Resonant scattering in graphene with a gate-defined chaotic quantum dot

TL;DR

This paper studies how the shape of a quantum dot affects electron conductance in graphene, revealing distinct resonance behaviors for chaotic versus integrable geometries using Green function methods.

Contribution

It demonstrates the impact of quantum dot shape on conductance resonances in graphene, highlighting differences between chaotic and integrable geometries.

Findings

Stadium-shaped dots exhibit Fano resonances that cross over to Breit-Wigner resonances.

Disc-shaped dots show persistent sharp Breit-Wigner resonances.

Resonance behavior depends on the classical dynamics of the quantum dot shape.

Abstract

We investigate the conductance of an undoped graphene sheet with two metallic contacts and an electrostatically gated island (quantum dot) between the contacts. Our analysis is based on the Matrix Green Function formalism, which was recently adapted to graphene by Titov {\em et al.} [Phys.\ Rev.\ Lett.\ {\bf 104}, 076802 (2010)]. We find pronounced differences between the case of a stadium-shaped dot (which has chaotic classical dynamics) and a disc-shaped dot (which has integrable classical dynamics) in the limit that the dot size is small in comparison to the distance between the contacts. In particular, for the stadium-shaped dot the two-terminal conductance shows Fano resonances as a function of the gate voltage, which cross-over to Breit-Wigner resonances only in the limit of completely separated resonances, whereas for a disc-shaped dot sharp Breit-Wigner resonances resulting from higher angular momentum remain present throughout.