Superconducting pairing symmetries in charge-ordered kagomé metals

We investigate the superconducting state in a kagomé lattice, with intertwined charge order and time-reversal symmetry-breaking loop current, using self-consistent Bogoliubov-de Gennes formalism to find the emergent pairing symmetries. Using local and nearest-neighbor attractive interactions, treated within Hartree-Fock mean-field approximation, we obtain all possible pairing symmetries in position space. Our findings indicate that the uniform s-wave symmetry, arising in the absence of the charge order and the loop current, modifies to a pair density wave of s-wave symmetry of 2×2 lattice periodicity in the presence of the charge order, and a chiral pair density wave of dx²-y²\!+\!idxy-wave symmetry of the same 2×2 periodicity in the presence of the charge order and loop current order, in both onsite and nearest-neighbor channels. In the absence of inversion symmetry, such as in the thin-film geometry, Rashba spin-orbit coupling appears, inducing an additional nearest-neighbor triplet pₓ± ipy-wave pairing. The results are relevant to superconductivity found in AV₃Sb₅ (A = K, Rb, Cs), coexisting with a charge order that breaks time-reversal symmetry. We discuss fingerprints of these different pairing symmetries in scanning tunneling microscopy experiments.