Electronic correlations shape the low-energy optical response of the kagome antiferromagnets Mn$_3$Sn and Mn$_3$Ge
Using optical spectroscopy and density functional theory, we provide evidence that electron-electron interactions strongly affect the properties of the kagome antiferromagnet Mn$_3$Sn, since its low-energy optical interband transitions arise exclusively from the correlation-modified electronic band structure. Mn$_3$Sn possesses an optical effective mass about three times larger than that of its isostructural analog Mn$_3$Ge. The DFT+$U$ treatment in the Lichtenstein formulation, with an on-site Coulomb repulsion $U = 4$~eV and Hund's coupling $J = 0.25$~eV, accounts for the optical transitions in Mn$_3$Sn, whereas those in Mn$_3$Ge are already reproduced without Hubbard corrections ($U, J = 0$). The near-isotropic electronic structure of Mn$_3$Sn reveals a three-dimensional metal whose electronic response is shaped prominently by the Mn $d$-states. The apparent linear regime in $σ_1(ω)$ observed in Mn$_3$Sn and Mn$_3$Ge arises from several overlapping interband transitions and therefore should not be interpreted as the optical signature of the Weyl cones. The optical response does not alter with magnetic field up to 17 T, consistent with strong free-carrier screening. Our findings establish a comprehensive-correlated picture of Mn$_3$Sn and Mn$_3$Ge that offers a template for other correlated topological metals.