Limiting mechanism for critical current in topologically frustrated Josephson junctions

Abstract

Eutectic Sr 2 RuO 4 -Ru samples with μm-sized Ru-metal inclusions support inhomogeneous superconductivity above the bulk transition of Sr 2 RuO 4 in the so-called 3-Kelvin phase. In Pb/Ru/Sr 2 RuO 4 Josephson junctions as realized by Maeno et al., a Pb film is indirectly coupled to the superconductor Sr 2 RuO 4 mediated by the proximity-induced superconducting Ru inclusions, yielding an extended Josephson contact through the interface between Ru and Sr 2 RuO 4 . Motivated by this experimental setup, we formulate a sine-Gordon model for the Josephson phase of the interface, assuming a simple cylindrical shape for the Ru inclusion hosting the proximityinduced s-wave superconducting phase. Considering the Sr 2 RuO 4 as a chiral p-wave superconductor, we discuss two types of Josephson junctions, a frustrated one due to the nature of the order parameter in Sr 2 RuO 4 and an unfrustrated one for the topologically trivial 3-Kelvin phase. While the latter situation displays standard junction behavior, the former yields an unusual limiting mechanism for the critical current, based on a pinning-depinning transition of a spontaneously induced magnetic flux driven by an externally applied current. We analyze different coupling limits and show that different critical currents can arise for the two topologies. This concept fits well to recent experimental data obtained for the above setup showing an anomalous temperature dependence of the critical current at the transition temperature T c of bulk Sr 2 RuO 4 .

Evolution of the filamentary 3-Kelvin phase inPb−Ru−Sr2RuO4Josephson junctions

“…The experimental observation of the anomalous temperature dependence of the critical current in the Pb-Ru-SRO Josephson junction reflects this modification, demonstrating that the Josephson current is limited by distinct mechanisms in phases with N = 0 (A-and A ′ -phases) and with N = ±1 (B-phase) 30 . The complete description of the temperature dependence of the Josephson current requires the discussion of the third spatial dimension of the device, which we avoid in this paper.…”

“…Upon lowering the temperature further, I c quickly recovers. It is worth noting here, that the observation of a non-vanishing Josephson effect above T c,SRO demonstrates the presence of the 3K phase at the interface.It has been suggested that the anomalous temperature originates from a change of the limiting of the Josephson current between SRO and Ru (with proximityinduced s-wave pairing) 11,12,30 . While for the temperatures above T c,SRO the Josephson coupling could be as essentially uniform, below T c,SRO the chiral nature of the bulk superconducting state in SRO would yield a frustrated Josephson coupling with a considerably lower critical temperature.…”

“…The experimentally observed anomalous drop of I c at T c, SRO 11,12 can be attributed to a topology change of the superconducting state at the interface. In recent theoretical studies, the influence of the interface state topology on the critical Josephson current has been discussed assuming an s-wave order parameter within Ru inclusions 30,32 . When N = 0 (A-and A ′ -phase), the interface acts like an ordinary extended Josephson junction 33 , while N = ±1 (B-phase) yields a frustrated junction 32 .…”

“…At T cB , the topology of the Josephson contact changes. Because of the change from N = 0 to N = ±1, the Josephson critical current I c is reduced 30 . An anomalous drop should occur near T c,SRO , followed by an increase at lower temperatures, as shown in Fig.…”

Multicomponent order parameter superconductivity of Sr2RuO4 revealed by topological junctions

“…Recently, Etter et al 38 , proposed that transport properties of topological junctions based on the eutectic SRO-Ru system depend strongly on phase winding. They found that in the 3-K phase the phase winding is zero and junction exhibits ordinary or unfrustrated behaviour.…”