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The field of hydride superconductivity has recently been mired in a controversy that might divert attention from the question of central importance: do hydrides support genuine superconductivity or not? We examine some key papers from the field, and conclude that hydride superconductivity is real.

The electronic structure of the topmost layer in Sr2RuO4 in the close vicinity of the Fermi level is investigated by angle-resolved photoemission spectroscopy (ARPES) with a 7-eV laser. We find that the spin-orbit coupling (SOC) predicted as 100 meV by the density functional theory (DFT) calculations is enormously enhanced in a real material up to 250 meV, even more than that of bulk state (200 meV), by the electron-correlation effect increased by the octahedral rotation in the crystal structure. This causes the formation of highly orbital-mixing small Fermi pockets and reasonably explains why the orbital-selective Mott transition (OSMT) is not realized in perovskite oxides with crystal distortion. Interestingly, Hund's metal feature allows the quasiparticle generation only near EF, restricting the spectral gap opening derived by band hybridization within an extremely small binding energy (< 10 meV). Furthermore, it causes coherent-incoherent crossover, making the Fermi pockets disappear at elevated temperatures. The anomalous Fermi pockets are characterized by the dichotomy of the orbital-isolating Hund's coupling and the orbital-mixing SOC, which is key to understanding the nature of Sr2RuO4.

The layered perovskite Sr$_2$RuO$_4$ serves as a model material of the two-dimensional (2D) Fermi liquid but also exhibits various emergent phenomena including the non-Fermi-liquid (NFL) behavior under external perturbations such as uniaxial pressure and chemical substitutions. Here we present the thermoelectric transport of electron-doped system Sr$_{2-y}$La$_{y}$RuO$_4$, in which a filling-induced Lifshitz transition occurs at the Van Hove singularity (VHS) point of $y\approx 0.2$. We find that the sign of the low-temperature thermopower becomes negative only near the VHS point, where the NFL behavior has been observed in the earlier work. This observation is incompatible with either a numerical calculation within a constant relaxation-time approximation or a toy-model calculation for the 2D Lifshitz transition adopting an elastic carrier scattering. As a promising origin of the observed negatively enhanced thermopower, we propose a skewed NFL state, in which an inelastic scattering with a considerable odd-frequency term plays a crucial role to negatively enhance the thermopower., Comment: 10 pages, 7 figures, to be published in Phys. Rev. Research

An appealing direction to change the properties of strongly correlated materials is to induce nonequilibrium steady states by the application of a direct current. While access to these novel states is of high scientific interest, Joule heating due to current flow often constitutes a hurdle to identify nonthermal effects. The biggest challenge usually resides in measuring accurately the temperature of a sample subjected to direct current, and to use probes that give direct information of the material. In this work, we exploit the simultaneous measurement of electrical transport and magnetisation to probe non-equilibrium steady states in Ca2RuO4. In order to reveal non-thermal current-induced effects, we employ a simple model of Joule self-heating to remove the effects of heating and discuss the importance of temperature inhomogeneity within the sample. Our approach provides a solid basis for investigating current-induced phenomena in highly resistive materials.

Materials with strongly correlated electrons exhibit physical properties that are often difficult to predict as they result from the interactions of large numbers of electrons combined with several quantum degrees of freedom. The layered oxide perovskite Sr$_2$RuO$_4$ is a strongly correlated electron material that has been intensively investigated since its discovery due to its unusual physical properties. Whilst recent experiments have reopened the debate on the exact symmetry of the superconducting state in Sr$_2$RuO$_4$, a deeper understanding of the Sr$_2$RuO$_4$ normal state appears crucial as this is the background in which electron pairing occurs. Here, by using low-energy muon spin spectroscopy we discover the existence of magnetism at the surface of Sr$_2$RuO$_4$ in its normal state. We detect static weak dipolar fields yet manifesting below a relatively high onset temperature larger than 50 K, which reveals the unconventional nature of the observed magnetism. We relate the origin of this phase breaking time reversal symmetry to electronic ordering in the form of orbital loop currents that originate at the reconstructed Sr$_2$RuO$_4$ surface. Our observations set a reference for the discovery of the same magnetic phase in other materials and unveil an electronic ordering mechanism that can influence unconventional electron pairing with broken time reversal symmetry in those materials where the observed magnetic phase coexists with superconductivity., Comment: 20 pages, 5 figures

