Observation of negative refraction of Dirac fermions in graphene

Abstract

Half a century ago, Veselago(1) 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(2-4). However, an electronic counterpart has not been demonstrated owing to difficulties in creating repeated structures smaller than the electronic Fermi wavelength of the order similar to 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 structures(5). Analysis of both electron focusing through an n-p-n flat lens and negative refraction across n-p junctions confirms left-handed behaviour in the electronic system. This approach to electronic optics is of particular relevance to the on-going efforts to develop novel quantum devices with emergings layered materials.