Gradient-index electron optics in graphene pn junctions

TL;DR

This paper explores how smooth electrostatic potential variations in graphene pn junctions enable gradient-index electron optics, demonstrating potential for advanced electron beam control and novel device applications.

Contribution

It introduces the concept of gradient-index electron optics in graphene pn junctions and shows how semi-classical trajectories can predict current flow patterns.

Findings

Coherent current flow patterns align with semi-classical trajectories.

Forbidden regions increase reflections and create interference patterns.

Devices like Luneburg and Maxwell lenses are feasible in graphene.

Abstract

We investigate the electron transport in smooth graphene pn junctions, generated by gradually varying electrostatic potentials. The numerically calculated coherent current flow patterns can be understood largely in terms of semi-classical trajectories, equivalent to the ones obtained for light beams in a medium with a gradually changing refractive index. In smooth junctions, energetically forbidden regions emerge, which increase reflections and can generate pronounced interference patterns, for example, whispering gallery modes. The investigated devices do not only demonstrate the feasibility of the gradient-index electron optics in graphene pn junctions, such as Luneburg and Maxwell lenses, but may have also technological applications, for example, as electron beam splitters, focusers and waveguides. The semi-classical trajectories offer an efficient tool to estimate the current flow paths in such nano-electronic devices.