Evaluation of Spin-Triplet Superconductivity in Sr₂RuO₄

Abstract

This review presents a summary and evaluations of the superconducting properties of the layered ruthenate Sr 2 RuO 4 as they are known in the autumn of 2011. This paper appends the main progress that has been made since the preceding review by Mackenzie and Maeno was published in 2003. Here, special focus is placed on the critical evaluation of the spin-triplet, odd-parity pairing scenario applied to Sr 2 RuO 4 . After an introduction to superconductors with possible odd-parity pairing, accumulated evidence for the pairing symmetry of Sr 2 RuO 4 is examined. Then, significant recent progress on the theoretical approaches to the superconducting pairing by Coulomb repulsion is reviewed. A section is devoted to some experimental properties of Sr 2 RuO 4 that seem to defy simple explanations in terms of currently available spin-triplet scenario. The next section deals with some new developments using eutectic boundaries and micro-crystals, which reveals novel superconducting phenomena related to chiral edge states, odd-frequency pairing states, and half-fluxoid states. Some of these properties are intimately connected with the properties as a topological superconductor. The article concludes with a summary of knowledge emerged from the study of Sr 2 RuO 4 that are now more widely applied to understand the physics of other unconventional superconductors, as well as with a brief discussion of relatively unexplored but promising areas of ongoing and future studies of Sr 2 RuO 4 .KEYWORDS: Sr 2 RuO 4 , ruthenate, spin-triplet superconductivity, topological superconductor Spin-Triplet Superconductors Candidates of spin-triplet superconductorsIn the last three decades, and particularly since the discovery of high-transition-temperature (high-T c ) superconductivity of the cuprates, 1) studies of ''unconventional'' superconductivity have been one of the main topics in condensed-matter physics. Here we designate the term ''unconventional'' as the pairing based on non-phonon mechanisms.2) The unconventional superconductivity is mainly found in heavy-fermion superconductors (since 1978), 3) Unconventional superconductivity is characterized by the anisotropic gap function or order parameter which is integrated to be zero or a small value due to the variations of the wave function ''phase'', in contrast to an ordinary s-wave state. In many of them, including high-T c cuprates and iron pnictides, the electrons are clearly paired in spinsinglet states. In this point of view, they are similar to conventional s-wave superconductors, in which the spindegrees of freedom is lost in the charged superfluids. Spintriplet superfluid states are fully established in the Fermi liquid 3 He, 7,8) for which spin and mass supercurrents emerge in the charge-neutral superfluids. The question is then whether or not spin-triplet superconductors exist, and what novel superconducting properties they may exhibit due to their charge and spin supercurrents.There are several classes of candidates of spin-triplet superconductors represented in Table I. W...

Enhanced spin-triplet superconductivity near dislocations in Sr2RuO4

“…2c), comparable to that of the pure phase (75 mT), whereas sample C showed an H c2 of 0.3T (inset of Fig. 2i), closer to that of the eutectic phase 5,6 . Therefore, our experimental observations provide a direct confirmation that the presence of dislocations leads to the enhancement of T c in Sr 2 RuO 4 as predicted by the theory.…”

“…6), we assume that T ch ¼ 3.2 K. As a result, the experimentally observed typical onset T c of 2.5 K corresponds to d ¼ 3.5(K 2 /aT c0 ) 1/2 . This d-value is comparable to the superconducting coherence length given by…”

“…A large body of experimental data, including that obtained in phase-sensitive measurements 4 , has shown that the layered perovskite Sr 2 RuO 4 is a spin-triplet, odd-parity superconductor 5,6 . Assuming that superconductivity in this material is two-dimensional in nature, the fourfold tetragonal crystalline symmetry dictates that the pairing symmetry must be one of the five representations 7 .…”

“…In this regard, models based on ferromagnetic 10 or antiferromagnetic fluctuations 11 , spin-orbit coupling 12 , interaction theory 13,14 , Hund's rule coupling 15 and interplay of charge and spin fluctuations in the one-dimensional bands 16 have been proposed. The debate on these mechanisms is currently ongoing 6 .…”

Magnetic manipulation of topological states in p-wave superconductors

“…The number of known triplet superconductors has been growing steadily, and now includes UPt 3 [21], ferromagnetic superconductors such as UGe 2 , URhGe, UIr and UCoGe [22][23][24], quasi one-dimensional organic system (TMTSF) 2 X (X=ClO 4 and PF 6 ) [25,26] and transition metal lithium oxide [27]. In particular, hallmarks for spin-triplet superconductivity have emerged for Sr 2 RuO 4 [28,29], for which the existence of high-quality single crystals allowed the study of heterostructures based on spin-triplet super- conductivity [30,31].…”