No abstract

The electronic orders in Hubbard models on a Kagome lattice at van Hove filling are of intense current interest and debate. We study this issue using the singular-mode functional renormalization group theory. We discover a rich variety of electronic instabilities under short range interactions. With increasing on-site repulsion U , the system develops successively ferromagnetism, intra unitcell antiferromagnetism, and charge bond order. With nearest-neighbor Coulomb interaction V alone (U = 0), the system develops intra-unit-cell charge density wave order for small V , s−wave superconductivity for moderate V , and the charge density wave order appears again for even larger V . With both U and V , we also find spin bond order and chiral d x 2 −y 2 + idxy superconductivity in some particular regimes of the phase diagram. We find that the s-wave superconductivity is a result of charge density wave fluctuations and the squared logarithmic divergence in the pairing susceptibility. On the other hand, the d-wave superconductivity follows from bond order fluctuations that avoid the matrix element effect. The phase diagram is vastly different from that in honeycomb lattices because of the geometrical frustration in the Kagome lattice.

We study the electronic instabilities of near 1/4 electron doped graphene using the singular-mode functional renormalization group, with a self-adaptive k-mesh to improve the treatment of the van Hove singularities, and variational Monte-Carlo method. At 1/4 doping the system is a chiral spin density wave state exhibiting the anomalous quantized Hall effect. When the doping drops below 1/4, the d x 2 −y 2 + idxy Cooper pairing becomes the leading instability. Our results suggest that near 1/4 electron-or hole-doping (away from the neutral point) the graphene is either a Chern insulator or a topoligical superconductor.