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

TL;DR

This paper predicts a giant, quantized Goos-H"anchen effect on graphene in the quantum Hall regime, where the angular shift is directly related to quantized Hall conductivity and Landau levels, enabling optical measurement of these quantum properties.

Contribution

It introduces a theoretical prediction of a giant quantized GH effect on graphene in the quantum Hall regime, linking optical shifts to quantum Hall conductivity and Landau levels.

Findings

Quantized GH effect manifests as an angular shift of mrad.

The effect is enhanced near the Brewster angle.

The effect can be modulated by Fermi energy and magnetic field.

Abstract

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.