Robust $A_1$ superconductivity in the kagome lattice

We theoretically studied the superconducting pairing in a single-orbital kagome lattice. By taking the electron-electron correlation as the pairing mechanism, we obtained the spin and charge fluctuations based on the random-phase approximation and calculated the preferred pairing function based on the linearized Eliashberg equation. It turns out that the frequency dependence of the Eliashberg equation is of great importance in this model, and may lead to spin-triplet and odd-frequency pairing state. We further found a robust $A_1$ pairing symmetry, with respect to the correlation strength and Fermi surface variation. This pairing state does not break the time-reversal symmetry and can be nodal or nodeless. We concluded that, in the recently discovered kagome superconductors, the preferred pairing symmetry is $A_1$, even if the pairing originates from the electron-electron interaction.