Unconventional Superconductor Sr2RuO4 Research Articles

Uniaxial stress effect on the electronic structure of quantum materials

Uniaxial stress has proven to be a powerful experimental tuning parameter for effectively controlling lattice, charge, orbital, and spin degrees of freedom in quantum materials. In addition, its ability to manipulate the symmetry of materials has garnered significant attention. Recent technical progress to combine uniaxial stress cells with quantum oscillation and angle-resolved photoemission techniques allowed to study the electronic structure as function of uniaxial stress. This review provides an overview on experimental advancements in methods and examines studies on diverse quantum materials, encompassing the semimetal WTe2, the unconventional superconductor Sr2RuO4, Fe-based superconductors, and topological materials.

Distinct spin and orbital dynamics in Sr2RuO4

The unconventional superconductor Sr2RuO4 has long served as a benchmark for theories of correlated-electron materials. The determination of the superconducting pairing mechanism requires detailed experimental information on collective bosonic excitations as potential mediators of Cooper pairing. We have used Ru L3-edge resonant inelastic x-ray scattering to obtain comprehensive maps of the electronic excitations of Sr2RuO4 over the entire Brillouin zone. We observe multiple branches of dispersive spin and orbital excitations associated with distinctly different energy scales. The spin and orbital dynamical response functions calculated within the dynamical mean-field theory are in excellent agreement with the experimental data. Our results highlight the Hund metal nature of Sr2RuO4 and provide key information for the understanding of its unconventional superconductivity.

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.

Single-Crystal Growth of Sr2RuO4 by the Floating-Zone Method Using an Infrared Image Furnace with Improved Halogen Lamps

We report the single-crystal growth of the unconventional superconductor Sr2RuO4, on which research has reached a turning point recently. In order to optimize the quality of crystals grown by the floating-zone method using an infrared image furnace, we focus on an improvement of the structure of the filament in the halogen lamps. By reducing the thickness of the total filament, the form of the molten zone was narrowed. More importantly, the molten zone was observed to be more stable during the growth process. Finally, we obtained the crystals with a length of 12 cm. Additionally, the grown crystal has high quality, displaying the 1.5 K transition temperature expected only for the purest crystals. We also discuss the availability of the newly developed halogen lamps.

Heat-capacity measurements under uniaxial pressure using a piezo-driven device.

We report the development of a technique to measure heat capacity at large uniaxial pressure using a piezoelectric-driven device generating compressive and tensile strain in the sample. Our setup is optimized for temperatures ranging from 8 K down to millikelvin. Using an AC heat-capacity technique, we are able to achieve an extremely high resolution and to probe a homogeneously strained part of the sample. We demonstrate the capabilities of our setup on the unconventional superconductor Sr2RuO4. By replacing thermometer and adjusting the remaining setup accordingly, the temperature regime of the experiment can be adapted to other temperature ranges of interest.

Electronic nematicity in Sr2RuO4

We have measured the angle-resolved transverse resistivity (ARTR), a sensitive indicator of electronic anisotropy, in high-quality thin films of the unconventional superconductor Sr2RuO4 grown on various substrates. The ARTR signal, heralding the electronic nematicity or a large nematic susceptibility, is present and substantial already at room temperature and grows by an order of magnitude upon cooling down to 4 K. In Sr2RuO4 films deposited on tetragonal substrates the highest-conductivity direction does not coincide with any crystallographic axis. In films deposited on orthorhombic substrates it tends to align with the shorter axis; however, the magnitude of the anisotropy stays the same despite the large lattice distortion. These are strong indications of actual or incipient electronic nematicity in Sr2RuO4.

Topological Features in a Chiral p-wave Superconductor under Uniaxial Strain

Uniaxial strain effects in the superconducting phase are investigated assuming chiral p-wave pairing for the unconventional superconductor Sr2RuO4. The Fermi surface structure of the γ-band is espe...

Direct observation of a uniaxial stress-driven Lifshitz transition in Sr2RuO4

Pressure represents a clean tuning parameter for traversing the complex phase diagrams of interacting electron systems, and as such has proved of key importance in the study of quantum materials. Application of controlled uniaxial pressure has recently been shown to more than double the transition temperature of the unconventional superconductor Sr2RuO4, leading to a pronounced peak in Tc versus strain whose origin is still under active debate. Here we develop a simple and compact method to passively apply large uniaxial pressures in restricted sample environments, and utilise this to study the evolution of the electronic structure of Sr2RuO4 using angle-resolved photoemission. We directly visualise how uniaxial stress drives a Lifshitz transition of the γ-band Fermi surface, pointing to the key role of strain-tuning its associated van Hove singularity to the Fermi level in mediating the peak in Tc. Our measurements provide stringent constraints for theoretical models of the strain-tuned electronic structure evolution of Sr2RuO4. More generally, our experimental approach opens the door to future studies of strain-tuned phase transitions not only using photoemission but also other experimental techniques where large pressure cells or piezoelectric-based devices may be difficult to implement.

