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 Momentum-Dependent Scattering in Uniaxially Stressed Sr_{2}RuO_{4} through the Hall Effect.

The largest Fermi surface sheet of the correlated metal Sr_{2}RuO_{4} can be driven through a Lifshitz transition between an electronlike and an open geometry by uniaxial stress applied along the [100] lattice direction. Here, we investigate the effect of this transition on the longitudinal resistivity ρ_{xx} and the Hall coefficient R_{H}. ρ_{xx}(T), when Sr_{2}RuO_{4} is tuned to this transition, is found to have a T^{2}logT form, as expected for a Fermi liquid tuned to a Lifshitz transition. R_{H} is found to become more negative as the Fermi surface transitions from an electronlike to an open geometry, opposite to general expectations from this change in topology. The magnitude of the change in R_{H} implies that scattering changes throughout the Brillouin zone, not just at the point in k space where the transition occurs. In a model of orbital-dependent scattering, the electron-electron scattering rate on sections of Fermi surface with xy orbital weight is found to decrease dramatically.

Layered metals as polarized transparent conductors.

The quest to improve transparent conductors balances two key goals: increasing electrical conductivity and increasing optical transparency. To improve both simultaneously is hindered by the physical limitation that good metals with high electrical conductivity have large carrier densities that push the plasma edge into the ultra-violet range. Technological solutions reflect this trade-off, achieving the desired transparencies only by reducing the conductor thickness or carrier density at the expense of a lower conductance. Here we demonstrate that highly anisotropic crystalline conductors offer an alternative solution, avoiding this compromise by separating the directions of conduction and transmission. We demonstrate that slabs of the layered oxides Sr2RuO4 and Tl2Ba2CuO6+δ are optically transparent even at macroscopic thicknesses >2 µm for c-axis polarized light. Underlying this observation is the fabrication of out-of-plane slabs by focused ion beam milling. This work provides a glimpse into future technologies, such as highly polarized and addressable optical screens.

Hierarchy of Lifshitz Transitions in the Surface Electronic Structure of Sr_{2}RuO_{4} under Uniaxial Compression.

We report the evolution of the electronic structure at the surface of the layered perovskite Sr_{2}RuO_{4} under large in-plane uniaxial compression, leading to anisotropic B_{1g} strains of ϵ_{xx}-ϵ_{yy}=-0.9±0.1%. From angle-resolved photoemission, we show how this drives a sequence of Lifshitz transitions, reshaping the low-energy electronic structure and the rich spectrum of van Hove singularities that the surface layer of Sr_{2}RuO_{4} hosts. From comparison to tight-binding modeling, we find that the strain is accommodated predominantly by bond-length changes rather than modifications of octahedral tilt and rotation angles. Our study sheds new light on the nature of structural distortions at oxide surfaces, and how targeted control of these can be used to tune density of state singularities to the Fermi level, in turn paving the way to the possible realization of rich collective states at the Sr_{2}RuO_{4} surface.

Observation of a robust and active catalyst for hydrogen evolution under high current densities.

Despite the fruitful achievements in the development of hydrogen production catalysts with record-breaking performances, there is still a lack of durable catalysts that could work under large current densities (>1000 mA cm-2). Here, we investigated the catalytic behaviors of Sr2RuO4 bulk single crystals. This crystal has demonstrated remarkable activities under the current density of 1000 mA cm-2, which require overpotentials of 182 and 278 mV in 0.5 M H2SO4 and 1 M KOH electrolytes, respectively. These materials are stable for 56 days of continuous testing at a high current density of above 1000 mA cm-2 and then under operating temperatures of 70 °C. The in-situ formation of ferromagnetic Ru clusters at the crystal surface is observed, endowing the single-crystal catalyst with low charge transfer resistance and high wettability for rapid gas bubble removal. These experiments exemplify the potential of designing HER catalysts that work under industrial-scale current density.

The superconductivity of Sr2RuO4 under c-axis uniaxial stress.

Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr2RuO4 can be tuned through a single Van Hove point, resulting in strong enhancement of both Tc and Hc2. Out-of-plane (c axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, by pushing it towards two Van Hove points simultaneously. Here, we achieve a record uniaxial stress of 3.2 GPa along the c axis of Sr2RuO4. Hc2 increases, as expected for increasing density of states, but unexpectedly Tc falls. As a first attempt to explain this result, we present three-dimensional calculations in the weak interaction limit. We find that within the weak-coupling framework there is no single order parameter that can account for the contrasting effects of in-plane versus c-axis uniaxial stress, which makes this new result a strong constraint on theories of the superconductivity of Sr2RuO4.

