  An analysis of the stability of topological states induced by Coulomb
repulsion on decorated honeycomb lattices is presented. Based on a mean-field
treatment of a spinless extended Hubbard model on the decorated honeycomb
lattice we show how the quantum anomalous Hall (QAH) phase is a robust
topological phase which emerges at various electron fillings and involves
either quadratic band crossing points (QBCP) or Dirac points of the bands. The
topological QAH phase is also found to be most stable against thermal
fluctuations up to moderate temperatures when the Coulomb repulsion is
maximally frustrated. We show how a topological metal can be induced from the
QAH by electron doping the system in a broad electron doping range. Electrons
on the Fermi surface of such metallic states are characterized by having a
non-zero Berry phase which gives rise to a non-zero intrinsic quantum Hall
conductivity.
