Zero-index metamaterials for Dirac fermion in graphene

We study the response of ballistic electron waves in graphene to a square array composed of gate-defined quantum dots when the incident energy is at the neutral point of the Dirac conical dispersion. The effective medium theory shows that the array will behave as a zero-refractive-index medium. Our simulations based on the rigorous multiple scattering theory corroborate that it can indeed exhibit various typical applications of zero-refractive-index media, such as the focusing effect of electron waves, the control over the propagation direction, and directional emission. The array is usually about one-wavelength thick so that the incident wave can penetrate it and the wave front can be tailored by engineering the geometrical shape of the emergent surface. The wave-manipulating behaviors based on zero-index metamaterials could open unprecedented opportunities to steer the flow of graphene electrons in novel manners and shape the wave front of electron beams at will.