Genuine pair density wave order on the kagome lattice

The pair density wave (PDW) is a novel superconducting state with non-zero center-of-mass momentum Cooper pairing in the absence of external magnetic fields. Its realization in microscopic models as the ground state is very rare and extremely challenging, because a genuine PDW state is free of a uniform component or modulations by a pre-existing spin/charge density wave order at the same wavevector. Here, we report the discovery of a genuine primary PDW phase in a two-orbital Hubbard model on the kagome lattice by state-of-art functional renormalization group studies. It emerges out of competing orders over a wide physical parameter range suitable for realistic material realizations. The key ingredients in favor of the PDW order are the strongly sublattice and orbital polarized Bloch states on multiple Fermi pockets. They force the zero-momentum Cooper pairing to involve the same sublattices and be suppressed by onsite Coulomb repulsion, while pairing between different sublattices to be dominated by different Fermi pockets with nonzero total momentum. The degenerate PDW states at three momenta ${\bf M}_{1,2,3}$ on the Brillouin zone boundary exhibit novel intertwined order and can linearly combine into topologically nontrivial chiral PDW states. We propose that the model can be realized in multiorbital kagome materials such as CsCr$_3$Sb$_5$ as well as cold atom systems.