Goos-H\"anchen Shifts in Gapped Graphene subject to External Fields

TL;DR

This paper analytically investigates the Goos-H"anchen shifts in gapped graphene under external magnetic and oscillating potentials, revealing sign changes and zero shifts at resonances in tunneling modes.

Contribution

It provides a detailed analytical study of GH shifts in gapped graphene with external fields, highlighting their sign change and resonance behavior.

Findings

GH shifts change sign at Dirac points

GH shifts can be positive, negative, or zero

Zero GH shifts occur at transmission resonances

Abstract

We study Dirac fermions in gapped graphene that are subjected to a magnetic field and a potential barrier harmonically oscillating in time. The tunneling modes inside the gap and the associated Goos-H\"anchen (GH) shifts are analytically investigated. We show that the GH shifts in transmission for the central band and the first two sidebands change sign at the Dirac points $\epsilon+l\hbar\tilde{\omega}$ $(l=0,\pm 1)$. We also find that the GH shifts can be either negative or positive and becomes zero at transmission resonances.