Elastocaloric determination of the phase diagram of Sr2RuO4.

One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research1. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning2,3, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr2RuO4 (refs. 4-9). Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr2RuO4.

Evidence for even parity unconventional superconductivity in Sr2RuO4.

Unambiguous identification of the superconducting order parameter symmetry in [Formula: see text] has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid 3He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent 17O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of <10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates.

Unsplit superconducting and time reversal symmetry breaking transitions in Sr2RuO4 under hydrostatic pressure and disorder.

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.

High-sensitivity heat-capacity measurements on Sr2RuO4 under uniaxial pressure.

A key question regarding the unconventional superconductivity of [Formula: see text] 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 percent of that of the primary superconducting transition. The normalized jump in heat capacity, [Formula: see text], grows smoothly as a function of uniaxial pressure, favoring 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 [Formula: see text].

Electronically driven spin-reorientation transition of the correlated polar metal Ca3Ru2O7.

The interplay between spin-orbit coupling and structural inversion symmetry breaking in solids has generated much interest due to the nontrivial spin and magnetic textures which can result. Such studies are typically focused on systems where large atomic number elements lead to strong spin-orbit coupling, in turn rendering electronic correlations weak. In contrast, here we investigate the temperature-dependent electronic structure of [Formula: see text], a [Formula: see text] oxide metal for which both correlations and spin-orbit coupling are pronounced and in which octahedral tilts and rotations combine to mediate both global and local inversion symmetry-breaking polar distortions. Our angle-resolved photoemission measurements reveal the destruction of a large hole-like Fermi surface upon cooling through a coupled structural and spin-reorientation transition at 48 K, accompanied by a sudden onset of quasiparticle coherence. We demonstrate how these result from band hybridization mediated by a hidden Rashba-type spin-orbit coupling. This is enabled by the bulk structural distortions and unlocked when the spin reorients perpendicular to the local symmetry-breaking potential at the Ru sites. We argue that the electronic energy gain associated with the band hybridization is actually the key driver for the phase transition, reflecting a delicate interplay between spin-orbit coupling and strong electronic correlations and revealing a route to control magnetic ordering in solids.

Retraction: In Situ Control of Diamagnetism by Electric Current in Ca_{3}(Ru_{1-x}Ti_{x})_{2}O_{7} [Phys. Rev. Lett. 122, 196602 (2019)].

Retraction of DOI: 10.1103/PhysRevLett.122.196602.

In Situ Control of Diamagnetism by Electric Current in Ca_{3}(Ru_{1-x}Ti_{x})_{2}O_{7}.

Nonequilibrium steady state conditions induced by a dc current can alter the physical properties of strongly correlated electron systems. 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 a 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 nonequilibrium steady state of this material. The present results open up the possibility of creating novel electronic states in a variety of strongly correlated electron systems under dc current.

Emergence of californium as the second transitional element in the actinide series.

A break in periodicity occurs in the actinide series between plutonium and americium as the result of the localization of 5f electrons. The subsequent chemistry of later actinides is thought to closely parallel lanthanides in that bonding is expected to be ionic and complexation should not substantially alter the electronic structure of the metal ions. Here we demonstrate that ligation of californium(III) by a pyridine derivative results in significant deviations in the properties of the resultant complex with respect to that predicted for the free ion. We expand on this by characterizing the americium and curium analogues for comparison, and show that these pronounced effects result from a second transition in periodicity in the actinide series that occurs, in part, because of the stabilization of the divalent oxidation state. The metastability of californium(II) is responsible for many of the unusual properties of californium including the green photoluminescence.

Dimensional and coordination number reductions in a large family of lanthanide tellurite sulfates.

Twenty-two new lanthanide tellurite sulfates with five distinct structures, Ln2(Te2O5)(SO4)2 (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb; LnTeSO-1), Ho3(TeO3)2(SO4)2(OH)(H2O) (LnTeSO-2), Ln2TeO3(SO4)2(H2O)2 (Ln = Dy, Ho, Er; LnTeSO-3), Ln2(Te2O5)(SO4)2 (Ln = Er, Tm, Yb, Lu; LnTeSO-4), and Ln2(Te4O10)(SO4) (Ln = Gd, Dy, Ho, Er, Tm, Yb; LnTeSO-5), have been prepared and characterized. The topologies of LnTeSO-1, LnTeSO-2, LnTeSO-3, LnTeSO-4, and LnTeSO-5 are substantially different with respect to the connectivity between Ln polyhedra and the coordination environments of the lanthanide ions. For the first four topologies, the dimensionality changes from layered (LnTeSO-1) to chains (LnTeSO-2) to tetramers (LnTeSO-3) and finally to a monomer (LnTeSO-4). The coordination numbers of lanthanides decrease from nine (LnTeSO-1) to eight (LnTeSO-2 and LnTeSO-3) to seven and six (LnTeSO-4). We attribute the transitions to a decrease in the ionic radii of the 4f ions. Magnetic susceptibility measurements reveal no evidence for long-range magnetic ordering in these materials. However, diverse short-range magnetic correlations were observed within LnTeSO-1.

