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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The recently discovered kagome superconductor CsV3Sb5 (Tc ≃ 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 γλ(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.

The recently discovered vanadium-based kagome metals AV 3 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 muonspin rotation/relaxation is used to study the signatures of TRSB of the charge order in CsV 3 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 TRSB = T CDW 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 * 30 K. Remarkably, this two-step feature becomes well pronounced when a magnetic field of 8 T is applied along the crystallographic c axis, thus indicating a field-induced enhancement of the electronic response at the CDW transition. These results point to a TRSB in CsV 3 Sb 5 by charge order with an onset of 95 K, followed by an enhanced electronic response below 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.

We present results of our comprehensive studies on single crystalline LaPtSi. Pronounced anomaly in electrical resistivity and heat capacity confirms the bulk nature of superconductivity (SC) and charge density wave (CDW) transition in the single crystals. While the charge density wave transition temperature is lower, the superconducting transition temperature is higher in single crystal compared to the polycrystalline sample. This result confirms the competing nature of CDW and SC. Another important finding is the anomalous temperature dependence of upper critical field H (T). We also report the anisotropy in the transport and magnetic measurements of the single crystal.