Electrostatic confinement of electrons in an integrable graphene quantum dot

TL;DR

This study investigates how the shape of a gated region in graphene influences electron confinement, showing that regular shapes support confined states while chaotic shapes do not, affecting conductance behavior.

Contribution

It provides a comparative analysis of conductance in graphene quantum dots with regular and chaotic classical dynamics, highlighting the role of shape in electron confinement.

Findings

Sharp conductance resonances in regular (disc-shaped) regions

Loss of conductance dependence in chaotic (stadium-shaped) regions

Confined electronic states are linked to regular classical dynamics

Abstract

We compare the conductance of an undoped graphene sheet with a small region subject to an electrostatic gate potential for the cases that the dynamics in the gated region is regular (disc-shaped region) and classically chaotic (stadium). For the disc, we find sharp resonances that narrow upon reducing the area fraction of the gated region. We relate this observation to the existence of confined electronic states. For the stadium, the conductance looses its dependence on the gate voltage upon reducing the area fraction of the gated region, which signals the lack of confinement of Dirac quasiparticles in a gated region with chaotic classical electron dynamics.