Topological insulators
Topological insulator is a bulk insulator with a conducting state on the surface. Unlike ordinary metals, conducting surface states are topologically protected and characterized by spin helicity whereby the direction of the electron spin is locked to the momentum direction. This leads to a number of unusual and nontrivial transport properties, such as quantum spin Hall effect, surface weak antilocalization and the halfinteger quantum Hall effect. Unusual electrodynamics, such as a universal Faraday effect and an anomalous Kerr rotation have been also predicted for these surface states.
Using terahertz spectroscopy in external magnetic fields we investigate, the charge dynamics in strained HgTe, a three dimensional topological insulator. From the Faraday rotation angle and ellipticity a complete characterization of charge carriers is obtained, including the density, the scattering rate and the Fermi velocity. The combination of the unique band structure and the high electron mobility of HgTe results in a giant Faraday effect at room temperature.
Faraday effect in HgTe
(a) Detection of the transmission energy in crossed (T_{C}) and parallel (T_{P}) configurations of the polarizer and analyzer and the definitions of the Faraday rotation θ and ellipticity η. (b) Calculated evolution of θ scans with frequency in the 1μm thick sample at T=200 K. Experimental Faraday rotation (c) Experimental (giant) Faraday rotation and (d) Faraday ellipticity as functions of magnetic field in 70nm and 1μm thick samples. (e) Faraday rotation as a function of frequency at B=0.6 T for both samples. (f) Faraday rotation as a function of 2D conductivity at 174 GHz and B=0.6 T in a single HgTe layer (d = 0μm) and a HgTe/CdTe periodic structure. 
Selected publications

A. M. Shuvaev, G. V. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. W. Molenkamp
Giant MagnetoOptical Faraday Effect in HgTe Thin Films in the Terahertz Spectral Range
Phys. Rev. Lett. 106, 107404 (2011) 
A. M. Shuvaev, G. V. Astakhov, G. Tkachov, C. Brüne, H. Buhmann, L. W. Molenkamp, A. Pimenov
Terahertz Quantum Hall Effect in a Topological Insulator
[condmat/1208.1115]