Atomic Collapse in Disordered Graphene Quantum Dots

TL;DR

This study numerically investigates how disorder in graphene quantum dots affects atomic collapse, revealing that defects and potential fluctuations increase the critical Coulomb coupling needed for collapse, explaining experimental subcritical behavior.

Contribution

It demonstrates that disorder amplifies the critical coupling constant for atomic collapse in graphene quantum dots, providing new insights into experimental observations.

Findings

Disorder causes up to 34% increase in critical coupling.

Both lattice defects and potential fluctuations amplify atomic collapse threshold.

Results suggest atomic collapse can be observed in defect-rich graphene samples.

Abstract

In this paper, we numerically study a Coulomb impurity problem for interacting Dirac fermions restricted in disordered graphene quantum dots. In the presence of randomly distributed lattice defects and spatial potential fluctuations, the response of the critical coupling constant for atomic collapse is mainly investigated by local density of states calculations within the extended mean-field Hubbard model. We find that both types of disorder cause an amplification of the critical threshold. As a result, up to thirty-four percent increase in the critical coupling constant is reported. This numerical result may explain why the Coulomb impurities remain subcritical in experiments, even if they are supercritical in theory. Our results also point to the possibility that atomic collapse can be observed in defect-rich samples such as Ar$^{+}$ ion bombarded, He$^{+}$ ion irradiated, and hydrogenated graphene.