This review describes recent significant research developments made on the layered perovskite Sr2RuO4 and discusses current issues from both experimental and theoretical perspectives. Since the discovery of superconductivity in Sr2RuO4 in 1994, studies using high-quality single crystals quickly revealed it to be an archetypal unconventional superconductor among strongly correlated electron systems. In particular, it was thought that the spin-triplet chiral p-wave superconducting state, which breaks time-reversal symmetry, was a prominent possibility. In 2019, however, a new development overturned the past experimental results, and spin-singlet-like behavior became conclusive. Furthermore, innovation in uniaxial strain devices has stimulated researchers to explore changes in the superconducting state by controlling the symmetry and dimensionality of the Fermi surfaces and enhancing the superconducting transition temperature Tc from 1.5 K to 3.5 K. A spin-singlet chiral d-wave superconducting state is consistent with most of these recent experimental results. Nevertheless, there are still unnatural aspects that remain to be explained. The focus of this review is on unraveling this mystery. Unlike many other unconventional superconductors, the normal state of Sr2RuO4 exhibits typical Fermi liquid behavior. Nevertheless, to elucidate its superconducting state, it may be essential to go beyond the traditional framework of unconventional superconductivity and recast the theory explicitly considering the multi-orbital aspects of its electronic states. In this review, we describe the frontiers of superconductivity research in Sr2RuO4 and discuss how the remaining issues may be resolved., Comment: 48 pages, 46 figures, 13 tables, invited review paper for J. Phys. Soc. Jpn

In the unconventional superconductor Sr$_2$RuO$_4$, uniaxial stress along the $[100]$ direction tunes the Fermi level through a Van Hove singularity (VHS) in the density of states, causing a strong enhancement of the superconducting critical temperature $T_\textrm{c}$. Here, we report measurements of the London penetration depth $\lambda$ as this tuning is performed. We find that the zero-temperature superfluid density, here defined as $\lambda(0)^{-2}$, increases by $\sim$15%, with a peak that coincides with the peak in $T_\textrm{c}$. We also find that the low temperature form of $\lambda(T)$ is quadratic over the entire strain range. Using scanning tunneling microscopy, we find that the gap increases from $\Delta_0 \approx 350~\mu$eV in unstressed Sr$_2$RuO$_4$ to $\Delta_0 \approx 600~\mu$eV in a sample strained to near the peak in $T_c$. With a nodal order parameter, an increase in the superconducting gap could bring about an increase in the superfluid density through reduced sensitivity to defects and through reduced non-local effects in the Meissner screening. Our data indicate that tuning to the VHS increases the gap throughout the Brillouin zone, and that non-local effects are likely more important than reduced scattering.

Intuitive entropic interpretations of the thermoelectric effect in metals predict an isotropic Seebeck coefficient at high temperatures in the incoherent regime even in anisotropic metals since entropy is not directional. $\mathrm{Sr}_2\mathrm{Ru}\mathrm{O}_4$ is an enigmatic material known for a well characterised anisotropic normal state and unconventional superconductivity. Recent ab-initio transport calculations of $\mathrm{Sr}_2\mathrm{Ru}\mathrm{O}_4$ that include the effect of strong electronic correlations predicted an enhanced high-temperature anisotropy of the Seebeck coefficient at temperatures above 300 K, but experimental evidence is missing. From measurements on clean $\mathrm{Sr}_2\mathrm{Ru}\mathrm{O}_4$ single crystals along both crystallographic directions, we find that the Seebeck coefficient becomes increasingly isotropic upon heating towards room temperature as generally expected. Above 300 K, however, $S$ acquires a new anisotropy which rises up to the highest temperatures measured (750 K), in qualitative agreement with calculations. This is a challenge to entropic interpretations and highlights the lack of an intuitive framework to understand the anisotropy of thermopower at high temperatures., Comment: 5 pages, 2 figures

More than two decades after the discovery of superconductivity in Sr$_2$RuO$_4$, it is still unclear whether the order parameter has a single component or two degenerate components. For any two-component scenario, application of uniaxial strain is expected to lift the degeneracy, generating two distinct phase transitions. The presence of a second (lower-temperature) transition may be observable by probes that are sensitive to changes in the London penetration depth, $\lambda$, as a function of temperature, $T$. Here, we use scanning SQUID microscopy combined with a uniaxial strain device to test for a second transition under strain. We only observe a single transition. Within the temperature range where a second transition has been suggested by $\mu$SR measurements, we further place a tight upper bound of less than 1% on the change in the zero temperature superfluid density $n_s\propto\lambda^{-2}(0)$ due to a second transition, suggesting that such a transition does not occur. These results constrain theories of the order parameter in Sr$_2$RuO$_4$.

