  The study of electronic and magnetic properties of kagome lattice has been an
active research area searching for topological phases of matters. In
particular, the kagome system with transition metal stannides and etc exhibit
interesting anomalous Hall effects driven by ferromagnetic or non-collinear
magnetic ordering. In this paper, motivated by these pioneer works, we study
strongly correlated spin-orbit coupled electrons in kagome lattice at 1/3
filling. Using both Hartree-Fock approach and effective model analysis, we
report quantum phase transitions accompanied with distinct charge and magnetic
ordered phases. Especially, for strongly interacting limit, we discover new
types of 1(2)-pinned metallic states which are understood by effective
localized electron models. Furthermore, when spin-orbit coupling is present, it
turns out that such pinned metallic states open a wide region of Chern
insulating phase with chiral spin ordering. Thus, quantum anomalous Hall effect
is expected with emergent scalar spin chirality. Our theory provides a
theoretical platform of strongly interacting kagome metal which is applicable
to transition metal stannides.
