Correlated charge order intertwined with time-reversal symmetry-breaking nodal superconductivity in the dual flat band kagome superconductor CeRu$_{3}$Si$_{2}$

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Kagome materials provide a powerful platform for exploring how flat electronic bands promote symmetry-breaking quantum states, yet studies have so far focused mainly on kagome-derived $d$-electron flat bands. In this paper, we introduce CeRu$_{3}$Si$_{2}$, a kagome superconductor in which our first-principles calculations show the coexistence of Ru $d$-orbital kagome flat bands and heavy-fermion flat bands derived from Ce$^{4+}$ $4f$-states. X-ray diffraction reveals a dominant 1/2 charge order with a much weaker 1/3 component persisting up to room temperature. Theoretical calculations further highlight the correlated nature of these charge-order states. Deep within the charge-ordered state, magnetoresistance emerges below 80 K and strengthens further below 30 K. Zero-field muon spin-rotation measurements show no time-reversal symmetry (TRS) breaking in the normal state, in contrast to LaRu$_{3}$Si$_{2}$ and YRu$_{3}$Si$_{2}$. However, an applied magnetic field induces weak magnetism. Across the $A$Ru$_{3}$Si$_{2}$ family ($A$ = La, Y, and Ce), the superconducting transition temperature $T_{\rm c}$ scales linearly with the onset temperature of normal-state TRS breaking $T_{\rm {TRSB}}$ and the magnitude of the field-induced magnetic response, revealing a direct positive correlation between normal-state symmetry breaking and superconductivity. Furthermore, we identify that CeRu$_{3}$Si$_{2}$ is the first 132-type kagome compound to host nodal superconductivity together with spontaneous internal magnetic fields, providing clear evidence for intrinsic TRS breaking in the superconducting state. These results establish CeRu$_{3}$Si$_{2}$ as a unique platform where intertwined kagome $d$- and heavy fermion $f$-electron flat bands generate a rich hierarchy of electronic orders.

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