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

Superconductivity is caused by electron pairs that are canonically isotropic, whereas some exotic superconductors are known to exhibit non-trivial anisotropy stemming from unconventional pairings. However, superconductors with hexagonal symmetry, the highest rotational symmetry allowed in crystals, exceptionally have strong constraint that is called emergent rotational symmetry (ERS): anisotropic properties should be very weak especially near the critical temperature Tc even for unconventional pairings such as d-wave states. Here, we investigate superconducting anisotropy of the recently-found hexagonal Kagome superconductor CsV3Sb5, which is known to exhibit various intriguing phenomena originating from its undistorted Kagome lattice formed by vanadium atoms. Based on calorimetry performed under accurate two-axis field-direction control, we discover a combination of six- and two-fold anisotropies in the in-plane upper critical field. Both anisotropies, robust up to very close to Tc, are beyond predictions of standard theories. We infer that this clear ERS violation with nematicity is best explained by multi-component nematic superconducting order parameter in CsV3Sb5 intertwined with symmetry breakings caused by the underlying charge-density-wave order., Comment: 35 pages, 5 figures, 1 table, 7 extended 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

We performed angle-resolved photoemission spectroscopy with micro-focused beam on a topological line-nodal compound CaSb2 which undergoes a superconducting transition at the onset Tc~1.8 K, to clarify the Fermi-surface topology relevant to the occurrence of superconductivity. We found that a three-dimensional hole pocket at the G point is commonly seen for two types of single-crystalline samples fabricated by different growth conditions. On the other hand, the carrier-doping level estimated from the position of the chemical potential was found to be sensitive to the sample fabrication condition. The cylindrical electron pocket at the Y(C) point predicted by the calculations is absent in one of the two samples, despite the fact that both samples commonly show superconductivity with similar Ts's. This suggests a key role of the three-dimensional hole pocket to the occurrence of superconductivity, and further points to an intriguing possibility to control the topological nature of superconductivity by carrier tuning in CaSb2., Comment: 7 pages, 3 figures

The Kagome lattice exhibits rich quantum phenomena owing to its unique geometric properties. Appealing realizations are the Kagome metals AV$_3$Sb$_5$ (A = K, Rb, Cs), where unconventional charge density wave (CDW) is intertwined with superconductivity and non-trivial band topology. Several experiments suggest that this CDW is a rare occurrence of chiral CDW characterized by orbital loop current. However, key evidences of loop current, spontaneous time-reversal symmetry-breaking (TRSB) and the coupling of its order parameter with the magnetic field remain elusive. Here, we investigate the CDW in CsV3Sb5 by magneto-optic polar Kerr effect with sub-microradian resolution. Under magnetic field, we observed a jump of the Kerr angle at the CDW transition. This jump is magnetic-field switchable and scales with field, indicating magneto--chirality coupling related to non-trivial band topology. At zero field, we found non-zero and field-trainable Kerr angle below CDW transition temperature, signaling spontaneous TRSB. Our results provide a crucial step to unveil quantum phenomena in correlated Kagome materials.

We report on the Fermi surfaces and superconducting parameters of CaSb$_2$ single crystals (superconducting below $T_{\text{c}}\sim 1.8~\text{K}$) grown by the self-flux method. The frequency of de-Haas-van-Alphen and Shubnikov-de-Haas oscillations evidences a quasi-two-dimensional (quasi-2D) Fermi surface, consistent with one of the Fermi surfaces forming Dirac lines predicted by first-principles calculations. Measurements in the superconducting state reveal that CaSb$_2$ is close to a type-I superconductor with the Ginzburg-Landau (GL) parameter of around unity. The temperature dependence of the upper critical field $H_{\text{c2}}$ is well described by a model considering two superconducting bands, and the enhancement of the effective mass estimated from $H_{\text{c2}}(0~\text{K})$ is consistent with the quasi-2D band observed by the quantum oscillations. Our results indicate that a quasi-2D band forming Dirac lines contributes to the superconductivity in CaSb$_2$., Comment: 13 pages, 13 figures

The fate of a Mott insulator under strong low frequency optical driving conditions is a fundamental problem in quantum many-body dynamics. Using ultrafast broadband optical spectroscopy, we measured the transient electronic structure and charge dynamics of an off-resonantly pumped Mott insulator Ca$_2$RuO$_4$. We observe coherent bandwidth renormalization and nonlinear doublon-holon pair production occurring in rapid succession within a sub-100 femtosecond pump pulse duration. By sweeping the electric field amplitude, we demonstrate continuous bandwidth tuning and a Keldysh cross-over from a multi-photon absorption to quantum tunneling dominated pair production regime. Our results provide a procedure to control coherent and nonlinear heating processes in Mott insulators, facilitating the discovery of novel out-of-equilibrium phenomena in strongly correlated systems., Comment: 6 pages main text, 4 figures, 16 pages supplementary information

