Chemical enhancement of superconductivity in LaRu3Si2 with mode-selective coupling between kagome phonons and flat bands

In kagome metals, flat electronic bands induced by frustrated hopping are a platform for strong electron correlations. In particular, a selective coupling of flat band states to certain kagome phonon modes is proposed as a universal origin of superconductivity in this material class. Here, we investigate the superconductivity in the kagome system LaRu${}_3$(Si${}_{1-x}$Ge${}_x$)${}_2$ by chemical pressure tuning while preserving the Ru-$4d$ states that constitute the kagome flat bands. We observe a sizable enhancement in the density of states up to $x=0.07$, as determined by the specific heat, with a concomitant increase in the superconducting transition temperature $T_{\mathrm{c}}$. Ge-dopants induce a uniaxial lattice expansion along the $c$-axis. Our first-principles calculations suggest that this mitigates the detrimental effect of hybridization between kagome layers and reduces the dispersion of the Ru-$4d_{x^2-y^2}$ flat band. The calculated chemical potential moves closer to the maximum in the energy-dependent density of states. Our result is consistent with a theoretical prediction of tunable flat band superconductivity in LaRu${}_3$Si${}_2$ by mode-selective coupling between specific kagome phonons and the Ru-$d_{x^2-y^2}$ orbitals.