Tunable Electronic Correlations in 135-Kagome Metals

Abstract

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.

Figures (4)

• Figure 1: Orbital-resolved quasiparticle weights $Z_\alpha$ as a function of the orbital-resolved occupancy $n_\alpha$ of the transition metal. Orange, blue and green colors refer to CsTi$_3$Sb$_5$, CsV$_3$Sb$_5$, and CsCr$_3$Sb$_5$, respectively. For the different compounds, in going from left to right in each orbital, the symbols refer to a compound's total number of electrons ($N=$ 27, 30, and 33 for CsTi$_3$Sb$_5$, CsV$_3$Sb$_5$, and CsCr$_3$Sb$_5$, respectively). In each panel, the filled symbols mark the undoped occupancy of the corresponding compound, while the empty ones indicate the results of the simulations upon doping. Regardless of the $N$, CsCr$_3$Sb$_5$ shows the highest degree of renormalization. For each compound, $Z_\alpha$ as a function of $N$ are reported in the inset.
• Figure 2: Top panels: projected density of states for the less correlated orbital ($A_g^{d_{x^2-y^2}}$ of CsTi$_3$Sb$_5$, on the left) and the most correlated orbital ($B_{3g}$ of CsCr$_3$Bi$_5$, on the right) of the series Crispino_Kagome-Supp. Bottom panels: Orbital-resolved standard deviation $\sigma_\alpha$ as determined by the square of the second centered moment of the density of states for CsM$_3$Sb$_5$ with M=Ti, V, Cr (left panel), and CsM$_3$Bi$_5$ with M=Ti, Cr (right panel).
• Figure 3: Orbital-resolved quasiparticle weights as a function of the orbital-resolved occupancy of the transition metal for the Bi-based kagome metals. Magenta and gold colors represent CsTi$_3$Bi$_5$ and CsCr$_3$Bi$_5$ respectively. Simulations' results at pristine filling, corresponding to $N=$ 27 for CsTi$_3$Bi$_5$ and to 33 for CsCr$_3$Bi$_5$, are marked by the filled symbols. Empty symbols refer to the results of simulations upon doping.
• Figure 4: Imaginary part of the hybridization function $\Delta(\omega)$, specific to the most correlated $B_{3g}$ orbital, for the Sb- and Bi-derived compounds.