Qualitative analysis of trapped Dirac fermions in graphene

TL;DR

This paper investigates how Dirac fermions in graphene can be confined using magnetic fields, deformations, or substrate inhomogeneities, providing theoretical conditions for confinement with practical examples.

Contribution

It introduces a variational approach to determine necessary and sufficient conditions for trapping Dirac fermions in graphene and related structures.

Findings

Derived conditions for fermion confinement in graphene

Applied variational principles to realistic trapping scenarios

Provided rigorous theoretical framework for quasi-particle trapping

Abstract

We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.