Anomalous switching in Nb/Ru/Sr2RuO4 topological junctions by chiral domain wall motion

A spontaneous symmetry breaking in a system often results in domain wall formation. The motion of such domain walls is utilized to realize novel devices like racetrack-memories, in which moving ferromagnetic domain walls store and carry information. Superconductors breaking time reversal symmetry can also form domains with degenerate chirality of their superconducting order parameter. Sr2RuO4 is the leading candidate of a chiral p-wave superconductor, expected to be accompanied by chiral domain structure. Here, we present that Nb/Ru/Sr2RuO4 topological superconducting-junctions, with which the phase winding of order parameter can be effectively probed by making use of real-space topology, exhibit unusual switching between higher and lower critical current states. This switching is well explained by chiral-domain-wall dynamics. The switching can be partly controlled by external parameters such as temperature, magnetic field and current. These results open up a possibility to utilize the superconducting chiral domain wall motion for future novel superconducting devices.

S ince the discovery of superconductivity in Sr 2 RuO 4 (SRO) 1 , various experiments [2][3][4][5][6][7] reveal that the pairing state of SRO is of chiral p-wave spin-triplet with broken time reversal symmetry 8,9 , analogous to the A-phase of superfluid 3 He 10,11 . However, the issue of chiral p-wave nature of SRO still remains controversial since some of the predicted behavior such as chiral edge current has not been observed 9 . Thus establishment of novel behavior specific to chiral p-wave superconductivity is much desirable. Recently, SRO is considered as one of the most promising materials for exploring topological superconducting phenomena originating from its orbital phase winding 9 . Because of nontrivial topological aspect of its superconducting order parameter, gapless chiral edge states consisting of Majorana quasiparticles (whose antiparticles are their own particles) are believed to emerge at its boundaries [12][13][14][15] .
Chiral p-wave superconductivity exhibits two-fold degeneracy corresponding to clockwise or counterclockwise winding of the superconducting phase. This degeneracy sets up two kinds of chiral domains separated by a chiral domain wall (chiral-DW) 16 . To date, there is no direct observation of the chiral-DW 17 . However, the existence of the chiral-DW has been strongly suggested by transport studies of SRO-based junctions 2,18 . Further accumulation of evidence of the chiral-DW and investigations of possible influences of chiral-DW dynamics on transport properties are important because the chiral-DW can be utilized for novel superconducting devices as in the case of the ferromagnetic-DW for racetrack memory devices 19 .
A ''topological junction'' consists of a superconductor surrounded by another in such a way that the difference in phase winding dictates the junction behavior 20,21 . The characteristics of a topological junction with a chiral pwave superconductor should be very sensitive to the chiral domain configuration. The SRO-Ru eutectic system 22 provides naturally existing topological junctions, once s-wave superconductivity is induced into Ru inclusions surrounded by SRO. Indeed, junctions fabricated using Pb as an s-wave superconductor deposited over many Ruinclusions 20,21 exhibit peculiar temperature dependence of critical current I c attributable to topological phase competition between the s-wave and p-wave superconductivity. Since previous devices containing many Ru junctions probe only averaged effects, it is much desirable to fabricate a device with a single junction to investigate the order parameter structure more sensitively, including the effect of chiral domains.

Results
We fabricate SRO-Ru based micron-sized junctions utilizing only one Ru inclusion shown in Figs. 1a-d. Figure 1e presents the junction resistance versus temperature. Junction A (Junction B) exhibits the first transition at 9.5 K (9 K) corresponding to the superconducting transition temperature T c of Nb. The final transition starting at around 2.8 K (for both junctions) leads to zero junction resistance at T c,A 5 1.68 K (T c,B 5 1.68 K) (inset of Fig. 1e). These temperatures are significantly higher than T c_bullk 5 1.42 K of SRO in the eutectic crystal used in this study because of enhanced superconductivity at the interface between Ru and SRO, the so-called 3-K phase 22 . A clear supercurrent branch with zero voltage is obvious in an I-V curve at 0.37 K (inset of Fig. 2a). These facts, as well as Fraunhofer pattern (see the supplementary information), indicate that our junctions exhibit a typical Josephson coupling. Figure 2a presents I c versus temperature data, accumulated from 0.34 K to 2.5 K with various cooling cycles (represented with different colors). Interestingly, we find a sharp jump in I c after ''each'' cooling cycle. Such jumps are prominent at T , T c_bullk ; at T . T c_bullk I c is rather stable. The changes in I c indicate the switching between two states of the junction with the cooling cycles.
