Isolated nearly flat higher Chern band in monolayer transition metal trihalides

Abstract

The interplay between non-trivial topology and strong electron interaction can generate a variety of exotic quantum matter. Here we theoretically propose that monolayer transition metal trihalides MoF$_3$ and W$X_3$ ($X$= Cl, Br, I) have isolated nearly flat band near the Fermi level with higher Chern number $\mathcal{C}=+3$ and $\mathcal{C}=-2$, respectively. The nontrivial topology of these flat Chern bands originates from the effective $sd^2$ hybridization of transition metal atom, which transform the apparent atomic $d$ orbitals on a hexagonal lattice into $(s, p_+, p_-)$ orbitals on a triangular lattice. Interestingly, the quantum geometry of flat Chern bands in these materials are comparable with those in moir\'e systems exhibiting fractional Chern insulator state. The Hofstadter butterfly of such flat Chern bands are further studied. These natural materials, if realized experimentally, could offer new platforms to explore correlated phenomena driven by flat Chern band with higher Chern number.