Magnetism and Correlations of Fractionally Filled Zero-energy States in Graphene Quantum Dots

We study electronic and magnetic properties of triangular graphene dots with zig-zag edges. Such structures have recently attracted attention due to the existance of a shell of degenerate states at the Fermi level, with half-filled shell exhibiting a magnetic moment[1,2,3]. In this work, we present new results demonstrating the important role of electronic correlations as a function of the filling fraction of the shell. The effect of degeneracy, finite size and electron-electron interactions are treated nonperturbatively using a combination of density functional theory, tight-binding, Hartree-Fock and configuration interaction methods. We show that the nature and magnetization of the ground state depend strongly on the filling fraction of the degenerate shell. Half-filled charge neutral shell leads to full spin polarization but this magnetic moment can be completely destroyed by adding a single electron. [1] J. Fernandez-Rossier and J.J. Palacios, Phys.Rev.Lett. {\bf 99}, 177204 (2007) [2] M. Ezawa, Phys.Rev.B, {\bf 77}, 155411 (2008) [3] Kaxiras {\it et al.}, Nano Lett. {\bf 8}, 241 (2008).