To study the I c variations further, we obtained I-V curves at various temperatures after zero-field cooling (Fig. 3a). An ordinary I-V curve is observed at 1.5 K. However, I-V curves at 1.4 K and 0.5 K exhibit oscillations between zero and non-zero voltages corresponding to switching between higher-I c and lower-I c states. At these three temperatures the voltage versus time V(t) is also recorded at constant excitation current I exc just below I c (Fig. 3b). At 1.5 K, V(t) exhibits constant zero voltage. However, at 1.4 K, V(t) shows sharp switching between zero and non-zero voltages <120 nV. This switching resembles telegraphic noise (TN). Nearly equal probabilities in the non-zero and zero voltage states indicate that the lower-I c state is as stable as the higher-I c state. The V(t) data at 0.5 K demonstrate rather sharp and short switching at the amplitude of ,200 nV. Thus, the junction tends to stay in the higher-I c state. These observations, as well as sudden disappearance of TN signal at T c_bulk in data (see the supplementary information) taken under a temperature upsweep, reveal that the switching behavior is strictly correlated with the bulk superconductivity in SRO; the junction is quite stable at T . T c_bullk and rather unstable at T , T c_bullk . Note that the switching is also observed at different temperatures between 1.4 K and 0.5 K. Although the transition temperature of bulk Ru is 0.49 K, we do The normal junction resistance R N is 128 mV for the junction A (blue curve) and 11.5 mV for the junction B (red curve). The different R N values are attributed to different interface transparency as well as cross sectional area. The drop in the resistance at around 9 K corresponds to superconducting transition of Nb (T c < 9.5 K) and the drop to zero resistance starts at 2.8 K because of proximity effect with 3-K phase. There are additional drops for the junction A, reflecting gradual development of proximity into Ru metal. The inset is an enlargement showing that the zero junction resistance persists to temperatures substantially above T c_bulk 5 1.42 K of SRO. The bulk resistance of SRO is negligible compared with the junction resistance.
www.nature.com/scientificreports SCIENTIFIC REPORTS | 3 : 2480 | DOI: 10.1038/srep02480 not observe any anomaly in I c (T) at a corresponding temperature (see fig. 2); this observation indicates that Ru is already fully proximitized.
We also preformed experiments to control the switching behavior. Figure 4a shows the influence of I exc at 1.4 K. The V(t) data at I exc 5 30 mA, about half of I c 5 62 mA, show zero resistance. At I exc 5 53 mA, V(t) exhibits voltage switching of the order of 120 nV. Note that switching between the high voltage state and an intermediate state is sometimes observed. Overall, a longer time in the zero-voltage state indicates that the junction is more stable in the higher-I c state.
Closer to I c (I exc 5 59 mA), the junction spends nearly equal time in both states. For I exc 5 53 mA . I c , V(t) exhibits constant non-zero voltage. Thus, the switching is only observed in the I exc range where the voltage oscillations are present in the corresponding I-V curves (Fig. 3a). Close to I c , where the junctions are rather unstable, we found that a small temperature variation can trigger the switching: in the V(t) curve at 1.4 K with intentional temperature variations of ,1.5 mK, the switching occurs in-phase to the temperature variations (Fig. 4b). Note that the temperature variations during V(t) measurements of the curves in Figs. 3&4a were smaller than 50 mK; this fact evidences that the temperature variations can stimulate the switching but is not the origin. We also found that switching is enhanced by small externally applied magnetic fields. Figure 4c shows the I-V curve at 0.5 K with the field of 0.10 Oe along the ab-plane exhibiting fine voltage variations, with the corresponding V(t) data also showing fast switching (inset of Fig. 4c).
We also demonstrate that switching behavior can be altered by cooling cycles. Figure 3 and Fig. 4d show data at different cooling cycles at 0.5 K. The switching, which is obvious in the former case, is not observed in the latter case. The switching is not observed for I exc , I c either (upper-left inset of Fig. 4d). It is interesting that the hysteresis loop in I-V curves for the latter case is reversed, in the sense that zero voltage state is realized with higher current for down sweep. This hysteretic behavior is also anomalous because the difference between the higher and lower I c is not constant; sometimes the hysteresis in I c disappears (bottom-right inset of Fig. 4d). These facts reveal that the system in this cooling cycle is rather stable but anomalous hysteresis suggests that some instability is present at I exc . I c . Indeed, we observed a small switching only at I exc 5 144 mA (I exc . I c ), but surprisingly not for I exc 5 143 or 145 mA (see the supplementary information).

