Quantum Goos-Hänchen Effect in Graphene

Abstract

The Goos-Hänchen (GH) effect is an interference effect on total internal reflection at an interface, resulting in a shift sigma of the reflected beam along the interface. We show that the GH effect at a p-n interface in graphene depends on the pseudospin (sublattice) degree of freedom of the massless Dirac fermions, and find a sign change of sigma at angle of incidence alpha=arcsin sqrt[sinalpha{c}] determined by the critical angle alpha{c} for total reflection. In an n-doped channel with p-doped boundaries the GH effect doubles the degeneracy of the lowest propagating mode, introducing a twofold degeneracy on top of the usual spin and valley degeneracies. This can be observed as a stepwise increase by 8e;{2}/h of the conductance with increasing channel width.

Topological Imbert-Fedorov Shift in Weyl Semimetals

“…2(c) shows the valley independence and potential dependence of GH shift ∆ GH , which can be tuned from positive to negative by external field V . This feature is analogous to the GH shift in graphene 15 . classical equation of motion (EOM) 1,35 of wave packet…”

“…Due to the IF shift being perpendicular to the incident plane, it is a generic 3D effect and could never appear in a 2D material, e.g. the graphene 15 . Furthermore, we demonstrate that the IF shift originates from the topological effect of the system, namely, the Berry curvature of the system.…”

“…For example, GH effect has been shown to exist in the systems of electrons [10][11][12] , neutrons 13 , atoms 14 , etc. Particularly for the 2D massless Dirac fermions in graphene systems, the GH shift can be manipulated from positive to negative by tuning an external electric field 15 . However, the IF effect has not been studied in non-optical systems.…”

Experimental Observation of Strong Edge Effects on the Pseudodiffusive Transport of Light in Photonic Graphene

“…The analogy between graphene and these structures strengthens our understanding of the physics common to these two-dimensional structures. In particular, the analogy with optics has already inspired researchers to predict known optical effects, such as negative refraction [10] and a Goos-Hänchen shift for electrons in graphene [11].Despite the success of graphene, the observation of effects predicted by theory often require samples with perfect edges of a well-defined configuration that can only be obtained by atomic scale engineering. In this Letter, we experimentally investigate a photonic crystal structure for microwave frequencies that is analogous to graphene and realize samples with ideal edges on a much more accessible millimeter length scale.…”

“…The analogy between graphene and these structures strengthens our understanding of the physics common to these two-dimensional structures. In particular, the analogy with optics has already inspired researchers to predict known optical effects, such as negative refraction [10] and a Goos-Hänchen shift for electrons in graphene [11].…”