Quantum Hall Goos-H\"anchen effect in graphene

Abstract

Strong Goos-H\"anchen (GH) effect at a prism-graphene interface in the quantum Hall effect (QHE) condition is reported. Based on the full quantum description of the temperature-dependent surface conductivity of graphene present in the unconventional quantum Hall regime, magnetically strong tunable QHE GH shifts emerge. Our approach is based on deriving the generalized Fresnel coefficients with antisymmetric conductivity tensor for the Kerr phase of the incident linearly polarized light. Moreover, it is demonstrated that at low temperatures, GH shifts map plateaus as the intensity of the magnetic field grows. This quantum modulation of the GH effect in graphene by an applied magnetostatic bias may open doors to new opportunities for optical devices and QHE sensing applications in 2D materials.