Reinforcement of flat bands in a bilayer kagome metal

The geometric frustration of kagome metals leads to flat bands, resulting in rich correlated states. However, there is a deeper question regarding the formation of flat bands, i.e., whether the flat-band-induced strong correlations would in turn stabilize the kagome lattice and further reinforce the flat bands. Recently, flat bands and Kondo-like physics are observed in a bilayer kagome metal ${\mathrm{CsCr}}_{6}{\mathrm{Sb}}_{6}$. The inter-kagome-layer coupling provides another degree of freedom to explore such physics. Here, based on density functional theory plus dynamical mean-field theory (DFT+DMFT) calculations, we show extremely flat bands in ${\mathrm{CsCr}}_{6}{\mathrm{Sb}}_{6}$, consistent with experiment. As temperature decreases, it undergoes an incoherence-to-coherence crossover and shows a resonance peak near the Fermi level. Surprisingly, we find that the inter-kagome-layer distance will collapse by about 20% if ignoring the strong electron correlation in DFT calculations, which will destroy the flat bands near the Fermi level due to a significant enhancement of the interlayer orbital hybridization. In contrast, it will not collapse after capturing the strong correlations in DFT+DMFT calculations. We thus reveal a positive feedback effect in the kagome metal that flat bands would reinforce themselves by stabilizing the lattice via the strong correlations they induced. This goes beyond our common understanding that the kagome lattice directly leads to flat bands because of the destructive interference of electron hopping, but ignoring the strong positive feedback effect between the electron correlations and kagome lattice.