Sublattice modulated superconductivity in the kagome Hubbard model

We identify a superconducting order featuring spatial pair modulations on the kagome lattice subject to on-site Hubbard $U$ and nearest-neighbor $V$ interactions. Within our functional renormalization group analysis, this state appears with a concomitant $d$-wave superconducting (SC) instability at zero lattice momentum, where it distinguishes itself through intra-unit-cell modulations of the pairing function thus breaking the discrete space group symmetry. The relative weight of the sublattice modulated superconductor (SMS) and $d$-wave SC is influenced by the absolute interaction strength and coupling ratio $V/U$. Parametrically adjacent to this domain at weak coupling, we find an intra-unit-cell modulated vestigial charge density wave and an $s$-wave SC instability. Our study provides a microscopic setting and thorough description of this novel SMS arising within a translation symmetry broken background.