Unconventional superconductivity in Sc$_2$Ir$_{4-x}$Si$_x$ by spin-orbit coupling driven flat band

The kagome lattice is very attractive as it can host many novel quantum states, such as the charge density wave, superconductivity, quantum spin liquid, etc. Meanwhile, iridates often exhibit a strong spin-orbit coupling (SOC) effect due to the large atomic mass of 5$d$ elements, which has important implications for both the energy bands and the pairing symmetry of superconductors. For the Laves phase superconductor Sc$_2$Ir$_4$ with a kagome lattice, by doping Si to the Ir sites, we observed a nonmonotonic and two-dome like doping dependence of the superconducting transition temperature $T_{\rm c}$, which is typically found in many unconventional superconducting systems. Interestingly, for some samples, especially Sc$_2$Ir$_{3.5}$Si$_{0.5}$ with the optimal $T_{\rm c}$, after the suppression of superconductivity, the normal-state resistivity exhibits a semiconducting behavior; meanwhile, the specific heat coefficient shows an upturn which follows the relation $C/T\propto{\rm ln}(T_0/T)$ at low temperatures. Around the optimal doping, the resistance measurements exhibit strong superconducting fluctuations. And the superconductivity related specific heat can be fitted by the model of a $d$-wave gap after subtracting the normal-state background. These strongly suggest unconventional superconductivity and correlation effect in the samples, which is mainly induced by a flat band near the Fermi level when considering the SOC, as supported by the first-principles calculations. Our results reveal a new unconventional superconducting system Sc$_2$Ir$_{4-x}$Si$_x$ with strong correlation effects induced by the flat band in the kagome system with strong SOC.