Observation of cyclotron antiresonance in the topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$

We report on the experimental observation of a cyclotron antiresonance in a canonical three-dimensional topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Magnetoreflectance response of single-crystal ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ was studied in 18-T magnetic field, and compared to other topological insulators studied before, the main spectral feature is inverted. We refer to it as an antiresonance. In order to describe this unconventional behavior we propose the idea of an imaginary cyclotron resonance frequency, which on the other hand indicates that the form of the Lorentz force that magnetic field exerts on charge carriers takes an unconventional form.

Figure 1

(a) Reflection ratios of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ at several magnetic field values. The feature around 800 ${\mathrm{cm}}^{-1}$ is identified as cyclotron antiresonance, because it is a mirror image of the feature observed in ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ (bottom panel). (b) Reflection ratios of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ at several magnetic field values. The feature around $1300{\mathrm{cm}}^{-1}$ is identified as the usual cyclotron resonance. Note different axis scales between the two panels.

Figure 2

(a) The best fits of reflectance ratios of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ at several selected field values, using Eq. (4). (b) The best fits of reflectance ratios of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ at several selected field values, using Eq. (2).

Figure 3

(a), (b) Optical conductivities for left and right circularly polarized light ${\sigma }_{+}\left(\omega \right)$ (right panel) and ${\sigma }_{-}\left(\omega \right)$ (left panel) for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ at different magnetic fields, generated from the best fits of reflection ratios (Fig. 2). (c), (d) Optical conductivities ${\sigma }_{+}\left(\omega \right)$ and ${\sigma }_{-}\left(\omega \right)$ for ${\mathrm{Sb}}_2{\mathrm{Te}}_3$. The same color coding is used in all four panels.

Figure 4

(a) Magnetic field dependence of cyclotron frequency ${\omega }_c^{{}^{\prime }}$ in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Dashed line is a linear fit of the data. (b) Cyclotron resonance frequency ${\omega }_c$ of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$. Dashed line is a linear fit, from which the cyclotron effective mass of $0.42m_e$ was extracted.