  A number of topological phases are found to emerge in the ferromagnetic
Kitaev-Heisenberg model on CaVO lattice in the presence of
Dzyaloshinskii-Moriya interaction. Heisenberg and Kitaev terms have been
considered on nearest and next-nearest neighbor bonds in a variety of ways.
Both isotropic and anisotropic couplings are taken into account. Topological
phases are characterized by Chern numbers for the distinct magnon bands as well
as the number of modes for topologically protected gapless magnon edge states.
Band structure, dispersion relation along the high-symmetric points of first
Brillouin zone, density of states and thermal Hall conductance have been
evaluated for every phase. An extensive Phase diagram has been constructed.
Topological phase transition in the parameter space is also studied.
