Effect of Energy Band Gap in Graphene on Negative Refraction through the Veselago Lens and Electron Conductance

Abstract

A remarkable property of intrinsic graphene is that upon doping, electrons and holes travel through the monolayer thick material with constant velocity which does not depend on energy up to about $0.3$ eV (Dirac fermions), as though the electrons and holes are massless particles and antiparticles which move at the Fermi velocity $v_F$. Consequently, there is Klein tunneling at a $p-n$ junction, in which there is no backscattering at normal incidence of massless Dirac fermions. However, this process yielding perfect transmission at normal incidence is expected to be affected when the group velocity of the charge carriers is energy dependent and there is non-zero effective mass for the target particle. We investigate how away from normal incidence the combined effect of incident electron energy $\epsilon$ and band gap parameter $\Delta$ can determine whether a $p-n$ junction would allow focusing of an electron beam by behaving like a Veselago lens with negative refractive index. We demonstrate that there is a specific region in $\epsilon -\Delta$ space where the index of refraction is negative, i.e., where monolayer graphene behaves as a metamaterial. Outside this region, the refractive index may be positive or there may be no refraction at all. We compute the ballistic conductance across a $p-n$ junction as a function of $\Delta$ and $\epsilon$ and compare our results with those for a single electrostatic potential barrier and multiple barriers.

15 pages and 8 figures

References in corpus (9)

• The electronic properties of graphene
• Energy Band Gap Engineering of Graphene Nanoribbons
• Chiral tunneling and the Klein paradox in graphene
• Substrate-induced band gap opening in epitaxial graphene
• Andreev reflection and Klein tunneling in graphene
• Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
• Caustics due to Negative Refractive Index in Circular Graphene p-n Junctions
• Bilayer graphene with single and multiple electrostatic barriers: band structure and transmission
• Lithography-free Fabrication of High Quality Substrate-supported and Freestanding Graphene devices

Cited by in corpus (5)

• Many-Body Effects and Optical Properties of Single- and Double Layer $\alpha$-${\mathcal{T}}_3$ Lattices
• Adatom Doping-Enriched Geometric and Electronic Properties of Pristine Graphene: a Method to Modify the Band Gap
• Coherent-scatterer enhancement and Klein-tunneling suppression by potential barriers in gapped graphene with chirality-time-reversal symmetry
• Floquet Control of Electron and Exciton Transport in Kekulé-Distorted Graphene
• Plasmon damping rates in Coulomb-coupled two-dimensional layers in a heterostructure