Giant Magneto-Optical Faraday Effect in HgTe Thin Films in the Terahertz Spectral Range

We report the observation of a giant Faraday effect, using terahertz (THz) spectroscopy on epitaxial HgTe thin films at room temperature. The effect is caused by the combination of the unique band structure and the very high electron mobility of HgTe. Our observations suggest that HgTe is a high-potential material for applications as optical isolator and modulator in the THz spectral range.

Figure 1

THz Faraday effect in HgTe. (a) Detection of the transmission energy in crossed ($T_C$) and parallel ($T_P$) configurations of the polarizer and analyzer. (b) Ratio $T_C/T_P$ in HgTe of thicknesses $L=1\mu \mathrm{m}$ and $L=70\mathrm{nm}$ obtained at $T=200\mathrm{K}$ for a frequency $\omega =0.35\mathrm{THz}$ (symbols). The lines correspond to the model calculation (see text for details). (c) Temperature evolution of $T_C/T_P(B)$ in HgTe with $L=1\mu \mathrm{m}$. For this calculation the experimental temperature dependencies of $m$, $N$, and $\mu$ [see insets of Fig. 3] are used.

Figure 2

Transmission spectra and optical conductivity. (a) Transmission spectra of a reference CdTe ($814\mu \mathrm{m}$) substrate at different temperatures. (b) Sketch of the dispersion of light-hole (LH) and heavy-hole (HH) bands of the ${\Gamma }_8$ doublet. The arrow indicates thermal excitation of electron-hole pairs. (c) Transmission spectra of the 70 nm-thick HgTe epilayer sample at different temperatures. (d) 2D optical conductivity $G_0={\sigma }_{0}L$ of HgTe as a function of temperature. The lines in (a) and (c) result from a model calculation (see text for details).

Figure 3

Transmission amplitude and phase shift of the THz radiation in a 70 nm-thick HgTe layer. (a) Transmission amplitude for parallel polarizers detected at different temperatures at a frequency of 0.35 THz. (b) Transmission amplitude for parallel polarizers detected at $T=100\mathrm{K}$ at a frequency of 0.75 THz. The arrows indicate cyclotron resonance (CR). Inset: cyclotron mass as a function of temperature. (c) Transmission amplitude for crossed polarizers detected at different temperatures at a frequency of 0.35 THz. (d) Transmission amplitude for crossed polarizers detected at $T=100\mathrm{K}$ at a frequency of 0.75 THz. Inset: electron concentration as a function of temperature. (e) Phase difference between parallel and crossed polarization detected at different temperatures at a frequency of 0.35 THz. (f) Phase difference between parallel and crossed polarization detected at $T=100\mathrm{K}$ at a frequency of 0.75 THz. Inset: mobility as a function of temperature. Lines in all panels correspond to the model calculation (see text for details).

Figure 4

Faraday rotation $\theta$ and Faraday ellipticity $\eta$ as a function of frequency and conductivity. (a) Definition of $\theta$ and $\eta$. The vertical double arrow indicates the linear polarization of the incoming radiation, and the ellipse stands for the elliptical polarization of the transmitted radiation. The orientation of this ellipse in the plane is determined by the angles $\theta$ and $\eta$. (b) Calculated evolution of $\theta (B)$ scans with frequency in the $1\mu \mathrm{m}$-thick sample, $T=200\mathrm{K}$. Experimental Faraday rotation, (c) and Faraday ellipticity, (d) as a function of magnetic field in both samples. (e) Faraday rotation as a function of frequency at $B=0.6\mathrm{T}$ in both samples. (f) Faraday rotation as a function of 2D conductivity at $\omega =0.174\mathrm{THz}$ and $B=0.6\mathrm{T}$ in a single HgTe layer ($d=0\mu \mathrm{m}$) and a $\mathrm{HgTe}/\mathrm{CdTe}$ periodic structure (shown in the inset). Experimental points are obtained from the temperature dependencies of the Faraday rotation $\theta (T)$ and conductivity $G_0(T)$.