Boundary conditions in the Dirac approach to graphene devices

TL;DR

This paper investigates boundary conditions for the Dirac equation in graphene, identifying MIT bag conditions as most consistent with experiments and calculating Casimir energy for nanotubes.

Contribution

It introduces a family of boundary conditions for graphene Dirac models and demonstrates that MIT bag conditions best match experimental data, also computing Casimir energy for nanotubes.

Findings

MIT bag boundary conditions align closely with experiments

Casimir energy for nanotubes evaluated using zeta function regularization

Limit of nanoribbons behavior clearly determined

Abstract

We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the ones which are in closest agreement with available experiments. For nanotubes of arbitrary chirality satisfying these last boundary conditions, we evaluate the Casimir energy via zeta function regularization, in such a way that the limit of nanoribbons is clearly determined.