Phase-Sensitive Tests of the Pairing State Symmetry inSr2RuO4

Abstract

Exotic superconducting properties of Sr2RuO4 have provided strong support for an unconventional pairing symmetry. However, the extensive efforts over the past decade have not yet unambiguously resolved the controversy about the pairing symmetry in this material. While recent phase-sensitive experiments using flux modulation in Josephson junctions consisting of Sr2RuO4 and a conventional superconductor have been interpreted as conclusive evidence for a chiral spin-triplet pairing, we propose here an alternative interpretation. We show that an overlooked chiral spin-singlet pairing is also compatible with the observed phase shifts in Josephson junctions and propose further experiments which would distinguish it from its spin-triplet counterpart.Unambiguous determination of the pairing state symmetry is one of the key steps towards understanding the pairing mechanism in a continously growing class of unconventional superconductors [1]. Phase-sensitive experiments, capable of identifying angular dependence of the superconducting order parameter, have provided a crucial evidence for a dominant d-wave orbital symmetry in cuprate superconductors [2,3,4]. However, much less is known for other unconventional superconductors such as heavy fermions, charge transfer salts, and cobaltates. In particular, there is compelling evidence for an unconventional pairing in Sr 2 RuO 4 [5,6], with the strong possibility of spin-triplet superconductivity which would be a solid-state analog of superfluid He 3 [7]. In superconductors with inversion symmetry an order parameter (gap matrix) can be expressed as∆(k) = ∆ 0 (k)iσ y for spin singlet and∆(k) =σ · d(k)iσ y for spin-triplet pairing. Hereσ are the Pauli spin matrices and scalar (vector) ∆ 0 (d) has even (odd) parity in the wavevector k. Often the symmetry of both the orbital and the spin part of∆(k) remains to be identified and the lack of related understanding comes from the difficulty in performing phase-sensitive experiments.While numerous previous experiments probed the pairing symmetry of Sr 2 RuO 4 [6], in this context, recent phase-sensitive experiments [8] that provide angleresolved information are particularly important. The corresponding measurements were performed in a superconducting quantum interference device (SQUID) geometry, consisting of a pair of Au 0.5 In 0.5 /Sr 2 RuO 4 Josephson junctions. Since Au 0.5 In 0.5 is a conventional s-wave superconductor, the observed modulation of critical current in an applied magnetic field was interpreted as conclusive support for the phase shifts from an odd-parity spin-triplet pairing in Sr 2 RuO 4 [8,9].A similar SQUID geometry was initially proposed [10] to study possible p-wave pairing in heavy fermions and later also used for identifying d-wave pairing in cuprates [2]. The critical current I c is modulated in the applied magnetic field as [11]where Φ is the flux threading the SQUID, Φ 0 is the flux quantum, and δ 12 is the intrinsic phase shift of the order parameter between the two tunneling directions. For a conventional ...

Strong peak in T c of Sr 2 RuO 4 under uniaxial pressure

“…However in this case a substantial body of experimental evidence [30] for triplet, chiral order would require alternative explanation. The evidence for chirality could be accommodated by a spin-singlet state, 7A ± :A [68]. This order parameter has horizontal line nodes, which requires interplane pairing, and would be surprising in such a highly two-dimensional material as Sr & RuO ' .…”

Phase Control of Majorana Bound States in a Topological X Junction

“…Majorana bound state (MBS), which are their own antiparticles [1] are usually sought in proximity-modified materials [2][3][4][5][6][7]. This approach overcomes the need for native spinless p-wave superconductivity, whose existence is debated even among the leading candidates such as Sr 2 RuO 4 [8,9]. Early MBS proposals have focused on proximity effects in one-dimensional (1D) geometries [10][11][12][13].…”

Anisotropy of the Superconducting State inSr2RuO4

“…c [26] that could possibly be locked along certain in-plane directions, recent multiband p-wave models [27], a field-dependent mixing of singlet and triplet states [28], or singlet superconductivity [10,29]. It should be noted, however, that s-wave superconductivity does not provide a satisfactory explanation for the extreme sensitivity of T c to impurities or to the chiral properties of Sr 2 RuO 4 [1,2,29]. Further experimental and theoretical work will be necessary to provide a definitive determination of the order parameter in this material.…”