Comparison of different methods for analyzing μSR line shapes in the vortex state of type-II superconductors

Tuning of the flat band and its impact on superconductivity in Mo5Si3-xPx

The superconductivity in systems containing dispersionless (flat) bands is seemingly paradoxical, as traditional Bardeen-Cooper-Schrieffer theory requires an infinite enhancement of the carrier masses. However, the combination of flat and steep (dispersive) bands within the multiple band scenario might boost superconducting responses, potentially explaining high-temperature superconductivity in cuprates and metal hydrides. Here, we report on the magnetic penetration depths, the upper critical field, and the specific heat measurements, together with the first-principles calculations for the Mo5Si3-xPx superconducting family. The band structure features a flat band that gradually approaches the Fermi level as a function of phosphorus doping x, reaching the Fermi level at x ≃ 1.3. This leads to an abrupt change in nearly all superconducting quantities. The superfluid density data placed on the 'Uemura plot' results in two separated branches, thus indicating that the emergence of a flat band enhances correlations between conducting electrons.

In-Plane Magnetic Penetration Depth in Sr_{2}RuO_{4}: Muon-Spin Rotation and Relaxation Study

We report on measurements of the in-plane magnetic penetration depth (λ_{ab}) in single crystals of Sr_{2}RuO_{4} down to ≃0.015  K by means of muon-spin rotation-relaxation. The linear temperature dependence of λ_{ab}^{-2} for T≲0.7  K suggests the presence of nodes in the superconducting gap. This statement is further substantiated by observation of the Volovik effect, i.e., the reduction of λ_{ab}^{-2} as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of λ_{ab}=124(3)  nm agrees with λ_{ab}≃130  nm, calculated based on results of electronic structure measurements reported in A. Tamai et al. [High-resolution photoemission on Sr_{2}RuO_{4} reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies, Phys. Rev. X 9, 021048 (2019)PRXHAE2160-330810.1103/PhysRevX.9.021048]. Our analysis reveals that a simple nodal superconducting energy gap, described by the lowest possible harmonic of a gap function, does not capture the dependence of λ_{ab}^{-2} on T, so the higher angular harmonics of the energy gap function need to be introduced.

Probing the superconducting pairing of the La4Be33Pt16alloy via muon-spin spectroscopy

We report a study of the superconducting pairing of the noncentrosymmetric La4Be33Pt16alloy using muon-spin rotation and relaxation (µSR) technique. BelowTc=2.4 K, La4Be33Pt16exhibits bulk superconductivity (SC), here characterized by heat-capacity and magnetic-susceptibility measurements. The temperature dependence of the superfluid densityρsc(T), extracted from the transverse-fieldµSR measurements, reveals a nodeless SC in La4Be33Pt16. The best fit ofρsc(T)using ans-wave model yields a magnetic penetration depthλ0=542 nm and a superconducting gapΔ0=0.37 meV at zero Kelvin. The single-gapped superconducting state is further evidenced by the temperature-dependent electronic specific heatCe(T)/Tand the linear field-dependent electronic specific-heat coefficientγH(H). The zero-fieldµSR spectra collected in the normal- and superconducting states of La4Be33Pt16are almost identical, confirming the absence of an additional field-related relaxation and, thus, of spontaneous magnetic fields belowTc. The nodeless SC combined with a preserved time-reversal symmetry in the superconducting state proves that the spin-singlet pairing is dominant in La4Be33Pt16. This material represents yet another example of a complex system showing only a conventional behavior, in spite of a noncentrosymmetric structure and a sizeable spin-orbit coupling.

Unconventional superconductivity in topological Kramers nodal-line semimetals

Crystalline symmetry is a defining factor of the electronic band topology in solids, where many-body interactions often induce a spontaneous breaking of symmetry. Superconductors lacking an inversion center are among the best systems to study such effects or even to achieve topological superconductivity. Here, we demonstrate that TRuSi materials (with T a transition metal) belong to this class. Their bulk normal states behave as three-dimensional Kramers nodal-line semimetals, characterized by large antisymmetric spin-orbit couplings and by hourglass-like dispersions. Our muon-spin spectroscopy measurements show that certain TRuSi compounds spontaneously break the time-reversal symmetry at the superconducting transition, while unexpectedly showing a fully gapped superconductivity. Their unconventional behavior is consistent with a unitary (s + ip) pairing, reflecting a mixture of spin singlets and spin triplets. By combining an intrinsic time-reversal symmetry-breaking superconductivity with nontrivial electronic bands, TRuSi compounds provide an ideal platform for investigating the rich interplay between unconventional superconductivity and the exotic properties of Kramers nodal-line/hourglass fermions.

