Electronic properties of gated triangular graphene quantum dots: Magnetism, correlations, and geometrical effects

We present a theory of electronic properties of gated triangular graphene quantum dots with zigzag edges as a function of size and carrier density. We focus on electronic correlations, spin and geometrical effects using a combination of atomistic tight-binding, Hartree-Fock and configuration interaction methods (TB+HF+CI) including long range Coulomb interactions. The single particle energy spectrum of triangular dots with zigzag edges exhibits a degenerate shell at the Fermi level with a degeneracy N_{edge} proportional to the edge size. We determine the effect of the electron-electron interactions on the ground state, the total spin and the excitation spectrum as a function of a shell filling and the degeneracy of the shell using TB+HF+CI for N_{edge} < 12 and approximate CI method for N_{edge}\geq 12. For a half-filled neutral shell we find spin polarized ground state for structures up to N=500 atoms in agreement with previous {\it ab initio} and mean-field calculations, and in agreement with Lieb's theorem for a Hubbard model on a bipartite lattice. Adding a single electron leads to the complete spin depolarization for N_{edge}\leq 9. For larger structures, the spin depolarization is shown to occur at different filling factors. Away from half-fillings excess electrons(holes) are shown to form Wigner-like spin polarized triangular molecules corresponding to large gaps in the excitation spectrum. The validity of conclusions is assessed by a comparison of results obtained from different levels of approximations. While for the charge neutral system all methods give qualitatively similar results, away from the charge neutrality an inclusion of all Coulomb scattering terms is necessary to produce results presented here.