Exotic Fractional Topological States in Two-Dimensional Organometallic Material

Fractional Chern insulators (FCIs), having properties similar to those of the fractional quantum Hall effect, have been established numerically in various toy models. To fully explore their fundamental physics and to develop practical applications, material realization is indispensable. Here we theoretically predict a realization of FCI in a two-dimensional organometallic material, which is known to have the prerequisite topological at bands. Using numerical exact diagonalization we demonstrate that the presence of strong electronic correlations and fractional filling of such a system could lead to a rich phase diagram, including Abelian fractional quantum Hall (FQH), Fermi-liquid, and Wigner crystal states. In particular, the FQH state has been confirmed systematically by calculating the topological ground-state degeneracies, topological Chern number, and the quasihole excitation spectrum as well as the particle entanglement spectrum. Future experimental realization of the FQH state in such material may provide a route for developing practical applications of FCI with no need of the extreme conditions.