Floating zone growth of Ba-substituted ruthenate Sr2−xBaxRuO4

We report on the exploration to synthesize Sr2−xBaxRuO4, the large volume variant of the unconventional superconductor Sr2RuO4. We have succeeded in growing single crystals for x-values up to 0.4 by making use of the traveling solvent floating zone method. The quality of the obtained crystals is confirmed by X-ray and neutron diffraction measurements and the properties of these Ba-substituted ruthenates were studied with magnetic and electrical transport measurements.

Electronic and elastic properties of Sr2RuO4 with pressure effects by first principles calculation

In this work, electronic and elastic properties along with the pressure effects of the unconventional superconductor Sr2RuO4 are investigated by first principles calculation. Band structure calculation reveals that Sr2RuO4 is a weak metal. The characteristic of the band structure has also been analyzed. The calculated elastic constants reproduce the experimental data well. Analyses disclose that Sr2RuO4 is mechanically stable but anisotropic. The calculated Debye temperature 475.0K is in good agreement with the experimental results. Surveys of the pressure effect on the lattice constants reveal that the a axis is less compressible than the c axis, as found in the experiment. Further investigations illustrate that Sr2RuO4 is mechanically stable up to 50GPa till the elastic constant C44 fails to meet the mechanical stability criterion. The pressure-dependent elastic parameters are also investigated to know their behaviors under pressure. In addition, the bonding properties of Sr2RuO4 at 0GPa and 50GPa are analyzed to explain its elastic behavior under pressure.

Spin-density-wave ordering inCa0.5Sr1.5RuO4studied by neutron scattering

The spin-density-wave ordering in Ca0.5Sr1.5RuO4 was studied by polarized and unpolarized neutron diffraction experiments. Below about 20 K Ca0.5Sr1.5RuO4 exhibits quasistatic correlations at exactly the incommensurate wave vector at which pure Sr2RuO4 shows strong inelastic fluctuations driven by Fermi-surface nesting. The magnetic character of the signal and the orientation of the ordered moments along the c direction can be ascertained by neutron polarization analysis. The magnetic ordering at low temperature is very similar to that found upon minor Ti substitution of Sr2RuO4, underlining that this incommensurate spin density wave is the dominant magnetic instability of the unconventional superconductor Sr2RuO4.

High-Energy Anomaly in the Band Dispersion of the Ruthenate Superconductor

We reveal a "high-energy anomaly" (HEA) in the band dispersion of the unconventional ruthenate superconductor Sr2RuO4, by means of high-resolution angle-resolved photoemission spectroscopy (ARPES) with tunable energy and polarization of incident photons. This observation provides another class of correlated materials exhibiting this anomaly beyond high-T(c) cuprates. We demonstrate that two distinct types of band renormalization associated with and without the HEA occur as a natural consequence of the energetics in the bandwidth and the energy scale of the HEA. Our results are well reproduced by a simple analytical form of the self-energy based on the Fermi-liquid theory, indicating that the HEA exists at a characteristic energy scale of the multielectron excitations. We propose that the HEA universally emerges if the systems have such a characteristic energy scale inside of the bandwidth.

Surface and bulk electronic structure of the unconventional superconductor Sr2RuO4: unusual splitting of the β band

We present an angle-resolved photoemission study of the surface and bulk electronic structure of the single layer ruthenate Sr2RuO4. As the early studies by photoemission and scanning tunneling microscopy were confronted with a problem of surface reconstruction, surface ageing was previously proposed as a possible remedy to access the bulk states. Here, we suggest an alternative way by demonstrating that, in the case of Sr2RuO4, circularly polarized light can be used to disentangle the signals from the bulk and surface layers, thus opening the possibility to investigate many-body interactions both in bulk and surface bands. The proposed procedure results in improved momentum resolution, which enabled us to detect an unexpected splitting of the surface β band. We discuss the origin of the splitting of the β band and the possible connection with the Rashba effect at the surface.

