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 vanadium-based kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$ = K, Rb, Cs) exhibit superconductivity at low temperatures and charge density wave (CDW) order at high temperatures. A prominent feature of the charge ordered state in this family is that it breaks time-reversal symmetry (TRSB), which is connected to the underlying topological nature of the band structure. In this work, a powerful combination of zero-field and high-field muon-spin rotation/relaxation is used to study the signatures of TRSB of the charge order in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, as well as its anisotropic character. By tracking the temperature evolution of the in-plane and out-of-plane components of the muon-spin polarization, an enhancement of the internal field width sensed by the muon-spin ensemble was observed below $T_{\mathrm{TRSB}}=T_{\mathrm{CDW}}\simeq 95$ K. Additional increase of the internal field width, accompanied by a change of the local field direction at the muon site from the $ab$ plane to the $c$ axis, was detected below $T^{*}\simeq 30$ K. Remarkably, this two-step feature becomes well pronounced when a magnetic field of 8 T is applied along the crystallographic $c\mathrm{axis}$, thus indicating a field-induced enhancement of the electronic response at the CDW transition. These results point to a TRSB in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ by charge order with an onset of $\simeq 95$ K, followed by an enhanced electronic response below $\simeq 30$ K. The observed two-step transition is discussed within the framework of different charge-order instabilities, which, in accordance with density functional theory calculations, are nearly degenerate in energy.

Magnetic topological phases of quantum matter are an emerging frontier in physics and material science. Along these lines, several kagome magnets have appeared as the most promising platforms. Here, we explore magnetic correlations in the kagome magnet Co₃Sn₂S₂. Using muon spin-rotation, we present evidence for competing magnetic orders in the kagome lattice of this compound. Our results show that while the sample exhibits an out-of-plane ferromagnetic ground state, an in-plane antiferromagnetic state appears at temperatures above 90 K, eventually attaining a volume fraction of 80% around 170 K, before reaching a non-magnetic state. Strikingly, the reduction of the anomalous Hall conductivity (AHC) above 90 K linearly follows the disappearance of the volume fraction of the ferromagnetic state. We further show that the competition of these magnetic phases is tunable through applying either an external magnetic field or hydrostatic pressure. Our results taken together suggest the thermal and quantum tuning of Berry curvature induced AHC via external tuning of magnetic order.