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=e2/2hc (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.

We review terahertz experiments on magnetoelectric excitations in rare earth multiferroic manganites RMnO 3 with R = Gd, Tb, Dy, (Eu:Y). In all these compounds characteristic excitations of the novel type, called electromagnons, have been observed for frequencies 10 cm −1 < ν < 30 cm −1 . From the spectroscopic point of view electromagnons are responsible for the magnetoelectric effects in RMnO 3 and, contrary to magnons, are excited only by electric components of the electromagnetic wave. In all compositions the electromagnons appear as a broad Debye-like contribution in the sinusoidally modulated antiferromagnetic phase and transform to well-defined excitations as the magnetic structure becomes spiral. At the lowest temperatures the fine structure of electromagnons is observed, reflecting the increasing complexity of the magnetic structure.

Magnetic and magnetoelectric excitations in the multiferroic TbMnO3 have been investigated at terahertz frequencies. Using different experimental geometries we can clearly separate the electroactive excitations (electromagnons) from the magneto-active modes, i.e. antiferromagnetic resonances (AFMR). Two AFMR resonances were found to coincide with electromagnons. This indicates that both excitations belong to the same mode and the electromagnons can be excited by magnetic ac-field as well. In external magnetic fields and at low temperatures distinct fine structure of the electromagnons appears. In spite of the 90 o rotation of the magnetic structure, the electromagnons are observable for electric ac-fields parallel to the a-axis only. Contrary to simple expectations, the response along the c-axis remains purely magnetic in nature.During the last years, materials with magnetoelectric (ME) coupling have attracted much interest especially due to their intriguing physical mechanisms and their potential for applications [1,2,3,4,5]. ME coupling is especially strong in multiferroics, i.e materials which are simultaneously ferroelectric and ferromagnetic. The strength of ME effects in multiferroics is due to direct coupling of the magnetic and electric order parameters and partly due to improper character of the ferroelectricity. This coupling allows, for example, switching of electric polarization in the sample in external magnetic fields [6,7]. One promising class of multiferroics is represented by frustrated magnets [3] in which magnetoelectricity is induced by complex spin arrangements like cycloidal or spiral antiferromagnetic structures.Given the observation of the static magnetoelectric effects in susceptibilities and polarizations, the existence of the dynamic effects can be expected from the first principles. This follows immediately from the optical sum rules which arises as a direct consequence of the causality. Indeed, strong magnetoelectric modes have been observed in multiferroic manganites TbMnO 3 and GdMnO 3 and termed electromagnons [9]. The electromagnons have been detected in the infrared spectra of 11,12], and DyMnO 3 [13] using similar experimental techniques. Soft magnon modes observed in the inelastic neutron scattering data of TbMnO 3 has been attributed to electromagnons as well [14,15]. Based on available experimental data and on existing theoretical models, electromagnons can be defined as spin modes which become excited by electric field due to ME coupling [9,16]. Large spectral weight of the electromagnons distinguishes them [16] from seignetomagnons in ME compounds, as predicted about forty years ago by Baryachtar and Chupis [17,18].In spite of an enormous progress in the field of ME effect the underlying microscopic mechanisms still remain under debate. In order to explain spin driven ferroelectricity and dynamical properties of frustrated magnets various approaches like phenomenological analysis [19,20], Brillouin-zone folding [21], spin current model [22,23], inverse Dzyaloshinskii-Moriy...

The investigation of the temperature dependences of microwave surface impedance and complex conductivity of V 3 Si single crystals with different stoichiometry allowed to observe a number of peculiarities which are in remarkable contradiction with single-gap Bardeen-Cooper-Schrieffer theory. At the same time, they can be well described by two-band model of superconductivity, thus strongly evidencing the existence of two distinct energy gaps with zero-temperature valuesPACS numbers: 74.25.Nf, 74.70.Ad, 74.20.Fg 1 The story of multi-gap superconductors goes to the middle of the last century, when the extension of Bardeen-Cooper-Schrieffer (BCS) theory [1] was proposed [2, 3]. The followed experimental investigations, however, contradicted each other showing the existence of single gap, multiple gaps and slightly anisotropic gap in various superconducting materials. The interest to this phenomenon has been stimulated by the discovery of two-gap superconductivity in MgB 2 . The existence of at least two different energy bands crossing the Fermi-level (particular feature of MgB 2 ) appears to be the prerequisite for the observation of multiple gaps. The second requirement, as follows from [3], is a weak interband scattering. Such processes can be significantly reduced if wave functions of electrons from two bands have different symmetry. For example this may happen when energy band structure has both flat and non-flat areas near the Fermi level. Flat areas lead to a singularity in the density of states at the Fermi level and can be experimentally detected for instance by non-linear temperature dependence of the resistivity ρ(T ) in the normal state. In the opposite case of more or less similar bands structures even small amount of impurities leads to high interband scattering and almost excludes the possibility to detect multi-gap response of the material. Apparently, the above requirements apply to the layered superconductor NbSe 2 and to A15 structure superconductors Nb 3 Sn, V 3 Si, V 3 Ga, in which the density of states has very high and narrow peak just in the vicinity of the Fermi level according to band-structure calculations [4]. Recently the existence of multiple gaps in Nb 3 Sn polycrystalline sample has been proposed to explain specific heat measurements [5]. The authors of [6] showed the similarity of the magnetic field dependence of thermal conductivity in NbSe 2 to that of MgB 2 and concluded about the presence of the second energy gap in NbSe 2 . Such a similarity was not found in V 3 Si. However, back in 1969 J.Brock denoted the existence of the second gap as one of the possible explanations of the peculiarities seen in the specific heat of V 3 Si [7].The measurements of the temperature dependences of microwave conductivity both in low-T c and high-T c superconductors were very informative. They proved the applicability of BCS theory to conventional superconductors, allowed to distinguish superconductors with different order parameter symmetry and to measure the values of energy gap, penetration depth,...