▎ 摘　　要

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 >= 12. 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 N-edge