Coherent field emission image of graphene predicted with a microscopic theory

TL;DR

This paper predicts a coherent field emission pattern from graphene edges, including a dark center and dragonfly pattern, due to quantum interference, which can be observed at high temperatures and used as a line electron source.

Contribution

It introduces a microscopic theory predicting observable interference patterns in graphene's field emission, highlighting coherence transmission into vacuum and novel electron source applications.

Findings

Interference pattern with dark center due to pi-electron parity

Dragonfly emission pattern predicted for armchair edges

Coherent emission observable up to thousand Kelvin

Abstract

Electrons in the mono-layer atomic sheet of graphene have a long coherence length of the order of micrometers. We will show that this coherence is transmitted into the vacuum via electric field assisted electron emission from the graphene edge. The emission current density is given analytically. The parity of the carbon pi-electrons leads to an image whose center is dark as a result of interference. A dragonfly pattern with a dark body perpendicular to the edge is predicted for the armchair edge whose emission current density is vanishing with the mixing angle of the pseudo-spin. The interference pattern may be observed up to temperatures of thousand Kelvin as evidence of coherent field emission. Moreover, this phenomenon leads to a novel coherent electron line source that can produce interference patterns of extended objects with linear sizes comparable to the length of the graphene edge.