Abstract
We present an analytical solution of the relativistic Dirac equation defined in the framework of quantum field theory in curved space and apply it to study the electronic properties of deformed monolayer graphene. We obtain as solution the Dirac oscillator equation where an effective vector potential term naturally appears. Such a term describes a pseudo-magnetic field which emerges due to the initially defined curvature, and influences the dynamics of the charge carriers as if these were under the influence of an applied external magnetic field.
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