2{\text{Se}}_3$

The complex Faraday angle and transmission for the topological insulator ${\text{Bi}}_2{\text{Se}}_3$ were measured in the far infrared in magnetic fields up to 8 T and analyzed in terms of a simple Drude-Lorentz magnetoplasma dielectric model. Bulk carriers dominate the optical response. The bulk carriers are electrons as we determined from the sign of the Faraday angle. We obtain the bulk band-edge cyclotron mass $m_{cb}=0.16\pm 0.01m_e$ and free-electron concentration in the ${10}^{17}$ range. Electron-phonon interaction effects were found to be weak.

Figure 1

(Color online) Transmission of ${\text{Bi}}_2{\text{Se}}_3$ flake for unpolarized light in magnetic field $B\parallel c$: (a) measured and (b) calculated; green dashed-dotted curve is calculated with surface states included.

Figure 2

(Color online) Measured (blue solid lines) and calculated (bulk only) transmission of nearly unpolarized light $\left(\beta =-0.02\right)$ for ${\text{Bi}}_2{\text{Se}}_3$ flake at the fixed laser frequency $42.3{\text{cm}}^{-1}$. (a) The calculated transmission for the regions of the flake with low-carrier concentration (green dotted curve), high concentration (red dashed-dotted curve), and a weighted admixture of the two which fits the 10 K data (pink dashed curve). (b) The same model and parameters used in (a) fit the 50 K data provided the scattering rate is raised to ${\gamma }_1={\gamma }_2=13.5{\text{cm}}^{-1}$ (pink dashed curve).

Figure 3

(Color online) (a) Transmission of circular polarized laser light at $42.3{\text{cm}}^{-1}$, (b) real, and (c) imaginary parts of $\text{tan}{\theta }_F$ (${\theta }_F$—complex Faraday angle).

Figure 4

(Color online) Reflectivity of a ${\text{Bi}}_2{\text{Se}}_3$ crystal with $N_b=8.5\times {10}^{18}$. Inset: model calculations for the phonon line shape in magnetic field using data of Ref. 17. Deviations in line shape and an apparent phonon frequency shift from the $B=0\text{T}$ (solid black) curve is due to the differences in the optical responses of left (dashed red) and right (dashed blue) circularly polarized light at fields of 8 T. Linearly or unpolarized light is an equal admixture of the two responses (solid green).