The motion of electrons in the vast majority of conductors is diffusive, obeying Ohm's law. However, the recent discovery and growth of high-purity materials with extremely long electronic mean free paths has sparked interest in non-ohmic alternatives, including viscous and ballistic flow. Although non-ohmic transport regimes have been discovered across a range of materials, including two-dimensional electron gases, graphene, topological semimetals, and the delafossite metals, determining their nature has proved to be challenging. Here, we report on a new approach to the problem, employing broadband microwave spectroscopy of the delafossite metal PdCoO$_{2}$ in three distinct sample geometries that would be identical for diffusive transport. The observed differences, which go as far as differing power laws, take advantage of the hexagonal symmetry of PdCoO$_{2}$. This permits a particularly elegant symmetry-based diagnostic for non-local electrodynamics, with the result favouring ballistic over strictly hydrodynamic flow. Furthermore, it uncovers a new effect for ballistic electron flow, owing to the highly facetted shape of the hexagonal Fermi surface. We combine our extensive dataset with an analysis of the Boltzmann equation to characterize the non-local regime in PdCoO$_{2}$. More broadly, our results highlight the potential of broadband microwave spectroscopy to play a central role in investigating exotic transport regimes in the new generation of ultra-high conductivity materials.

Investigating the pressure dependence of the superconducting (SC) transition temperature $T_{\rm c}$ is crucial for understanding the SC mechanism. Herein, we report on the pressure dependence of $T_{\rm c}$ in the nonmagnetic topological line-nodal material CaSb$_2$, based on measurements of electric resistance and alternating current magnetic susceptibility. $T_{\rm c}$ initially increases with increasing pressure and peaks at $\sim$ 3.1~GPa. With a further increase in pressure, $T_{\rm c}$ decreases and finally becomes undetectable at 5.9~GPa. Because no signs of phase transition or Lifshitz transition are observed in the normal state, the peculiar peak structure of $T_{\rm c}$ suggests that CaSb$_2$ has an unconventional SC character., Comment: 5 pages, 5 figures

We performed 121/123Sb-nuclear quadrupole resonance (NQR) measurements on the superconducting (SC) line-nodal material CaSb2 in order to investigate electronic properties in the normal and SC states from a microscopic point of view. In the normal state, the nuclear spin-lattice relaxation rate 1/T1 for the Sb(1) site, which is responsible for the line-nodal parts, is approximately proportional to temperature, indicating the conventional Fermi liquid state. From comparison with band structure calculations, it is considered that the NQR properties related to the line-nodal character are hidden because the conventional behavior originating from Fermi-surface parts away from the nodes is dominant. In the SC state, a clear coherence peak just below the transition temperature and an exponential decrease at lower temperatures were observed in 1/T1. These results strongly suggest that conventional s-wave superconductivity with a full gap is realized in CaSb2., Comment: 6 pages, 5 figures

There is considerable evidence that the superconducting state of Sr$_2$RuO$_4$ breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking its onset temperature, $T_\text{TRSB}$, is generally found to match the critical temperature, $T_\text{c}$, within resolution. In combination with evidence for even parity, this result has led to consideration of a $d_{xz} \pm id_{yz}$ order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding $T_\text{TRSB} = T_\text{c}$, but it has a hard-to-explain horizontal line node at $k_z=0$. Therefore, $s \pm id$ and $d \pm ig$ order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain $T_\text{TRSB} \approx T_\text{c}$. 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 Sr$_2$RuO$_4$ under hydrostatic pressure, and Sr$_{1.98}$La$_{0.02}$RuO$_4$ at zero pressure. Both hydrostatic pressure and La substitution alter $T_\text{c}$ without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected $T_\text{TRSB}$ should track changes in $T_\text{c}$, while if it is accidental, these transition temperatures should generally separate. We observe $T_\text{TRSB}$ to track $T_\text{c}$, supporting the hypothesis of $d_{xz} \pm id_{yz}$ order., Comment: 14 pages, 8 Figures

