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 and ultra-low temperature muon spin spectroscopy to uncover the unconventional nature of superconductivity in RbV₃Sb₅ and KV₃Sb₅. At ambient pressure, we observed time-reversal symmetry breaking charge order below $${T}_{{{{{{{{\rm{1}}}}}}}}}^{*}\simeq$$T 1 * ≃ 110 K in RbV₃Sb₅ with an additional transition at $${T}_{{{{{{{{\rm{2}}}}}}}}}^{*}\simeq$$T 2 * ≃ 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.

The recently discovered kagome superconductor CsV₃Sb₅ (T_c ≃ 2.5 K) has been found to host charge order as well as a non-trivial band topology, encompassing multiple Dirac points and probable surface states. Such a complex and phenomenologically rich system is, therefore, an ideal playground for observing unusual electronic phases. Here, we report anisotropic superconducting properties of CsV₃Sb₅ by means of transverse-field muon spin rotation (μSR) experiments. The fits of temperature dependences of in-plane and out-of-plane components of the magnetic penetration depth suggest that the superconducting order parameter may have a two-gap (s + s)-wave symmetry. The multiband nature of superconductivity could be further supported by the different temperature dependences of the anisotropic magnetic penetration depth γ_λ(T) and upper critical field $${\gamma }_{{{{{\rm{B}}}}}_{{{{\rm{c}}}}2}}(T)$$γ B c 2 ( T ) . The relaxation rates obtained from zero field μSR experiments do not show noticeable change across the superconducting transition, indicating that superconductivity does not break time reversal symmetry.

We report muon spin rotation ($\mu \mathrm{SR}$) experiments together with first-principles calculations on microscopic properties of superconductivity in the kagome superconductor ${\mathrm{LaRu}}_3{\mathrm{Si}}_2$ with $T_{\mathrm{c}}\simeq$ 7K. Below $T_{\mathrm{c}}$, $\mu \mathrm{SR}$ reveals type-II superconductivity with a single s-wave gap, which is robust against hydrostatic pressure up to 2 GPa. We find that the calculated normal state band structure features a kagome flat band, and Dirac as well as van Hove points formed by the Ru-$d{z}^2$ orbitals near the Fermi level. We also find that electron-phonon coupling alone can only reproduce a small fraction of $T_{\mathrm{c}}$ from calculations, which suggests other factors in enhancing $T_{\mathrm{c}}$ such as the correlation effect from the kagome flat band, the van Hove point on the kagome lattice, and the high density of states from narrow kagome bands. Our experiments and calculations taken together point to nodeless moderate coupling kagome superconductivity in ${\mathrm{LaRu}}_3{\mathrm{Si}}_2$.