The influence of AA and AB stacking on the ground state magnetic properties of triangular bilayer graphene quantum dots

Abstract

Using the tight-binding model, we have studied the impact of AA and AB (Bernal) stacking on eigenstates and eigenvalues of bilayer graphene nanoflakes with triangular geometry. The zero eigenvalues of any single layer nanoflake will be doubled through AB stacking. However, we have noticed that in AA stacking, the eigenvalues are simply achievable through merging two sets of single layer eigenvalues that once added to and once subtracted from inter-layer hopping. Besides, in a single layer within some strict zero energies, the AB stacking still maintains them sublattice-polarized. However, the AA-stacking neglects the sublattice-polarized character of zero states in single layers constituent. Next, we consider onsite electron–electron interaction utilizing single-orbital Hubbard model to show how the different stacking affects the onset of the ground state magnetization in bilayer quantum dots with different stackings. Especially, in AA stacking bilayer, the system always needs a nonzero onsite interaction strength (Uc) to be magnetized.