Muon-spin rotation measurements of an unusual vortex-glass phase in the layered superconductor Bi2.15Sr1.85CaCu2O8+δ

Muon-spin rotation measurements, performed on the mixed state of the classic anisotropic superconductor Bi(2.15)Sr(1.85)CaCu(2)O(8+δ), obtain quantities directly related to two- and three-body correlations of vortices in space. A novel phase diagram emerges from such local probe measurements of the bulk, revealing an unusual glassy state at intermediate fields which appears to freeze continuously from the equilibrium vortex liquid but differs both from the lattice and the conventional high-field vortex glass state in its structure.

Strong pressure dependence of the magnetic penetration depth in single crystals of the heavy-fermion superconductor CeCoIn5 studied by muon spin rotation

In the tetragonal heavy fermion system CeCoIn(5) the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0-1 GPa) of the basal-plane magnetic penetration depth (λ(a)), the penetration depth anisotropy (γ = λ(c)/λ(a)) and the temperature dependence of 1/λ(i)(2) (i = a, c) were studied in single crystals. A strong decrease of λ(a) with pressure was observed, while γ and λ(i)(2)(0)/λ(i)(2)(T) are pressure independent. A linear relationship between 1/λ(a)(2)(270 mK) and T(c) was also found. The large decrease of λ(a) with pressure is the signature of an increase of the number of superconducting quasiparticles by a factor of about 2.

Concerning the superconducting gap symmetry in YBa₂Cu₃O₇- δ, YBa₂Cu₄O, and La₂ - xSrxCuO₄ determined from muon spin rotation in mixed states of crystals and powders

Muon spin rotation (μ(+)SR) measurements of square-root second moments of local magnetic fields σ in superconducting mixed states, as published for oriented crystals and powder samples of YBa(2)Cu(3)O(7 - δ) (δ≈0.05), YBa(2)Cu(4)O(8) and La(2 - x)Sr(x)CuO(4) (x ∼ 0.15-0.17), are subjected to comparative analysis for superconducting gap symmetry. For oriented crystals it is shown that anomalous dependences of σ on temperature T and applied field H, as-measured and extracted a- and b-axial components, are attributable to fluxon depinning and disorder that obscure the intrinsic character of the superconducting penetration depth. Random averages derived from oriented crystal data differ markedly from corresponding non-oriented powders, owing to the weaker influence of pinning in high-quality crystals. Related indicators for pinning perturbations, such as non-monotonic H dependence of σ, irreproducible data and strong H dependence of apparent transition temperatures, are also evident. Strong intrinsic pinning suppresses thermal anomalies in c-axis components of σ, which reflect nodeless gap symmetries in YBa(2)Cu(3)O(7 - δ) and YBa(2)Cu(4)O(8). For YBa(2)Cu(3)O(7 - δ), the crystal (a-b components, corrected for depinning) and powder data all reflect a nodeless gap (however, a-b symmetries remain unresolved for crystalline YBa(2)Cu(4)O(8) and La(1.83)Sr(0.17)CuO(4)). Inconsistencies contained in multiple and noded gap interpretations of crystal data, and observed differences between bulk μ(+)SR and surface-sensitive measurements are discussed.

Superfluid density and energy gap function of superconducting PrPt4Ge12

The filled skutterudite superconductor PrPt4Ge12 was studied in muon-spin rotation (muSR), specific heat, and electrical resistivity experiments. The continuous increase of the superfluid density with decreasing temperature and the dependence of the magnetic penetration depth lambda on the magnetic field obtained by means of muSR, as well as the observation of a T3 dependence of the electronic specific heat indicate the presence of pointlike nodes in the superconducting energy gap. The gap and the specific heat are found to be well described by two models with point nodes, similar to results obtained for the unconventional heavy fermion skutterudite superconductor PrOs4Sb12.

Superconductivity and field-induced magnetism in SrFe_{1.75}Co_{0.25}As_{2}

Using muon-spin rotation, we studied the in-plane (lambda_{ab}) and the out of plane (lambda_{c}) magnetic field penetration depth in SrFe_{1.75}Co_{0.25}As_{2} (T_{c} approximately 13.3 K). The penetration depth anisotropy gamma_{lambda} = lambda_{c}/lambda_{ab} increases from gamma_{lambda} approximately 2.1 at T_{c} to 2.7 at 1.6 K. The mean internal field in the superconducting state increases with decreasing temperature, just opposite to the diamagnetic response seen in magnetization experiments. This unusual behavior suggests that the external field induces a magnetic order which is maintained throughout the whole sample volume.