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The tight-binding method is employed to investigate the effects of threetypical in-plane electric fields on the electronic structure of a triangularzigzag graphene quantum dot. The calculation shows that the single-electroneigenstates evolute independently in two subspaces no matter how the electricfields change. The electric field with fixed-geometry gates chooses severalscattered parts of the zero-energy eigenspace as the new zero-energyeigenstates, regardless of the field strength. Moreover, the new zero-energyeigenstates remain unchanged and the associated levels are linear as the fieldstrength. In contrast, the new nonzero-energy eigenstates mix mutually and theassociated levels are nonlinear as the field strength. By comparing the effectsof three electric fields, we demonstrate that the degeneracy of the zero-energyeigenstates accounts for the linearity of the associated levels.

The electronic structure of a graphene quantum dot: Electric-field-induced evolution in two subspaces