Atomic collapse in graphene quantum dots in a magnetic field

We investigate finite size and external magnetic field effects on the atomic collapse due to a Coulomb impurity placed at the center of a hexagonal graphene quantum dot within tight binding and mean-field Hubbard approaches. For large quantum dots, the atomic collapse effect persists when the magnetic field is present, characterized by a series of Landau level crossings and anticrossings, in agreement with previous bulk graphene results. However, we show that a new regime arises if the size of the quantum dot is comparable to or smaller than the magnetic length: While the lowest bound states cross the Fermi level at a lower value of coupling constant beta < 0.5, a size independent critical coupling constant beta(c)* > 0.5 emerges in the local density of states spectrum, which increases with the applied magnetic field. These effects are found to be persistent in the presence of electron-electron interactions within mean-field Hubbard approximation.