Zero-energy states of graphene triangular quantum dots in a magnetic field

We present a tight-binding theory of triangular graphene quantum dots (TGQD) with zigzag edge and broken sublattice symmetry in an external magnetic field. The lateral size quantization opens an energy gap, and broken sublattice symmetry results in a shell of degenerate states at the Fermi level. We derive a semianalytical form for zero-energy states in a magnetic field and show that the shell remains degenerate in a magnetic field, in analogy to the zeroth Landau level of bulk graphene. The magnetic field closes the energy gap and leads to the crossing of valence and conduction states with the zero-energy states, modulating the degeneracy of the shell. The closing of the gap with increasing magnetic field is present in all graphene quantum dot structures investigated irrespective of shape and edge termination.