Tunable unconventional kagome superconductivity in charge ordered RbV(3)Sb(5) and KV(3)Sb(5)

Unconventional superconductors often feature competing orders, small superfluid density, and nodal electronic pairing. While unusual superconductivity has been proposed in the kagome metals AV(3)Sb(5), key spectroscopic evidence has remained elusive. Here we utilize pressure-tuned and ultra-low temperature muon spin spectroscopy to uncover the unconventional nature of superconductivity in RbV(3)Sb(5) and KV(3)Sb(5). At ambient pressure, we observed time-reversal symmetry breaking charge order below [Formula: see text] 110 K in RbV(3)Sb(5) with an additional transition at [Formula: see text] 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 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, 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.