A key question regarding the unconventional superconductivity of Sr$_2$RuO$_4$ remains whether the order parameter is single- or two-component. Under a hypothesis of two-component superconductivity, uniaxial pressure is expected to lift their degeneracy, resulting in a split transition. The most direct and fundamental probe of a split transition is heat capacity. Here, we report measurement of heat capacity of samples subject to large and highly homogeneous uniaxial pressure. We place an upper limit on the heat-capacity signature of any second transition of a few per cent of that of the primary superconducting transition. The normalized jump in heat capacity, $\Delta C/C$, grows smoothly as a function of uniaxial pressure, favouring order parameters which are allowed to maximize in the same part of the Brillouin zone as the well-studied van Hove singularity. Thanks to the high precision of our measurements, these findings place stringent constraints on theories of the superconductivity of Sr$_2$RuO$_4$., Comment: This manuscript is an extended version of the scientific part of arXiv:1906.07597, which is being split into two separate papers. An extended discussion on the experimental methods can be found at arXiv:2009.03125. It includes supplemental material

A large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table currently used worldwide is of a long form pioneered by Werner in 1905. As the first topic, we describe the work of Pfeiffer (1920), who refined Werner's work and rearranged the rare-earth elements in a separate table below the main table for convenience. Today's widely used periodic table essentially inherits Pfeiffer's arrangements. Although long-form tables more precisely represent electron orbitals around a nucleus, they lose some of the features of Mendeleev's short-form table to express similarities of chemical properties of elements when forming compounds. As the second topic, we compare various three-dimensional helical periodic tables that resolve some of the shortcomings of the long-form periodic tables in this respect. In particular, we explain how the 3D periodic table "Elementouch" (Maeno 2001), which combines the s- and p-blocks into one tube, can recover features of Mendeleev's periodic law. Finally we introduce a topic on the recently proposed nuclear periodic table based on the proton magic numbers (Hagino and Maeno 2020). Here, the nuclear shell structure leads to a new arrangement of the elements with the proton magic-number nuclei treated like noble-gas atoms. We show that the resulting alignments of the elements in both the atomic and nuclear periodic tables are common over about two thirds of the tables because of a fortuitous coincidence in their magic numbers., Comment: 14 pages. To appear in Foundations of Chemistry

It was recently reported that a continuous electric current is a powerful control parameter to trigger changes in the electronic structure and metal-insulator transitions (MITs) in Ca2RuO4. However, the spatial evolution of the MIT and the implications of the unavoidable Joule heating have not been clarified yet, often hindered by the difficulty to asses the local sample temperature. In this work, we perform infrared thermal imaging on single-crystal Ca2RuO4 while controlling the MIT by electric current. The change in emissivity at the phase transition allows us to monitor the gradual formation and expansion of metallic phase upon increasing current. Our local temperature measurements indicate that, within our experimental resolution, the MIT always occurs at the same local transition temperatures, irrespectively if driven by temperature or by current. Our results highlight the importance of local heating, phase coexistence, and microscale inhomogeneity when studying strongly correlated materials under the flow of electric current.

We report a $\mu$SR study on the antiperovskite oxide superconductor Sr$_{3-x}$SnO. With transverse-field $\mu$SR, we observed the increase of the muon relaxation rate upon cooling below the superconducting transition temperature $T_{\mathrm{c}}=5.4$ K, evidencing bulk superconductivity. The exponential temperature dependence of the relaxation rate $\sigma$ at low temperatures suggests a fully gapped superconducting state. We evaluated the zero-temperature penetration depth $\lambda(0)\propto1/\sqrt{\sigma(0)}$ to be around 320-1020 nm. Such a large value is consistent with the picture of a doped Dirac semimetal. Moreover, we revealed that the ratio $T_{\mathrm{c}}/\lambda(0)^{-2}$ is larger than those of ordinary superconductors and is comparable to those of unconventional superconductors. The relatively high $T_{\mathrm{c}}$ for small carrier density may hint at an unconventional pairing mechanism beyond the ordinary phonon-mediated pairing. In addition, zero-field $\mu$SR did not provide evidence of broken time-reversal symmetry in the superconducting state. These features are consistent with the theoretically proposed topological superconducting state in Sr$_{3-x}$SnO, as well as with $s$-wave superconductivity., Comment: 9 pages, 9 figures, to be published in Physical Review B

In the search of material properties out-of-equilibrium, the non-equilibrium steady states induced by electric current are an appealing research direction where unconventional states may emerge. However, the unavoidable Joule heating caused by flowing current calls for the development of new measurement protocols, with a particular attention to the physical properties of the background materials involved. Here, we demonstrate that localised heating can give rise to a large, spurious diamagnetic-like signal. This occurs due to the local reduction of the background magnetisation caused by the heated sample, provided that the background material has a Curie-like susceptibility. Our experimental results, along with numerical calculations, constitute an important building block for performing accurate magnetic measurements under the flow of electric current.

