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We measure the Hall conductivity of a two-dimensional electron gas formed at a GaAs/AlGaAs heterojunction in the terahertz regime close to the cyclotron resonance frequency using highly sensitive Faraday rotation measurements. The sample is electrically gated, allowing the electron density to be changed continuously by more than a factor of 3. We observe clear plateaulike and steplike features in the Faraday rotation angle vs electron density and magnetic field (Landau-level filling factor) even at fields or frequencies very close to cyclotron resonance absorption. These features are the high frequency manifestation of quantum Hall plateaus-a signature of topologically protected edge states. We observe both odd and even filling factor plateaus and explore the temperature dependence of these plateaus. Although dynamical scaling theory begins to break down in the frequency region of our measurements, we find good agreement with theory.

We report the THz response of thin films of the topological insulator Bi2Se3. At low frequencies, transport is essentially thickness independent showing the dominant contribution of the surface electrons. Despite their extended exposure to ambient conditions, these surfaces exhibit robust properties including narrow, almost thickness-independent Drude peaks, and an unprecedentedly large polarization rotation of linearly polarized light reflected in an applied magnetic field. This Kerr rotation can be as large as 65° and can be explained by a cyclotron resonance effect of the surface states.

We employ Faraday and Kerr effect spectroscopy in the infrared range to investigate the electronic structure of Ga_{1-x}Mn_{x}As near the Fermi energy. The band structure of this archetypical dilute-moment ferromagnetic semiconductor has been a matter of controversy, fueled partly by previous measurements of the unpolarized infrared absorption and their phenomenological impurity-band interpretation. Unlike the unpolarized absorption, the infrared magneto-optical effects we study are intimately related to ferromagnetism, and their interpretation is much more microscopically constrained in terms of the orbital character of the relevant band states. We show that the conventional theory of the disordered valence band with an antiferromatnetic exchange term accounts semiquantitatively for the overall characteristics of the measured infrared magneto-optical spectra.

Far infrared dielectric response is used to characterize the collective mode density of states for cytochrome c as a function of oxidation state and hydration using terahertz time domain spectroscopy. A strong absorbance and refractive index increase was observed with the oxidation. A simple phenomenological fitting using a continuous distribution of oscillators reproduces the frequency dependence of the complex dielectric response as well as demonstrates quantitative agreement with a uniform increase in either mode density or polarizability with oxidation in the 5-80 cm(-1) frequency range. Hydration dependence measurements find that a difference in the equilibrium water content for ferri and ferro cytochrome c is not sufficient to account for the large change in terahertz response. The large dielectric increase at terahertz frequencies with oxidation suggests either a significant global softening of the potential and/or a significant increase in polarizability with oxidation.

Infrared ( 20-120 and 900-1100 cm(-1)) Faraday rotation and circular dichroism are measured in high- T(c) superconductors using sensitive polarization modulation techniques. Optimally doped YBa2Cu3O7 thin films are studied at temperatures in the range ( 15