Abstract
We derive the necessary conditions for creating electrostatically bounded electron or hole states in a suspended graphene monolayer by means of gate electrodes located underneath the graphene sheet. We show on the basis of semiclassical arguments and the Weyl-Dirac theory that electrons at the Dirac point can be confined by a resulting central potential provided it satisfies certain constraints that can be met by properly tuning the potential parameters, that is, the electrode charges or its distance from the graphene layer. As a result, a series of zero energy, stable, bounded eightfold degenerate quantum states of fixed angular momentum will form sequentially as the potential parameters are varied. The system considered has large extend so boundaries play no role in this effect.
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