Consecutive Flat Chern Bands and Correlated States in Monolayer ReAg$_2$Cl$_6$

Abstract: We theoretically propose that van der Waals monolayer ReAg$2$Cl$_6$ have four consecutive flat Chern bands in the 120$^\circ$ spiral antiferromagnetic ground state. The nontrivial topology of these Chern bands emerges from the synergy between Re $t{2g}$ band folding with non-collinear spin configuration and spin-orbit coupling. By constructing maximally localized Wannier functions directly from first-principles calculations, the tight-binding model is developed to describe the consecutive Chern bands. Interestingly, many-body exact diagonalization and entanglement spectrum analysis suggest that correlated states such as fractional Chern insulator and charge density wave may appear in these Chern bands with $1/3$ filling. Furthermore, the spin configurations and band topology of Chern bands are tunable by external magnetic field. The general physics from the $d$ orbitals here applies to a large class of materials such as ReAg$_2$Br$_6$, ReAu$_2$I$_6$ and ReCu$_2X_6$ ($X$=Cl, Br, I). These notable predictions in pristine 2D materials, if realized experimentally, could offer a new playground for exploring correlated topological states at elevated temperature.