The electrodynamics of topological insulators (TIs) is described by modified Maxwell’s equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e²/2"Equation missing"<!-- image only, no MathML or LaTex -->hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.

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.

Magnetic and magnetoelectric excitations in the multiferroic ${\mathrm{TbMnO}}_3$ have been investigated at terahertz frequencies. Using different experimental geometries we can clearly separate the electroactive excitations (electromagnons) from the magnetoactive modes, i.e., antiferromagnetic resonances. Two antiferromagnetic resonances were found to coincide with electromagnons. This indicates that both excitations belong to the same mode and the electromagnons can be excited by a magnetic ac field as well. In spite of the 90° rotation of the magnetic cycloid in external magnetic fields, the electromagnons are observable for electric ac fields parallel to the $a$ axis only.

Terahertz electromagnetic excitations in the multiferroic TbMnO3 single crystals are investigated across the magnetic field induced rotation of the magnetic spin cycloid. In addition to the electromagnon along the a~axis, the detailed polarization analysis of the experimental spectra suggests the existence of an electroactive excitation for ac electric fields of the electromagnetic wave along the crystallographic c~axis. This excitation is possibly the electroactive eigenmode of the spin-cycloid in TbMnO3, which has been predicted within the inverse Dzyaloshinskii-Moriya mechanism of magnetoelectric coupling.

Using terahertz spectroscopy in external magnetic fields, we investigate the low-temperature charge dynamics of strained HgTe, a three-dimensional topological insulator. In resonator experiments, we observe quantum Hall oscillations at terahertz frequencies, which offer direct access to the unusual electrodynamic properties of the surface states of topological insulators. The 2D density estimated from the period of the quantum Hall oscillations agrees well with dc transport experiments on the topological surface state. The Dirac character of the surface state is further evidenced by the observation of the characteristic Berry phase in the dependence of the Landau levels on magnetic field.