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 N₄₃₆₄ 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 N₄₃₆₄<12 and approximate CI method for N₄₃₆₄12. For a half-filled neutral shell we find spin-polarized ground state for structures up to N=500 atoms in agreement with previous 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 N₄₃₆₄9. 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.