Abstract
We explain the dynamics of charge carriers in graphene using a two dimensional Dirac oscillator in the presence of an external magnetic field. The energy dispersion relation with linear behavior corresponds to monolayer graphene in a relativistic regime, whereas parabolic behavior appears in the case of bilayer graphene in a non-relativistic regime. We show that in the bilayer graphene model, a magnetic field-dependent energy gap exists, whereas a changing external magnetic field leads to a chiral phase transition. Our model explains the phenomenon of collapse and revivals and chiral phase transition in the presence of a magnetic field in monolayer and bilayer graphene. The displayed collapses and revivals occur due to Zitterbewegung and classical cyclotron motion.
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