Discussion
Prior to discussion, we summarize the behavior of the Nb/Ru/SRO junctions. With decreasing temperature below T c_Nb 5 9.5 K, the proximity effect of the s-wave superconductivity develops in Ru. Below 3 K, the interfacial 3-K superconductivity in SRO sets in and the junctions start to show finite I c below ,1.8 K, forming SNS9 junctions. Although the junction behavior is conventional and highly reproducible down to T c_bullk , a number of anomalous   behaviors emerge at temperatures precisely below T c_bullk . First is the anomalous hysteresis in the I-V curves, often accompanied by asymmetry with respect to the direction of current. A similar hysteresis has been reported by Kambara et al., in SRO-Ru micro-bridge 18 . Second is the presence of mainly two branches of I c , between which junctions switch back and forth. Third is the TN, which corresponds to the telegraphic switching between the multiple branches of I c . The junctions at temperatures just below T c_bulk show rather active TN with mainly two different states. At low temperature the junctions are more stable in the higher-I c state. Whenever the TN is active I c drops down by <50% to I c in the most stable state. The junctions can be driven into unstable state with active TN either by different cooling cycle or by tiny external magnetic fields. Comparing Junctions A and B, Junction A with smaller junction area is relatively stable. These behaviors cannot be explained by the motion of ordinary vortex (see the supplementary information). Below, we examine the possible origins of the unusual behavior in terms of self-induced vortex dynamics specific to chiral superconductor, and in terms of chiral-DW dynamics.
Self-induced vortex: For a Ru-inclusion below its T c (0.49 K) surrounded by SRO, it is theoretically predicted that a selfinduced vortex appears due to a competition between s-wave superconductivity in Ru metal and the chiral p-wave superconductivity in SRO. Such a vortex can switch between two states: one at the Ru/SRO interface and the other at the center of the Ru-inclusion. The switching should occur at lower temperatures and more likely for smaller Ru-inclusions 23 . In our junctions, similar self-induced vortex is anticipated even above 0.5 K because of the proximity-induced superconductivity in Ru via Nb electrode. However, our junctions become stable at lower temperatures and also for smaller Ru-inclusion. Thus, the observed behavior is unlikely caused by the selfinduced vortex dynamics.
Chiral-DW dynamics: Chiral domain structure of superconducting bulk SRO around the Ru-inclusion is expected to play a crucial role in determining I c . It is considered to appear only below T c_bullk 20,21 , in accord with the emergence of unusual behavior observed only below T c_bullk . Expectedly, it becomes more stable at low temperatures with increasing condensation energy of SRO. To illustrate the effect of chiral-DW dynamics, let us introduce a simplest model. We consider a single Ru-inclusion having a smooth circular-shape in pure SRO and two chiral-DWs separating the imbedded in SRO into two domains with opposite chirality (g 1 5 e ih and g 2 5 e 2ih , Fig. 5a). The chiral-DWs intersect with the Ru/SRO interface fixed at h(F) 5 0u with Q 1 (F) 5 DQ (h is the direction normal to the interface, Q 6 is the phase difference of the p-wave SRO in the domain g 6 with respect to the s-wave Ru) and at h(M) 5 h DW which is assumed movable. The free energy of a chiral-DW depends on the orientation and the phase difference a across the chiral-DW, which would be determined by minimizing the junction energy for a given ''M'' and I exc with the distribution of the pinning potential for chiral-DWs, etc. in an intricate way 16 . Here, the effect of the additional energy associated with the induced magnetic flux is not included. This is because the phase winding mismatch between swave and p-wave is resolved by presence of a chiral domain wall and as a consequence the flux energy is expected to be much reduced. Thus, we introduce a conjecture that I c is determined by the following current-phase relation for a given h DW which is varied from 0 to p, By symmetry and for single-valuedness of the order parameter we consider a(M) 5 2a(F) 5 p 2 h DW . This in fact is the condition to maximize I c for a given value of h DW . In this scenario, maximum I c is realized at h DW 5 p and a 5 DQ 5 0 (Fig. 5b). This can be understood as the absence of current cancelation over the Ru circumference in the presence of multiple chiral-DWs (see the supplementary information). A