Quantitative study of electronic whispering gallery modes in electrostatic-potential induced circular graphene junctions

TL;DR

This study demonstrates that electronic whispering gallery modes can emerge in various electrostatically induced circular graphene junctions, with small quality factors and nanometer-scale mode radii, aligning well with experimental observations.

Contribution

It provides a theoretical analysis showing EWGMs can occur in any electrostatic potential induced circular graphene junctions, expanding understanding of their formation and properties.

Findings

EWGMs can emerge in all types of electrostatic circular graphene junctions.

Quality factors of EWGMs are generally below 100.

Mode radii can be tuned to nanometer scales.

Abstract

Electronic Whispering Gallery Modes (EWGMs) have been recently observed in several circular graphene junctions, pn and pp0, created in scanning tunnelling microscope experiments. By computing the local density of states within the Dirac-Weyl formalism for massless fermions we demonstrate that the EWGMs may really be emerged in any type of the electrostatic potential induced circular graphene junctions, including uni-junctions (e.g. np- or pp0-junctions) as well as bipolar-junctions (e.g. pnp-heterojunctions). Surprisingly, quantitative analyses show that for all the EWGMs identified (regardless of junction types) the quality (Q) factors seem to be smaller than 100, very small compared to those in ordinary optical whispering gallery modes microresonators, while the corresponding mode radii may tunably be in nanometer-scale. Our theoretical results are in good agreement with existent experimental data, putting a question to the application potential of the EWGMs identified.