Straightforward reductive routes to air-stable uranium(III) and neptunium(III) materials.

Studies of trivalent uranium (U(3+)) and neptunium (Np(3+)) are restricted by the tendency of these ions to oxidize in the presence of air and water, requiring manipulations to be carried out in inert conditions to produce trivalent products. While the organometallic and high-temperature reduction chemistry of U(3+) and, to a much smaller extent, Np(3+) has been explored, the study of the oxoanion chemistry of these species has been limited despite their interesting optical and magnetic properties. We report the synthesis of U(3+) and Np(3+) sulfates by utilizing zinc amalgam as an in situ reductant with absolutely no regard to the exclusion of O2 or water. By employing this method we have developed a family of alkali metal U(3+) and Np(3+) sulfates that are air and water stable. The structures, electronic spectra, and magnetic behavior are reported.

An orthophosphate semiconductor with photooxidation properties under visible-light irradiation.

The search for active semiconductor photocatalysts that directly split water under visible-light irradiation remains one of the most challenging tasks for solar-energy utilization. Over the past 30 years, the search for such materials has focused mainly on metal-ion substitution as in In(1-x)Ni(x)TaO(4) and (V-,Fe- or Mn-)TiO(2) (refs 7,8), non-metal-ion substitution as in TiO(2-x)N(x) and Sm(2)Ti(2)O(5)S(2) (refs 9,10) or solid-solution fabrication as in (Ga(1-x)Zn(x))(N(1-x)O(x)) and ZnS-CuInS(2)-AgInS(2) (refs 11,12). Here we report a new use of Ag(3)PO(4) semiconductor, which can harness visible light to oxidize water as well as decompose organic contaminants in aqueous solution. This suggests its potential as a photofunctional material for both water splitting and waste-water cleaning. More generally, it suggests the incorporation of p block elements and alkali or alkaline earth ions into a simple oxide of narrow bandgap as a strategy to design new photoelectrodes or photocatalysts.

A comparison study of rhodamine B photodegradation over nitrogen-doped lamellar niobic acid and titanic acid under visible-light irradiation.

A solid-state reaction method with urea as a nitrogen precursor was used to prepare nitrogen-doped lamellar niobic and titanic solid acids (i.e., HNb(3)O(8) and H(2)Ti(4)O(9)) with different acidities for visible-light photocatalysis. The photocatalytic activities of the nitrogen-doped solid acids were evaluated for rhodamine B (RhB) degradation and the results were compared with those obtained over the corresponding nitrogen-doped potassium salts. Techniques such as XRD, BET, SEM, X-ray photoelectron spectroscopy, and UV-visible diffuse reflectance spectroscopy were adopted to explore the nature of the materials as well as the characteristics of the doped nitrogen species. It was found that the intercalation of the urea precursor helped to stabilize the layered structures of both lamellar solid acids and enabled easier nitrogen doping. The effects of urea intercalation were more significant for the more acidic HNb(3)O(8) sample than for the less acidic H(2)Ti(4)O(9). Compared with the nitrogen-doped KNb(3)O(8) and K(2)Ti(4)O(9) samples, the nitrogen-doped HNb(3)O(8) and H(2)Ti(4)O(9) solid acids absorb more visible light and exhibit a superior activity for RhB photodegradation under visible-light irradiation. The nitrogen-doped HNb(3)O(8) sample performed the best among all the samples. The results of the current study suggest that the protonic acidity of the lamellar solid-acid sample is a key factor that influences nitrogen doping and the resultant visible-light photocatalysis.

Non-fermi-liquid behavior in Sr2RuO4 with nonmagnetic impurities.

We report that the quasi-two-dimensional Fermi-liquid behavior of the spin-triplet superconductor Sr2RuO4 breaks down in the vicinity of the critical impurity concentration for the onset of magnetic order induced by nonmagnetic Ti4+ impurities. The non-Fermi-liquid behavior is interpreted in terms of the two-dimensional antiferromagnetic fluctuations, which arise mainly from the nesting within one of the Fermi-surface sheets. We argue against the main role of such magnetic fluctuations in the pairing mechanism.