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Breakdown of the Quantum Hall Regime in a ‘Confined’ Graphene

Our focus is on the graphene under a magnetic field with Landau levels i.e. quantum Hall regime where a ‘confining potential’ is imposed by a finite electric field. In our theory, the graphene is modelled by a conventional fermion on a honeycomb lattice and the finite electric field is by a static potential. We reveal the fate/breakdown of the quantum Hall regime. A possible candidate of this kind of system is a grapheneQuantumDot, which we also discussed in the light of our theory.