Boundary conditions in the Dirac approach to graphene devices

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.

10 pages, no figure. Section on Casimir energy added

References in corpus (11)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Graphene: Status and Prospects
• Energy Band Gap Engineering of Graphene Nanoribbons
• Electronic States of Graphene Nanoribbons
• Electron Transport in Disordered Graphene Nanoribbons
• Conductance Quantization in Graphene Nanoribbons
• Casimir interaction between a perfect conductor and graphene described by the Dirac model
• Observation of excited states in a graphene quantum dot
• Spectrum of $\pi$ Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance
• Dirac electrons in graphene-based quantum wires and quantum dots

Cited by in corpus (10)

• The Casimir effect for fermionic currents in conical rings with applications to graphene ribbons
• Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons
• Induced fermionic charge and current densities in two-dimensional rings
• Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession
• Worldline approach for spinor fields in manifolds with boundaries
• Zeroes of combinations of Bessel functions and mean charge of graphene nanodots
• Casimir effect for fermion condensate in conical rings
• Finite temperature fermionic charge and current densities in conical space with a circular edge
• Conditions for Conductance Quantization in Mesoscopic Dirac Systems on the Examples of Graphene Nanoconstrictions
• Massive fermion between two parallel chiral plates