Tunable electronic correlations in 135-kagome metals

Kagome metals exhibit rich correlated-electron physics, yet a systematic understanding of the degree of correlation across transition-metal species remains elusive. Using density-functional theory plus multi-orbital slave-spin mean-field theory, we investigate electronic correlations in the Ti-, V-, and Cr-based 135 compounds with Sb and Bi pnictogens. We find that the significantly stronger degree of correlation of the Cr-based materials compared to Ti and V can only be explained through the synergy of two effects: the larger electron filling of the $d$-shell and the reduced characteristic kinetic energy. We put forward that the substitution of Sb with Bi strengthens correlations in all compounds and make the prediction that the-yet-to-be-synthesized CsCr$_3$Bi$_5$ must be the most strongly correlated member of the entire family. These findings provide a quantitative, band-structure-based framework for understanding and predicting correlation strength in Kagome metals.