High pressure de Haas–van Alphen studies of Sr2RuO4 using an anvil cell

Abstract We have developed a novel way to perform de Haas–van Alphen (dHvA) measurements under high pressure using a microcoil system in an anvil cell, allowing us to track the electronic structure of strongly correlated electronic systems as a function of pressure. The unconventional superconductor Sr2RuO4 is chosen to illustrate the feasibility of this technique. The dHvA frequencies are obtained from the oscillatory data and they are compared with the values reported earlier in the literature. The quasiparticle effective masses are extracted from our high resolution dHvA data.

First-principles study of spin-orbit effects and NMR inSr2RuO4

We present a first principles study of NMR and spin orbit effects in the unconventional superconductor Sr2RuO4. We have calculated the uniform magnetic susceptibility, which agrees rather well with the experiment in amplitude, but, as in an earlier model result we found the calculated hard axis to be z, opposite to the experiment. We have also calculated the Knight shifts and the NMR relaxation rates for all atoms, and again found an overall good agreement, but important deviations from the experiment in same particular characteristic, such as the Knight shift anisotropy. Our results suggest that correlations in Sr2RuO4 lead to underestimations of the orbital effects in density-functional based calculations. We also argue that the accepted ``experimental'' value for the relative contribution of orbital polarization in susceptibility, 10-15%, is also an underestimation. We discuss the puzzling invariance of the the O and Ru Knight shift across the superconducting transition for all directions of the applied field. We show that this fact cannot be explained by accidental cancellations or spin-flip scattering, as it happens in some elemental superconductors. We also point out that large contribution of the dipole and orbital hyperfine field into the Knight shifts in Sr2RuO4, combined with the possibility of an orbital-dependent superconductivity, calls for a revision of the standard theory of the Knight shift in the superconducting state.

Unconventional superconductivity and magnetism in Sr2RuO4 and related materials

AbstractWe review the normal and superconducting state properties of the unconventional triplet superconductor Sr2RuO4 with an emphasis on the analysis of the magnetic susceptibility and the role played by strong electronic correlations. In particular, we show that the magnetic activity arises from the itinerant electrons in the Ru d‐orbitals and a strong magnetic anisotropy occurs (χ+‐ < χzz) due to spin‐orbit coupling. The latter results mainly from different values of the g‐factor for the transverse and longitudinal components of the spin susceptibility (i.e. the matrix elements differ). Most importantly, this anisotropy and the presence of incommensurate antiferromagnetic and ferromagnetic fluctuations have strong consequences for the symmetry of the superconducting order parameter. In particular, reviewing spin fluctuation‐induced Cooper‐pairing scenario in application to Sr2RuO4 we show how p‐wave Cooper‐pairing with line nodes between neighboring RuO2‐planes may occur. We also discuss the open issues in Sr2RuO4 like the influence of magnetic and non‐magnetic impurities on the superconducting and normal state of Sr2RuO4. It is clear that the physics of triplet superconductivity in Sr2RuO4 is still far from being understood completely and remains to be analyzed more in more detail. It is of interest to apply the theory also to superconductivity in heavy‐fermion systems exhibiting spin fluctuations.

Quasi-two-dimensional Fermi liquid properties of the unconventional superconductor Sr2RuO4

In this paper, we review a large set of experimental data acquired over the past decade by several groups, and demonstrate how it can be used to construct a detailed picture of the low-temperature metallic state of the unconventional superconductor Sr2RuO4. We show how the normal state properties can be consistently and quantitatively explained in terms of Landau quasi-particles moving on a quasi-two-dimensional Fermi surface. Besides presenting our full and extensive data sets, we explain the details of some novel data analysis tools that can be used within the general context of quasi-two-dimensional metals. We then use the experimental Fermi surface and band dispersion to reassess several issues relevant to the unconventional superconductivity in Sr2RuO4, such as the spin-fluctuation spectrum, quasi-particle renormalization, interlayer dispersion and pressure dependence.

Superconducting order parameter of Sr2RuO4

We will discuss selected issues on our current understanding of the symmetry of order parameter of the unconventional superconductor Sr2RuO4. We point out the importance of the orbital dependence of the superconducting gap in interpreting its probable nodal structure. We also present the effect of impurities which may be used to probe the pairing mechanism.

Electronic Structure of Sr2MoO4

The band structure for Sr2MoO4, which is isostructural with the unconventional spin-triplet superconductor Sr2RuO4, has been calculated within the local-density approximation. The results of the neutron-diffraction structure refinement used in the calculation are also presented. The elecronic structure of Sr2MoO4 resembles that of Sr2RuO4, while in Sr2MoO4 the anisotropy of Fermi velocity is considerably larger than that in Sr2RuO4. The neutron diffraction results and the structure optimization result suggest that the MoO6 octahedron is less elongated than the previously reported value.