We found superconductivity in CaSb$_2$ with the transition temperature of 1.7 K by means of electrical-resistivity, magnetic-susceptibility, and specific-heat measurements. This material crystallizes in a nonsymmorphic structure and is predicted to have multiple Dirac nodal lines in the bulk electronic band structure protected by symmetry even in the presence of spin-orbit coupling. We discuss a possible topological superconductivity for the quasi-2-dimensional band originating mainly from one of the antimony sites., Comment: 7 pages, 5 figures

The chiral p-wave order parameter in Sr$_\mathsf{2}$RuO$_\mathsf{4}$ would make it a special case amongst the unconventional superconductors. A consequence of this symmetry is the possible existence of superconducting domains of opposite chirality. At the boundary of such domains, the locally supressed condensate can produce an intrinsic Josephson junction. Here, we provide evidence of such junctions using mesoscopic rings, structured from Sr$_\mathsf{2}$RuO$_\mathsf{4}$ single crystals. Our order parameter simulations predict such rings to host stable domain walls across their arms. Thisis verified with transport experiments on loops, with a sharp transition at 1.5 K, which show distinct critical current oscillations with periodicity corresponding to the flux quantum. In contrast, loops with broadened transitions at around 3 K are void of such junctions and show standard Little-Parks oscillations. Our analysis demonstrates the junctions are of intrinsic origin and makes a compelling case for the existence of superconducting domains., Comment: 27+11 pages, 6+4 figures

Among unconventional superconductors, Sr$_2$RuO$_4$ has become a benchmark for experimentation and theoretical analysis because its normal-state electronic structure is known with exceptional precision, and because of experimental evidence that its superconductivity has, very unusually, a spontaneous angular momentum, i.e. a chiral state. This hypothesis of chirality is however difficult to reconcile with recent evidence on the spin part of the order parameter. Measurements under uniaxial stress offer an ideal way to test for chirality, because under uniaxial stress the superconducting and chiral transitions are predicted to split, allowing the empirical signatures of each to be identified separately. Here, we report zerofield muon spin relaxation (ZF-$\mu$SR) measurements on crystals placed under uniaxial stresses of up to 1.05 GPa. We report a clear stress-induced splitting between the onset temperatures of superconductivity and time-reversal symmetry breaking, consistent with qualitative expectations for chiral superconductivity. We also report the appearance of unexpected bulk magnetic order under a uniaxial stress of ~ 1.0 GPa in clean Sr$_2$RuO$_4$., Comment: 28 pages, 12 figures

Sr$_2$RuO$_4$ has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap $\Delta_i(\mathbf{k})$ on each band $i$ that encodes its unknown superconducting order-parameter. But, because the energy scales are so low, it has never been possible to directly measure the $\Delta_i(\mathbf{k})$ of Sr$_2$RuO$_4$. Here we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband $\Delta_i(\mathbf{k})$. At T=90 mK we visualize a set of Bogoliubov scattering interference wavevectors $q_j:j=1-5$ consistent with eight gap nodes/minima, that are all closely aligned to the $(\pm1,\pm1)$ crystal-lattice directions on both the $\alpha$-and $\beta$-bands. Taking these observations in combination with other very recent advances in directional thermal conductivity (E. Hassinger et al. Phys. Rev. X 7, 011032 (2017)), temperature dependent Knight shift (A. Pustogow et al. Nature 574, 72 (2019)), time-reversal symmetry conservation (S. Kashiwaya et al. arXiv:1907.030939) and theory (A.T. Romer et al. Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising et al. Phys. Rev. Research 1, 033108 (2019),O. Gingras et al. Phys. Rev. Lett. 123, 217005 (2019)), the BQPI signature of Sr$_2$RuO$_4$ appears most consistent with $\Delta_i(\mathbf{k})$ having $d_{x^2-y^2}$ $(B_{1g})$ symmetry., Comment: accepted in PNAS

We report the temperature variation of the $^{119}$Sn-M\"{o}ssbauer spectra of the antiperovskite (inverse perovskite) oxide superconductor Sr$_{3-x}$SnO. Both superconductive (Sr-deficient) and non-superconductive (nearly stoichiometric) samples exhibit major $\gamma$-ray absorption with isomer shift similar to that of Mg$_2$Sn. This fact shows that Sr$_{3-x}$SnO contains the metallic anion Sn$^{4-}$, which is rare especially among oxides. In both samples, we observed another $\gamma$-ray absorption with a larger isomer shift, indicating that there is another ionic state of Sn with a higher oxidation number. The temperature dependence of the absorption intensities reveals that the Sn ions exhibiting larger isomer shifts have a lower energy of the local vibration. The larger isomer shift and lower vibration energy are consistent with the values estimated from the first-principles calculations for hypothetical structures with various Sr-deficiency arrangements. Therefore, we conclude that the additional $\gamma$-ray absorptions originate from the Sn atoms neighboring the Sr deficiency., Comment: 10 pages, 7 figures

