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In this paper, we perform a systematic study on the electronic, magnetic, andtransport properties of the hexagonal graphene quantum dots (GQDs) witharmchair edges in the presence of a charged impurity using two differentconfigurations: (1) a central Coulomb potential and (2) a positively chargedcarbon vacancy. The tight binding (TB) and the half-filled extended Hubbardmodels are numerically solved and compared with each other in order to revealthe effect of electron interactions and system sizes. Numerical results pointout that off-site Coulomb repulsion leads to an increase in the criticalcoupling constant to $\beta_{\text{c}}$ = 0.6 for a central Coulomb potential.This critical value of the $\beta$ is found to be independent of GQD size,reflecting its universality even in the presence of electron-electroninteractions. In addition, a sudden downshift in the transmission peaks shows aclear signature of the transition from subcritical $\beta$ $<$$\beta_{\text{c}}$ to supercritical $\beta$ $>$ $\beta_{\text{c}}$ regime. Onthe other hand, for a positively charged vacancy, the collapse of the lowestbound state occurs at $\beta_{\text{c}}$ = 0.7 for the interacting case.Interestingly, the local magnetic moment, induced by a bare carbon vacancy, istotally quenched when the vacancy is subcritically charged, whereas the valleysplittings in electron and hole channels continue to exist in both regimes.

Collapse of the vacuum in hexagonal graphene quantum dots: a comparative study between the tight-binding and the mean-field Hubbard models