Observation of negative refraction of Dirac fermions in graphene

TL;DR

This paper demonstrates negative refraction of Dirac fermions in graphene, showing that electrons can behave like left-handed waves without complex nanostructuring, advancing electronic optics and quantum device development.

Contribution

It provides the first experimental evidence of negative refraction in graphene's Dirac fermions, leveraging its relativistic band structure without sub-wavelength engineering.

Findings

Electron focusing through a flat lens confirms negative refraction.

Negative refraction observed across n-p junctions in graphene.

Left-handed behavior demonstrated in electronic system.

Abstract

Half a century ago, Veselago proposed left-handed materials with negative permittivity and permeability, in which waves propagate with phase and group velocities in opposite directions. Significant work has been undertaken to attain this left-handed response, such as establishing a negative refractive index in so-called metamaterials, which consist of periodic sub-wavelength structures. However, an electronic counterpart has not been demonstrated owing to difficulties in creating repeated structures smaller than the electronic Fermi wavelength (\lambda_F) of the order ~ 10 nm. Here, without needing to engineer sub-wavelength structures, we demonstrate negative refractive behaviour of Dirac fermions in graphene, exploiting its unique relativistic band structure. Analysis of both electron focusing through a n-p-n flat lens and negative refraction across n-p junctions confirms left-handed behaviour in the electronic system. This new approach to electronic optics is of particular relevance to the on-going efforts to develop novel quantum devices with emerging layered materials.