Superradiant and transport lifetimes of the cyclotron resonance in the topological insulator HgTe

We investigate the superradiance effects in three-dimensional topological insulator HgTe with conducting surface states. We demonstrate that the superradiance can be explained using the classical electrodynamic approach. Experiments using the continuous-wave spectroscopy allowed us to separate the energy losses in the system into intrinsic and radiation losses, respectively. These results demonstrate that the superradiance effects are not sensitive to the details of the band structure of the material.

Figure 1

Calculated amplitudes of parallel $|t_p|$ and crossed $|t_c|$ magneto-optical transmission at $\nu =208$ GHz using Eqs. (5) and (6). The spectra corresponds to a thin film with electronic carriers with the cyclotron mass $m=0.02m_e$, scattering time ${\tau }_0=2\times {10}^{-12}$ s, and with varied density as indicated. The apparent width of the cyclotron resonance is determined by $\mathrm{\Gamma }=1/{\tau }_0+1/{\tau }_{\mathrm{SR}}$ (see text). At low 2D densities $n$ the intrinsic scattering $1/{\tau }_0$ determines the resonance width. By increasing the density the superradiant decay becomes the dominating mechanism for the energy loss in the film.

Figure 2

Experimental amplitudes of parallel $|t_p|$ and crossed $|t_c|$ magneto-optical transmission at $\nu =208$ GHz through HgTe film on a GaAs substrate and for different gate voltages. Symbols: Experimental data, lines: model fit using the Drude model. Black arrows and $w_{\mathrm{B}}$ represent the apparent width of the resonance curves.

Figure 3

Parameters of the surface states obtained from fitting the experimental data in Fig. 2. The effective mass $m$ (a), 2D density $n$ (b), and the transport scattering time constant ${\tau }_0$ (c) are plotted with respect to the applied gate voltage. (d) Solid circles: transport scattering rate $1/{\tau }_0$ and radiative scattering rate obtained via $1/{\tau }_{\mathrm{SR}}=n{e}^2{Z}_0/(1+n_{\mathrm{CdTe}})m$. Solid squares: Total scattering rate $\mathrm{\Gamma }$ as compared to the scattering rate calculated directly from the estimated widths $w_{\mathrm{B}}$ of the resonances in Fig. 2 (solid triangles).