Violation of Hund's rule and quenching of long-range electron-electron interactions in graphene nanoflakes

Hund's rule of maximum multiplicity controls the spin configuration of a system with degenerate midgap states, while Lieb's theorem determines the total spin of the ground state of a bipartite lattice. Most of graphene nanostructures follow both Hund's rule and Lieb's theorem, except that a number of nanoflakes with degenerate midgap states violates Hund's rule by exhibiting antiferromagnetic ground states as predicted by Lieb's theorem. To determine why Hund's rule fails and Lieb's theorem can predict correct spin configuration beyond the Hubbard model for which it was proved, we solve the strongly correlated electron states in such graphene nanoflakes where Hund's rule is violated by using a full configuration interaction approach. We find that long-range electron-electron interactions are quenched in both the ground and low-lying excited states of these systems. As there are no interactions between electrons with parallel spins in the system where long-range interactions are absent, we point out that a graphene nanoflake with degenerate midgap states and an antiferromagnetic ground state, in fact, falls very close to an ideal Hubbard system. Quenching of long-range interactions is therefore believed to be the natural explanation for the advantage of Lieb's theorem over Hund's rule in graphene nanostructures.