Electron optics with ballistic graphene junctions

TL;DR

This paper demonstrates electron refraction, including negative refraction, across graphene pn junctions using transverse magnetic focusing, confirming theoretical predictions and guiding future electron optics device design.

Contribution

It provides the first robust experimental evidence of negative refraction and perfect lensing in graphene pn junctions, aligning with theoretical models.

Findings

Confirmed Snell's law for electrons in graphene

Observed both positive and negative refraction

Measured angle-dependent transmission coefficients

Abstract

Electrons transmitted across a ballistic semiconductor junction undergo refraction, analogous to light rays across an optical boundary. A pn junction theoretically provides the equivalent of a negative index medium, enabling novel electron optics such as negative refraction and perfect (Veselago) lensing. In graphene, the linear dispersion and zero-gap bandstructure admit highly transparent pn junctions by simple electrostatic gating, which cannot be achieved in conventional semiconductors. Moreover ballistic transport over micron length scales at ambient temperature has been realized, providing an ideal platform to realize a new generation of device based on electron lensing. Robust demonstration of these effects, however, has not been forthcoming. Here we employ transverse magnetic focusing to probe propagation across an electrostatically defined graphene junction. We find perfect agreement with the predicted Snells law for electrons, including observation of both positive and negative refraction. Resonant transmission across the pn junction provides a direct measurement of the angle dependent transmission coefficient, and we demonstrate good agreement with theory. Comparing experimental data with simulation reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing novel electron optics based on graphene pn junctions.