Magnetic dispersion of Dirac fermions in graphene under inhomogeneous field profiles
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We address the exact relations for the energy spectrum of massive Dirac fermions of graphene for a class of position-dependent magnetic field profiles, which could be created under inhomogeneous strain fields, with possibility of inducing a Dirac gap. We then show that in the linear regime our results correspond well to the earlier approaches for the massless case. We also prove that our approach for obtaining the relativistic Landau levels of Dirac fermions created by a constant magnetic field together with a spatially varying normal pseudo-magnetic profile, which varies as \( 1/x^2\) , recovers well the earlier results in this regard. It turns out that, in this case, the associated Landau energy levels are obtained by considering two shape-invariant potentials which belong to the family of isotonic oscillators with a set of equally spaced energy levels.