Nematic states are characterized by rotational symmetry breaking without translational ordering. Recently, nematic superconductivity, in which the superconducting gap spontaneously lifts the rotational symmetry of the lattice, has been discovered. However the pairing mechanism and the mechanism determining the nematic orientation remain unresolved. A first step is to demonstrate control of the nematicity, through application of an external symmetry-breaking field, to determine the sign and strength of coupling to the lattice. Here, we report for the first time control of the nematic orientation of the superconductivity of Sr$_x$Bi$_2$Se$_3$, through externally-applied uniaxial stress. The suppression of subdomains indicates that it is the $\Delta_{4y}$ state that is most favoured under compression along the basal Bi-Bi bonds. These results provide an inevitable step towards understanding the microscopic origin of the unique topological nematic superconductivity., Comment: Main text: 18 pages (incl. reference list), 4 figures. Supplementary text: 20 pages, 15 figures

Quite recently, a pronounced drop of $^{17}$O NMR Knight shift in the superconducting (SC) state of an unstrained Sr$_2$RuO$_4$ was reported by Pustogow and Luo ${\it et al.}$ They revealed such behavior from the free-induction decay (FID) signal after a weak RF pulse. We examined this behavior with our single-crystalline Sr$_2$RuO$_4$, and reproduced their result: the peaks of the $^{17}$O-NMR spectra shift in the SC state as long as the RF-pulse power is smaller than a threshold. Furthermore, we measured the temperature variation of the Knight shift by a standard spin-echo method with small-power RF pulses, and found that the spin susceptibility decreases in the SC state. We conclude that our previous results of the invariance of the Knight shift in the SC state were due to instantaneous destruction of superconductivity by the RF pulses. The heat-up effect was characterized by the temperature variation of the Knight shift under various measurement conditions., Comment: 18 pages, 7 figures

Sr$_{2}$RuO$_{4}$ is one of the most promising candidates of a topological superconductor with broken time-reversal symmetry, because a number of experiments have revealed evidences for a spin-triplet chiral $p$-wave superconductivity. In order to clarify the time-reversal symmetry of Sr$_{2}$RuO$_{4}$, we introduce a novel test that examines the invariance of the Josephson critical current under the inversion of both the current and magnetic fields, in contrast to the detection of a spontaneous magnetic field employed in past experiments. Analyses of the transport properties of the planar and corner Josephson junctions formed between Sr$_{2}$RuO$_{4}$ and Nb reveal the time-reversal invariant superconductivity, most probably helical $p$-wave, of Sr$_{2}$RuO$_{4}$. This state corresponds to a yet-to-be confirmed $topological crystalline superconductivity$ that can host two Majorana edge modes at the surface protected by crystalline mirror symmetry., Comment: 10 pages 6 figures

Non-equilibrium steady state (NESS) conditions induced by DC current can alter the physical properties of strongly correlated electron systems (SCES). In this regard, it was recently shown that DC current can trigger novel electronic states, such as current-induced diamagnetism, which cannot be realized in equilibrium conditions. However, reversible control of diamagnetism has not been achieved yet. Here, we demonstrate reversible in situ control between a Mott insulating state and a diamagnetic semimetal-like state by DC current in the Ti-substituted bilayer ruthenate Ca$_3$(Ru$_{1-x}$Ti$_x$)$_2$O$_7$ ($x=0.5$%). By performing simultaneous magnetic and resistive measurements, we map out the temperature vs current-density phase diagram in the NESS of this material. The present results open up the possibility of creating novel electronic states in a variety of SCES under DC current., Comment: Main text (5 pages, 4 figures) + Supplementary Materials (5 pages, 9 figures)

We have performed $^{119}$Sn-NMR measurements on the antiperovskite oxide superconductor Sr$_{3-x}$SnO to investigate how its normal state changes with the Sr deficiency. A two-peak structure was observed in the NMR spectra of all the measured samples. This suggests that the phase separation tends to occur between the nearly stoichiometric and heavily Sr-deficient Sr$_{3-x}$SnO phases. The measurement of the nuclear spin-lattice relaxation rate $1/T_1$ indicates that the Sr-deficient phase shows a conventional metallic behavior due to the heavy hole doping. In contrast, the nearly stoichiometric phase exhibits unusual temperature dependence of $1/T_1$, attributable to the presence of a Dirac-electron band., Comment: 5 pages, 4 figures

