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Giant quantized Goos-Hanchen effect on the surface of graphene in quantum Hall regime

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 Added by Hailu Luo
 Publication date 2017
  fields Physics
and research's language is English




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We theoretically predict a giant quantized Goos-H{a}nchen (GH) effect on the surface of graphene in quantum Hall regime. The giant quantized GH effect manifests itself as an angular shift whose quantized step reaches the order of mrad for light beams impinging on a graphene-on-substrate system. The quantized GH effect can be attributed to quantized Hall conductivity, which corresponds to the discrete Landau levels in quantum Hall regime. We find that the quantized step can be greatly enhanced for incident angles near the Brewster angle. Moreover, the Brewster angle is sensitive to the Hall conductivity, and therefore the quantized GH effect can be modulated by the Fermi energy and the external magnetic field. The giant quantized GH effect offers a convenient way to determine the quantized Hall conductivity and the discrete Landau levels by a direct optical measurement.

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We report the observation of the Goos-Hanchen effect in graphene via a weak value amplification scheme. We demonstrate that the amplified Goos-Hanchen shift in weak measurements is sensitive to the variation of graphene layers. Combining the Goos-Hanchen effect with weak measurements may provide important applications in characterizing the parameters of graphene.
We examine the photonic spin Hall effect (SHE) in a graphene-substrate system with the presence of external magnetic field. In the quantum Hall regime, we demonstrate that the in-plane and transverse spin-dependent splittings in photonic SHE exhibit different quantized behaviors. The quantized SHE can be described as a consequence of a quantized geometric phase (Berry phase), which corresponds to the quantized spin-orbit interaction. Furthermore, an experimental scheme based on quantum weak value amplification is proposed to detect the quantized SHE in terahertz frequency regime. By incorporating the quantum weak measurement techniques, the quantized photonic SHE holds great promise for detecting quantized Hall conductivity and Berry phase. These results may bridge the gap between the electronic SHE and photonic SHE in graphene.
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