  Motivated by the research interests on realizing flat bands and magnetization
plateaus in kagome lattices, we study the electronic properties and magnetic
interactions in both zero- and one-dimensional triangular Kagome lattice
(1D-TKL) models, by using the real-space Greens function approach in
tight-binding model. We firstly study the electronic properties of both 0D and
1D-TKL in the presence of staggered sublattice potential, then, by analyzing
the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction in these lattice
structures, the magnetic ground states of both 0D and 1D-TKL in the presence of
two magnetic adatoms are evaluated. It is found that the 1D channels of TKL
show different electronic and magnetic behaviors due to different values of the
hopping integrals and spin-orbit couplings. Two important salient features of
these TKLs are the presence of flat bands in their band structure as well as
the emergence of the RKKY plateaus versus the Fermi energy. These RKKY plateaus
have not been reported before, to the best of our knowledge. The most
remarkable observation is the potential and Fermi energy variation of the width
and location of the RKKY plateaus in both 0D and 1D TKLs. The spatial
configurations of the magnetic impurities can also dramatically change the
quality and quantity of the RKKY plateaus. We believe that our results provide
significant insights towards designing further experiments to search for the
realizing of the flat bands and magnetization plateau phases in spintronics and
pseudospin electronics devices based on TKLs.
