Graphene physics via the Dirac oscillator in (2+1) dimensions
We show how the two-dimensional Dirac oscillator model can describe some properties of 
electrons in graphene. This model explains the origin of the left-handed chirality observed for 
charge carriers in monolayer and bilayer graphene. The relativistic dispersion relation observed 
for monolayer graphene is obtained directly from the energy spectrum, while the parabolic 
dispersion relation observed for the case of bilayer graphene is obtained in the non-relativistic 
limit. Additionally, if an external magnetic field is applied, the unusual Landau-level spectrum for 
monolayer graphene is obtained, but for bilayer graphene the model predicts the existence of a magnetic 
field-dependent gap. Finally, this model also leads to the existence of a chiral phase transition.