Heavy-fermions in frustrated Hund's metal with portions of incipient flat-bands

Flat-bands induced by destructive interference of hoppings in frustrated lattices such as kagome metals, have been extensively studied in recent years. However, such flat-bands usually appear in small portions of Brillouin zone and are away from Fermi level in the non-interacting limit (dubbed as ``incipient"). Whether such incipient flat-band portions can induce very strong electron correlations is an open question. Recently, such incipient flat-bands are found in frustrated kagome CsCr${}_3$Sb${}_5$ and triangular CrB${}_2$, which show moderately heavy-fermion behaviors and unconventional superconductivity. Here, by density functional theory plus dynamical mean-field theory calculations, we show that both compounds are typical Hund’s metals. The incipient flat-band portions induce dips in hybridization functions, which further enhance the Kondo-like effect of Hund’s metal, resulting in moderately heavy-fermion behaviors. This explains the origin of the heavy-fermion behaviors and pave the way for understanding the unconventional superconductivity in CsCr${}_3$Sb${}_5$ and CrB${}_2$. Our work demonstrates a flexible route for generating $d$-electron heavy-fermion and for inducing unconventional superconductivity based on frustrated Hund’s metals with portions of incipient flat-bands. A large family of materials with kagome, triangular, pyrochlore lattices consisting of Cr (d${}^4$), Ru (d${}^4$), Fe (d${}^6$) ions are promising candidates.