In a micro ring of a superconductor with a spin-triplet equal-spin pairing state, a fluxoid, a combined object of magnetic flux and circulating supercurrent, can penetrate as half-integer multiples of the flux quantum. A candidate material to investigate such half-quantum fluxoids is Sr$_\mathsf{2}$RuO$_\mathsf{4}$. We fabricated Sr$_\mathsf{2}$RuO$_\mathsf{4}$ micro rings using single crystals and measured their resistance behavior under magnetic fields controlled with a three-axes vector magnet. Proper Little-Parks oscillations in the magnetovoltage as a function of an axially applied field, associated with fluxoid quantization are clearly observed, for the first time using bulk single crystalline superconductors. We then performed magnetovoltage measurements with additional in-plane magnetic fields. By carefully analyzing both the voltages $V_+$ ($V_-$) measured at positive (negative) current, we find that, above an in-plane threshold field of about 10 mT, the magnetovoltage maxima convert to minima. We interpret this behavior as the peak splitting expected for the half-quantum fluxoid states., Comment: 16 pages, 15 figures

We report the results of a combined study of the normal state resistivity and superconducting transition temperature $T_c$ of the unconventional superconductor Sr$_2$RuO$_4$ under uniaxial pressure. There is strong evidence that as well as driving $T_c$ through a maximum at $\sim$3.5 K, compressive strains $\varepsilon$ of nearly 1 % along the crystallographic [100] axis drive the $\gamma$ Fermi surface sheet through a Van Hove singularity, changing the temperature dependence of the resistivity from $T^2$ above and below the transition region to $T^{1.5}$ within it. This occurs in extremely pure single crystals in which the impurity contribution to the resistivity is $<$100 n$\Omega$cm, so our study also highlights the potential of uniaxial pressure as a more general probe of this class of physics in clean systems.

In this short review, we aim to provide a topical update on the status of efforts to understand the superconductivity of Sr2RuO4. We concentrate on the quest to identify a superconducting order parameter symmetry that is compatible with all the major pieces of experimental knowledge of the material, and highlight some major discrepancies that have become even clearer in recent years. As the pun in the title suggests, we have tried to start the discussion from scratch, making no assumptions even about fundamental issues such as the parity of the superconducting state. We conclude that no consensus is currently achievable in Sr2RuO4, and that the reasons for this go to the heart of how well some of the key probes of unconventional superconductivity are really understood. This is therefore a puzzle that merits continued in-depth study.

The single-layered ruthenate Sr$_2$RuO$_4$ has attracted a great deal of interest as a spin-triplet superconductor with an order parameter that may potentially break time reversal invariance and host half-quantized vortices with Majorana zero modes. While the actual nature of the superconducting state is still a matter of controversy, it has long been believed that it condenses from a metallic state that is well described by a conventional Fermi liquid. In this work we use a combination of Fourier transform scanning tunneling spectroscopy (FT-STS) and momentum resolved electron energy loss spectroscopy (M-EELS) to probe interaction effects in the normal state of Sr$_2$RuO$_4$. Our high-resolution FT-STS data show signatures of the \beta-band with a distinctly quasi-one-dimensional (1D) character. The band dispersion reveals surprisingly strong interaction effects that dramatically renormalize the Fermi velocity, suggesting that the normal state of Sr$_2$RuO$_4$ is that of a 'correlated metal' where correlations are strengthened by the quasi 1D nature of the bands. In addition, kinks at energies of approximately 10meV, 38meV and 70meV are observed. By comparing STM and M-EELS data we show that the two higher energy features arise from coupling with collective modes. The strong correlation effects and the kinks in the quasi 1D bands may provide important information for understanding the superconducting state. This work opens up a unique approach to revealing the superconducting order parameter in this compound., Comment: 17 pages, 4 figures

We performed $^{17}$O nuclear magnetic resonance measurements on superconducting (SC) Sr$_2$RuO$_4$ under in-plane magnetic fields. We found that no new signal appears in the SC state and that the $^{17}$O Knight shifts obtained from the double-site measurements remain constant across the first-order phase-transition line, as well as across the second-order phase-transition line as already reported. The present results indicate that the SC spin susceptibility does not decrease in the high-field region, although a magnetization jump in the SC state was reported at low temperatures. Because the spin susceptibility is unchanged in the SC state in Sr$_2$RuO$_4$, we suggest that the first-order phase transition across the upper critical field should be interpreted as a depairing mechanism other than the conventional Pauli-paramagnetic effect., Comment: 5 pages, 3 figures; to appear in Physical Review B Rapid Communications