rotation of domain wall M by 610u around h DW 5 p affects I c very little, but the rotation around h DW 5 p/2 significantly changes I c ( Fig. 5c; I-V curves are calculated using the relation for an overdamped junction). This character captures features of our experimental observations (Fig. 5d): stable and maximum I c is observed in one cooling cycle, and unstable and lower I c is realized in a different cooling cycle. In reality, it is reasonable that h DW 5 p gives the most stable state because the actual Ru inclusion is elongated with the maximum curvature (maximum disorder) at its corners providing maximum pinning for chiral-DWs. Note that the observed I c is always ,50% lower when voltage oscillations emerge in the I-V curves. In our model such lower and unstable I c occurs for the chiral-DW motion around h DW 5 p/2, corresponding to the flat part of the actual Ru/SRO interface. These calculations confirm that the aspects of the observed anomalous behavior of our junctions are well explained by the chiral-DW motion. We studied Sr 2 RuO 4 -based micron-sized junctions, Nb/Ru/SRO, using one Ru inclusion, and found unusual temperature dependence of I c , anomalous hysteresis with current, and switching in I c . It is difficult to explain the overall behavior by vortex dynamics (ordinary and self-induced). Instead, a simple model based on the chiral-DW motion captures the main features of the observed junction behavior. Our results provide further evidence for chiral p-wave order parameter in SRO and reveal the crucial effects of chiral-DW motion on Josephson coupling. The switching raised by chiral-DW motion can be controlled by various external parameters and provides a ground for novel superconducting devices, analogous to memory devices based on ferromagnetic-DW motion. Our work also demonstrates the scientific importance of the concept of the topological junctions to expose the phase winding of superconducting order parameter by making use of the real-space topology.

Methods
We fabricated Nb/Ru/SRO micron-sized Josephson junctions using a polished (the basal ab-plane) rectangular pieces (3 3 3 3 0.5 mm 3 ) of SRO-Ru eutectic crystals grown by a floating-zone method 24 . Contact resistance between the ab-surface of SRO and Nb is rather large but Ru metal works as an adhesive layer to provide a good contact. Although, a technique of using Nb/Cu bilayer has recently been developed to establish a good contact to the surface parallel to the c-axis to enhance the J c of the junction 25 , here we need to deal with the ab-plane surface contact. After polishing its ab-surface, SiO x layer of thickness of ,300 nm was deposited using RF sputtering technique with a backing pressure of ,10 27 mbar. Then a photoresist (TSMR-8800) was coated, exposed with laser lithography over only one Ru inclusion. The exposed resist was removed with TMAH2.83% developer for 120 sec followed by rinsing in DI-water for 30 sec and dried with N 2 gas. A part of the SiO x film covering single Ru inclusion was etched with CHF 3 gas, which opened the windows over a single Ru inclusion (Fig. 1a). In this process, a fluoride thin film may be generated on the surface of the sample. We performed an O 2 plasma cleaning step to etch away a fluoride film. The resist was removed using N-Methyl-2-pyrolidone (NMP) and cleaned with acetone and isopropanol. In the next step to deposit the Nb electrodes, we used a liftoff technique using bilayer photoresist (LOR-10A and TSMR-8800) and laser lithography. A Nb film of the thickness of ,1 mm was sputtered with a base pressure of ,10 27 mbar. Finally, the lift-off was accomplished with NMP. Note that Nb is not only in contact with Ru but also with SRO along ab-plane. It is well known that abplane is less conductive because of atomic reconstruction at the surface and does not allow supercurrent to flow directly from Nb. Instead, supercurrent from Nb passes only through the Ru metal with proximity induced superconductivity from Nb. Figure 1b shows an overall scanning electron microscope (SEM) picture of the device with two junctions. We measured the I-V curves using four-point technique with two contacts at Nb over the ab-plane and the other two contacts on the side directly connected via silver paste with SRO crystal as shown in the schematic of the side view in Fig. 1c. The measurements are performed with a 3 He cryostat down to 300 mK. The cryostat was magnetically shielded with high-permeability material (Hamamatsu Photonics, mu-metal). Inside the shield, we placed a superconducting magnet to apply the magnetic fields.