The kagome lattice1, which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders2, 3,4,5,6,7,8 and, most rarely, to unconventional su-perconductivity6,9. Recently, charge sensitive probes have indicated that the kagome superconductors AV3Sb5 (A = K, Rb, Cs)9,10,11 exhibit unconventional chiral charge order12, 13,14,15,16,17,18,19, which is analogous to the long-sought-after quantum order in the Haldane model20 or Varma model21. However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV3Sb5. We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV3Sb5 and that the Tc/−2ab ratio (where Tc is the superconducting transition temperature and ab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.

Precise measurements of the thermodynamic critical field (Bc) in type-I noncentrosymmetric superconductor BeAu were performed by means of the muon-spin rotation/relaxation technique. The temperature evolution of Bc can not be described within the single gap scenario and it requires the presence of at least two different types of the superconducting order parameters. The selfconsistent two-gap approach, adapted for analysis of Bc(T ) behavior, suggests the presence of two superconducing energy gaps with the gap to Tc ratios 2∆/kBTc 4.52 and 2.37 for the big and the small gap, respectively. This implies that the superconductivity in BeAu is unconventional and that the supercarrier pairing occurs at various energy bands.BeAu is an old known superconductor with the transition temperature T c 3.2 K. Superconductivity in BeAu was originally discovered by Matthias in 1959, 1 i.e. just in two years after the formulation of the BCS theory. 2 In this short report, Matthias was noted the absence of a superconductivity in a pure Be and Au (Be was later found to have T c 26 mK, Ref.3) and performed a search within the gold-rich site of the Be-Au phase diagram. The superconductivity was found to appear in a stoichiometric (i.e. 1:1 Be to Au ratio) BeAu sample. 1Recently, the interest to BeAu was renewed. [4][5][6][7][8] This mostly relates to the realisation of their noncentrosymmetric crystal structure, which was expected to give rise to unconventional superconductivity due to spin-orbit coupling and/or mixed singlet/triplet pairing state (see e.g. Refs. 9-16 and references therein). In addition, the B20 FeSi-type of the crystal structure of BeAu becomes particualry interesting since such materials were predicted to host chiral fermions in topological semimetals. [17][18][19] Moreover, B20 structure is the only known crystal structure for bulk magnetic skyrmions in materials such as MnSi, Fe 1−x Co x Si, FeGe, MnGe, Cu 2 OSeO 3 etc. [20][21][22][23][24] All these make BeAu an intriguing candidate material to search for unconventional superconductivity, associated with its noncentrosymmetric crystal structure in combination with the possible existence of exotic quasiparticles.

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.

There is considerable evidence that the superconducting state of Sr2RuO4 breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking, its onset temperature, TTRSB, is generally found to match the critical temperature, Tc, within resolution. In combination with evidence for even parity, this result has led to consideration of a dxz ± idyz order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding TTRSB = Tc, but it has a hard-to-explain horizontal line node at kz = 0. Therefore, s ± id and d ± ig order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain TTRSB ≈ Tc. To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr2RuO4 under hydrostatic pressure, and Sr1.98La0.02RuO4 at zero pressure. Both hydrostatic pressure and La substitution alter Tc without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected, TTRSB should track changes in Tc, while if it is accidental, these transition temperatures should generally separate. We observe TTRSB to track Tc, supporting the hypothesis of dxz ± idyz order.

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