Lieb-Thirring and Cwickel-Lieb-Rozenblum inequalities for perturbed graphene with a Coulomb impurity

TL;DR

This paper investigates spectral properties of a two-dimensional Coulomb-Dirac operator relevant to graphene with impurities, establishing bounds on negative eigenvalues caused by electromagnetic disturbances.

Contribution

It provides new estimates on negative eigenvalues for the Coulomb-Dirac operator in graphene, extending spectral analysis to perturbed systems with Coulomb impurities.

Findings

Derived bounds on negative eigenvalues induced by electromagnetic perturbations.

Extended spectral analysis techniques to two-dimensional Coulomb-Dirac operators.

Applicable to understanding impurity effects in graphene's electronic properties.

Abstract

We study the two dimensional massless Coulomb-Dirac operator restricted to its positive spectral subspace and prove estimates on the negative eigenvalues created by electromagnetic perturbations.