Terahertz Hall effect and Berry phase

When linearly polarized light is incident on a sample which is under external magnetic field, the polarization of the transmitted (reflected) light rotates, which phenomenon is called magneto-optical Faraday (Kerr) effect. When the materials are conducting ,the phenomenon is nothing but the high frequency version of Hall effect, arising from the off-diagonal (or Hall) conductivity $\sigma_{xy}$. Inversely, one can obtain the frequency dependent Hall conductivity $\sigma_{xy}(\omega)$, from the measured rotation spectrum. This technique allows one to determine the carrier density and the mobility in non-contact way.

The similar phenomenon occurs in ferromagnets, known as anomalous Hall effect (AHE) , in which the effect is caused by the magnetization instead of the external magnetic field. The origin can be classified into extrinsic and intrinsic one and the intrinsic mechanism of the AHE is related to Berry phase curvature of Bloch electrons.

By using the THz-spectrscopic technique, we are trying to measure the energy structure of the Hall conductivity in meV range, to reveal the topological nature of the AHE.

Ref.1)"Characterization of doped silicon in low carrier density region by terahertz frequency Faraday effect",
Y. Ikebe, R. Shimano,
Appl. Phys. Lett. 92(1), 012111-1-3 (2008).

Ref.2)"Optical Hall effect in the integer quantum Hall regime"
Y. Ikebe, T. Morimoto, R. Masutomi, T. Okamoto, H. Aoki, and R. Shimano,
Phys. Rev. Lett. 104, 256802 (2010).

Ref.3)"Terahertz Faraday rotation induced by an anomalous Hall effect in the itinerant ferromagnet SrRuO3"
R. Shimano, Y. Ikebe, K. S. Takahashi, M. Kawasaki, N. Nagaosa and Y.Tokura,
EPL 95, 17002 (2011).

Ref.4)"Quantum Faraday and Kerr rotations in graphene"
R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki,
Nature Commun. 4, 1841 (2013).

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Shimano Laboratory Department of Physics, School of Science, The University of Tokyo