Individual band with higher Chern numbers in double perovskite {001} monolayers

We show a tight-binding model for double perovskite monolayers grown in the {001} crystallographic direction can exhibit higher Chern numbers for the lowest band of the model dispersion in the absence of an applied magnetic field, including $\pm2$, $\pm4$, $\pm6$, and $\pm8$, for model parameters and terms relevant to Sr$_2$CrWO$_6$ (SCWO). We further show it is possible to tune between these different topological phases by applying a weak in-plane magnetic field. These results may be important for experimentally realizing exotic band topologies -- and even quantum anomalous Hall insulators with higher Chern numbers -- based on this physics.