Universal Hall conductivity in graphene Maxwell fish-eye quantum dot

TL;DR

This paper investigates the Hall conductivity in a graphene quantum dot with a Maxwell fish eye potential, revealing a universal value near zero energy using a quasiclassical approximation.

Contribution

It introduces a model of a graphene quantum dot with Maxwell fish eye potential and derives a universal Hall conductivity value at zero energy.

Findings

Universal Hall conductivity value identified near zero energy

Electron trajectories are closed circles classified by angular momentum

Spectrum degenerates macroscopically at zero energy

Abstract

Graphene quantum dot with Maxwell fish eye potential energy profile is studied. A quasiclassical approximation is used given that potential energy is a slowly varying function of coordinates. Near the zero energy the spectrum of electron macroscopically degenerates. All the electron trajectories are closed circles that are classified by angular momentum and an additional integral of motion. Provided the complete filling of the lower Dirac zone, a universal value for Hall conductivity is found.