Ferromagnetism and Wigner crystallization in Kagome graphene and its derivatives.

Electron interactions can be significantly magnified in regions of flat bands due to a divergence in the density of states, which gives rise to a variety of exotic many-body phenomena, despite that an experimental realization of the flat bands is still challenging. Here, we propose a type of carbon systems, dubbed "Kagome graphene/graphyne", for which our first-principles calculations showed a good mechanical stability, as well as a robust flat-band structure right below the Fermi level. These flat bands provide a testbed to explore strong correlation effects within the carbon family in a controllable way. Upon hole doping, the band splits due to spin polarization to result in a flat-band ferromagnetism. The maximum splitting strength at half filling is 0.77 eV. When the filling is reduced to 1/6, on the other hand, Wigner crystallization appears in which the electrons form localized closed circles to spontaneously break the translation symmetry. A possible experimental route to synthesize the Kagome graphenes is proposed.