Ground state magnetic properties in AA-stacking bilayer graphene quantum dots using Lieb's theorem

We have studied magnetic properties of ground state in perfect AA-stacking bilayer graphene quantum dots. Our main model is the single-orbital tight-binding Hamiltonian that is supplemented with a mean field Hubbard term. In addition, density functional method has been exploited to gain more confidence in our findings. The calculations are performed for some random and triangular shape of AA-stacking bilayer quantum dots and always yield an antiferromagnetic ordering with a total spin S = 0 ground state. Despite computational results of Hubbard model is admirably compatible with Lieb's theorem, conventional crystallographic sublattices are not appropriate to interpret our computational results in terms of the theorem. Therefore, we have suggested a new sublattice decomposition to settle our numerical output to the consequences of Lieb's theorem. Especially we demonstrate some characteristic including polarization of local magnetization, degeneracies in the energy spectrum, the ferromagnetic and antiferromagnetic coupling of vacancies in our system have decisive compatibility with new proposed sublattice decomposition.