Tunable unconventional kagome superconductivity in charge ordered RbV₃Sb₅ and KV₃Sb₅

Unconventional superconductors often feature competing orders, small superfluid density, and nodal electronic pairing. While unusual superconductivity has been proposed in the kagome metals AV₃Sb₅, key spectroscopic evidence has remained elusive. Here we utilize pressure-tuned (up to 2.25 GPa) and ultra-low temperature (down to 18 mK) muon spin spectroscopy to uncover the unconventional nature of superconductivity in RbV₃Sb₅ and KV₃Sb₅. At ambient pressure, we detect a two-step enhancement of the width of the internal magnetic field distribution sensed by the muon ensemble in RbV₃Sb₅, indicative of time-reversal symmetry breaking charge order below T₁^' = 110 K with an additional transition at T₂^' = 50 K. Remarkably, the superconducting state displays a nodal energy gap and a reduced superfluid density, which can be attributed to the competition with the novel charge order. Upon applying pressure, the charge-order transitions are suppressed, the superfluid density increases, and the superconducting state progressively evolves from nodal to nodeless. Once optimal superconductivity is achieved, after either full or partial suppression of charge order, we find a superconducting pairing state that is not only fully gapped, but also spontaneously breaks time-reversal symmetry. Our results point to unprecedented tunable nodal kagome superconductivity competing with time-reversal symmetry-breaking charge order and offer unique insights into the nature of the pairing state.