Search

We report on studies of charge carrier plasmon excitations in Sr2RuO4 by transmission Electron Energy-Loss Spectroscopy. In particular, we present results on the plasmon dispersion and its width as a function of momentum transfer. The dispersion can be qualitatively explained in the framework of RPA calculations, using an unrenormalized tight-binding band structure. The constant long-wavelength width of the plasmon indicates, that it is caused by a decay into inter-band transition and not by quantum critical fluctuations. The results from these studies on a prototypical bad metal system show that the long-wavelength plasmon excitations near 1 eV are caused by resilient quasiparticles and are not influenced by correlation effects., Comment: 6 pages, 3 figures

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 tuning, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr$_2$RuO$_4$. 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 Sr$_2$RuO$_4$., Comment: 34 pages, 23 figures, published version, manuscript and supplementary information in one document

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 research

Unambiguous identification of the superconducting order parameter symmetry of Sr$_2$RuO$_4$ has remained elusive for more than a quarter century. While a chiral $p$-wave ground state analogue to superfluid $^3$He-$A$ was ruled out only very recently, other proposed $p$-wave scenarios are still viable. Here, field-dependent $^{17}$O Knight shift measurements are compared to corresponding specific heat measurements, previously reported. We conclude that the shift results can be accounted for by the expected field-induced quasiparticle response only. An upper bound for the condensate magnetic response of $, Main Article: 4 pages 3 figures Supplement: 6 pages 4 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

Sr2RuO4 has stood as the leading candidate for a spin-triplet superconductor for 26 years1. However, recent NMR experiments have cast doubt on this candidacy2,3 and it is difficult to find a theory of superconductivity that is consistent with all experiments. The order parameter symmetry for this material therefore remains an open question. Symmetry-based experiments are needed that can rule out broad classes of possible superconducting order parameters. Here, we use resonant ultrasound spectroscopy to measure the entire symmetry-resolved elastic tensor of Sr2RuO4 through the superconducting transition. We observe a thermodynamic discontinuity in the shear elastic modulus c66, which implies that the superconducting order parameter has two components. A two-component p-wave order parameter, such as px + ipy, naturally satisfies this requirement. As this order parameter appears to have been precluded by recent NMR experiments, we suggest that two other two-component order parameters, namely $$\{{d}_{xz},{d}_{yz}\}$$ and $$\{{d}_{{x}^{2}-{y}^{2}},{g}_{xy({x}^{2}-{y}^{2})}\}$$ , are now the prime candidates for the order parameter of Sr2RuO4. Ultrasound measurements show that the superconducting order parameter in strontium ruthenate must have two components.

Phases of matter are usually identified through spontaneous symmetry breaking, especially regarding unconventional superconductivity and the interactions from which it originates. In that context, the superconducting state of the quasi-two-dimensional and strongly correlated perovskite Sr2RuO4 is considered to be the only solid-state analogue to the superfluid 3He-A phase1,2, with an odd-parity order parameter that is unidirectional in spin space for all electron momenta and breaks time-reversal symmetry. This characterization was recently called into question by a search for an expected ‘split’ transition in a Sr2RuO4 crystal under in-plane uniaxial pressure, which failed to find any such evidence; instead, a dramatic rise and a peak in a single-transition temperature were observed3,4. Here we use nuclear magnetic resonance (NMR) spectroscopy of oxygen-17, which is directly sensitive to the order parameter via hyperfine coupling to the electronic spin degrees of freedom, to probe the nature of superconductivity in Sr2RuO4 and its evolution under strain. A reduction of the Knight shift is observed for all strain values and at temperatures below the critical temperature, consistent with a drop in spin polarization in the superconducting state. In unstrained samples, our results contradict a body of previous NMR work reporting no change in the Knight shift5 and the most prevalent theoretical interpretation of the order parameter as a chiral p-wave state. Sr2RuO4 is an extremely clean layered perovskite and its superconductivity emerges from a strongly correlated Fermi liquid, and our work imposes tight constraints on the order parameter symmetry of this archetypal system. Postprint

This work was supported in part by the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory under Project No. 20170204ER. Y. L. acknowledges partial support through the LDRD and 1000 Youth Talents Plan of China. N. K. acknowledges the support from JSPS KAKNHI (Grant No. 18K04715). I. I.M. is supported by ONR through the NRL basic research program. This work is supported in part by the National Science Foundation (Grants No. DMR-1410343 and No. DMR-1709304).

INTRODUCTION A central challenge of modern condensed matter physics is to understand the range of possible collective states formed by assemblies of strongly interacting electrons. Most real materials contain high levels of disorder, which can disrupt possible ordered states and so substantially hinder the path to understanding. There is a premium, therefore, on working with extremely clean materials and identifying clean ways to tune their physical properties. Here, we show that uniaxial pressure can induce profound changes in the superconductivity of one of the model materials in the field, Sr 2 RuO 4 , and demonstrate using explicit calculations how our findings provide strong constraints on theory. RATIONALE Superconductivity remains arguably the most intriguing collective electron state. All superconductors form from the condensation of pairs of electrons into a single ground state, but in “unconventional” superconductors, a rich variety of qualitatively different ground states is possible. One of the most celebrated examples, and the one with the lowest known levels of disorder, is Sr 2 RuO 4 . Previous experimental results suggest that its superconducting condensate has odd parity, that is, its phase is reversed upon inversion of spatial coordinates. A relatively unexplored route to test this possibility is to perturb the assembly of conduction electrons through lattice distortion, which introduces no additional disorder. Electronic structure calculations suggest that if sufficient uniaxial pressure could be applied to compress the lattice along the pressure axis by about 0.8%, the largest Fermi surface of Sr 2 RuO 4 would undergo a topological transition. One of the consequences of tuning to this transition would be to substantially lower the velocity of some of charge carriers, and because slow carriers are generally favorable for superconductivity, the superconductivity might be profoundly affected. Although this topological transition has been achieved with other experimental techniques, too much disorder was introduced for the superconductivity to survive. RESULTS Our central experimental result is summarized in the figure. We prepare the sample as a beam and use piezoelectric stacks to compress it along its length. Compressing the a axis of the Sr 2 RuO 4 lattice drives the superconducting transition temperature ( T c ) through a pronounced maximum, at a compression of ≈0.6%, that is a factor of 2.3 higher than T c of the unstrained material. At the maximum T c , the superconducting transition is very sharp, allowing precise determination of the superconducting upper critical magnetic fields for fields along both the a and c directions. The c -axis upper critical field is found to be enhanced by more than a factor of 20. We perform calculations using a weak-coupling theory to compare the T c ’s and upper critical fields of possible superconducting order parameters. The combination of our experimental and theoretical work suggests that the maximum T c is likely associated with the predicted Fermi surface topological transition and that at this maximum T c , Sr 2 RuO 4 might have an even-parity rather than an odd-parity superconducting order parameter. The anisotropic distortion is key to these results: Hydrostatic pressure is known experimentally to decrease T c of Sr 2 RuO 4 . CONCLUSION Our data raise the possibility of an odd-parity to even-parity transition of the superconducting state of Sr 2 RuO 4 as a function of lattice strain and fuel an ongoing debate about the symmetry of the superconducting state even in the unstrained material. We anticipate considerable theoretical activity to address these issues, and believe that the technique developed for these experiments will also have a broader significance to future study of quantum magnets, topological systems, and electronic liquid crystals as well as superconductors.