Fluctuation Phenomena in Chaotic Dirac Quantum Dots: Artificial Atoms on Graphene Flakes

TL;DR

This paper develops a theoretical model for Dirac quantum dots on graphene, providing analytical results for conductance and correlations, confirming the applicability of Random Matrix Theory to Dirac electrons in confined geometries.

Contribution

It introduces a stub model for Dirac quantum dots on graphene and derives analytical expressions for conductance and correlation functions, validating the use of Random Matrix Theory.

Findings

Analytical expressions match previous semiclassical results.

Random Matrix Theory effectively describes Dirac electrons in quantum dots.

Comparison with experimental data supports the model's validity.

Abstract

We develop the stub model for the Dirac Quantum Dot, an electron confining device on a grapheme surface. Analytical results for the average conductance and the correlation functions are obtained and found in agreement with those found previously using semiclassical calculation. Comparison with available data are presented. The results reported here demonstrate the applicability of Random Matrix Theory in the case of Dirac electrons confined in a stadium.