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

Giant quantized Goos-H\"anchen effect on the surface of graphene in quantum Hall regime