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The uncertainty of the nature of the normal state and superconducting condensate of unconventional superconductors continues to stimulate considerable speculation about the mechanism of superconductivity in these materials. Of particular interest are the type of symmetry of the order parameter and the basic electronic characteristics of the superconducting and normal states. We report the derivation of temperature dependences of the superconducting condensate plasma frequency, superfluid density, and London penetration depth by measuring terahertz spectra of conductivity and dielectric permittivity of the Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$ thin films with different Ni concentrations. A comprehensive analysis of the experimental data was performed in the framework of the simple three-band Eliashberg model under the assumption that the superconducting coupling mechanism is mediated by antiferromagnetic spin fluctuations. The results of independent experiments support the choice of model parameters. Based on calculations of the temperature dependences of superconducting gaps, we may conclude that the obtained results are compatible with the scenario, in which Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$ is a multiband superconductor with s$_\pm $-wave pairing symmetry., Comment: 26 pages, 9 figures, 2 tables. arXiv admin note: text overlap with arXiv:2006.00522

Recent experiments have pointed to the formation of a new state of matter, the electron quadrupling condensate in Ba$_{1-x}$K$_x$Fe$_2$As$_2$. The state spontaneously breaks time-reversal symmetry and is sandwiched between two critical points, separating it from the superconducting and normal-metal states. We report a theory of the acoustic effects of systems with an electron quadrupling phase based on ultrasound-velocity measurements of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ single crystals. The theoretical analysis suggests that the ultrasound data can be understood by considering a plain $s$+i$d_{xy}$ order parameter or an $s$+i$s$ order parameter with symmetry-breaking deformations in this material with enhanced nematic susceptibility for the [110] direction, or when the transition to the quartic state is a weakly first-order. Our work provides the theoretical basis and proposes the experimental strategy to study the order parameter symmetry of emerging quadrupling condensates in superconductors., Comment: v2: The crystal orientation is corrected and the ultrasound data re-analyzed. Data for a reference sample at a different doping without the BTRS state is added. 11 pages, 6 figures

We report on measurements of the in-plane magnetic penetration depth ($\lambda_{\rm ab}$) in single crystals of Sr$_2$RuO$_4$ down to $\simeq 0.015$ K by means of muon-spin rotation/relaxation. The linear temperature dependence of $\lambda^{-2}_{\rm ab}$ for $T\lesssim 0.7$ 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 $\lambda_{ab}^{-2}$ as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of $\lambda_{\rm ab}=124(3)$ nm agrees with $\lambda_{\rm ab}\simeq 130$ nm, calculated based on results of electronic structure measurements reported in [Phys. Rev X 9, 021048 (2019)]. 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 $\lambda_{\rm ab}^{-2}$ on $T$, so the higher angular harmonics of the energy gap function need to be introduced., Comment: 7 pages, 3 figures

Muon spin rotation/relaxation ($\mu$SR) and polar Kerr effect measurements provide evidence for a time-reversal symmetry breaking (TRSB) superconducting state in Sr$_2$RuO$_4$. However, the absence of a cusp in the superconducting transition temperature ($T_{\rm c}$) vs. stress and the absence of a resolvable specific heat anomaly at TRSB transition temperature ($T_{\rm TRSB}$) under uniaxial stress challenge a hypothesis of TRSB superconductivity. Recent $\mu$SR studies under pressure and with disorder indicate that the splitting between $T_{\rm c}$ and $T_{\rm TRSB}$ occurs only when the structural tetragonal symmetry is broken. To further test such behavior, we measured $T_\text{c}$ through susceptibility measurements, and $T_\text{TRSB}$ through $\mu$SR, under uniaxial stress applied along a $\langle 110 \rangle$ lattice direction. We have obtained preliminary evidence for suppression of $T_\text{TRSB}$ below $T_\text{c}$, at a rate much higher than the suppression rate of $T_\text{c}$., Comment: 9 pages, 4 figures and Appendix, accepted for publication in PRB

Theoretically, materials that break multiple symmetries allow, under certain conditions, the formation of four-fermion condensates above the superconducting critical temperature. Such states can be stabilized by phase fluctuations. Recently a fermionic quadrupling condensate that breaks the $Z_2$ time-reversal symmetry was reported in Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ [V. Grinenko et al., Nat. Phys. 17, 1254 (2021)]. Evidence for the new state of matter comes from muon-spin rotation, transport, thermoelectric, and ultrasound experiments. Observing a specific heat anomaly is a very important signature of a transition to a new state of matter. However, a fluctuation-induced specific heat singularity is usually very challenging to resolve from a background of other contributions. Here, we report on detecting two anomalies in the specific heat of Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ at zero magnetic field. The anomaly at the higher temperature is accompanied by the appearance of a spontaneous Nernst effect, indicating broken time-reversal ($Z_2$) symmetry. The second anomaly at the lower temperature coincides with the transition to a zero resistance state, indicating superconductivity breaking the $U(1)$ gauge symmetry. Our data provide calorimetric evidence for the $Z_2$ phase formation above the superconducting phase transition., Comment: 12 pages, 3 figures and Supplementary information