Josephson vortices and intrinsic Josephson junctions in the layered iron-based superconductor Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5

Qiang-Tao Sui(隨強濤) and Xiang-Gang Qui(邱祥岡)

1Beijing National Laboratory for Condensed Matter Physics,Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China

2School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

3Songshan Lake Materials Laboratory,Dongguan 523808,China

Keywords: iron-based superconductor,Abrikosov vortices,Josephson vortices,intrinsic Josephson junctions

1. Introduction

Nowadays the well-known applications based on Josephson junctions, such as superconducting quantum interference device (SQUID), superconducting qubit,[1-4]single-photon detector[5]and ac Josephson junction laser,[6]have demonstrated the possibility of potential large scale applications of superconductivity. In contrast to Josephson junctions made up of artificial superconducting heterostructures, the intrinsic Josephson junctions (iJJs)[7-13]formed inside single crystals possess atomic flatness and fewer defects,and provide unique applications, e.g., THz sources. In high-Tccuprate superconductors,measurements of dc and ac Josephson effects[7,8,12-18]indicate that iJJs are formed between CuO2superconducting layers, which provide direct evidence for alternating stacks of superconducting and non-superconducting layers. For anisotropic layered superconductors, the coherent length normal to the superconducting layersξ⊥and the interlayer distancedare two characteristic lengths that play a crucial role in determining the distribution of out-of-plane superconducting order parameter. Sinceξ⊥decreases with lower temperature, a reasonable expectation of shorterξ⊥is that Cooper pairs condense into the superconducting layers and a crossover from three-dimensional(3D)to quasi-two-dimensional(quasi-2D)superconductivity should occur at an intermediate temperatureT＊whenξ⊥becomes shorter thand/2.[19]Accordingly,iJJs can be formed in the anisotropic layered superconductors,such as the case of cuprate superconductors.[7,8,12-18]Since the iron-based superconductors discovered in 2008[20-23]have similar layered structure with the cuprates, whose superconductivity is assumed to emerge in the FeAs or FeSe layers,[24-28]a natural question to ask is whether iJJs are also formed in the iron-based superconductors or not.

For iJJs in a magnetic field parallel to the superconducting layers, there exist vortices in the form of Josephson vortices.Josephson vortices are free to flow along the superconducting layers driven by the current perpendicular to the superconducting layers, due to the fact that the cores of Josephson vortices are phase cores formed between the superconducting layers and thus the pinning effect of defects on Josephson vortices is weak.[29,30]In contrary to Josephson vortices,Abrikosov vortices suffer from strong pinning of defects due to their normal state cores. Consequently,the Abrikosov vortices flow is susceptible to the temperature because pinning of defects gets stronger upon cooling, e.g., in the iron-based superconductors.[31,32]When the magnetic field slightly deviates from the superconducting layers, the Josephson vortices flow is affected by the strong pinning of Abrikosov vortices due to the formation of composite vortex structures.[33]Therefore, to reveal the existence of Josephson vortices by the different behaviors of Josephson and Abrikosov vortices,the formation of iJJs in anisotropic layered superconductors can be confirmed.

In the iron-based superconductors,c-axis transport measurements on SmFeAs(O, F), LaFeAs(O, F)[34]and(V2Sr4O6)Fe2As2[35]as well as torque measurements on LaO0.9F0.1FeAs and SmO0.9F0.1FeAs[36]have suggested the existence of Josephson vortices. It is of great interest to explore the possibility of intrinsic Josephson junction behavior in other iron-based superconductors. In this work, by using the angular and temperature dependent transport measurements,we investigated the vortex dynamics of the iron-based superconductor single crystal Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5withTc?12 K. Our results show that the behaviors of flux flow present a remarkable change at a crossover temperatureT＊?7 K,which indicates the distinct transition of the intrinsic structure of the vortices from the well-pinned Abrikosov vortices aboveT＊to the weakly-pinned Josephson vortices belowT＊,suggesting the existence of Josephson vortices and the formation of iJJs in Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5.

2. Experimental details

The Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5single crystals were grown using the self-flux method, as described elsewhere.[37,38]The crystal structure was characterized by x-ray diffraction(RigakuD/MAX-Ultima III)using CuKαradiation (λ=0.154 nm) at room temperature. Magnetization measurements were done using a superconducting quantum interference device(SQUID-VSM,Quantum Design). Transport measurements were performed in a physical property measurement system(PPMS-9,Quantum Design),which was connected to an external digital lock-in amplifier (SR830).In order to apply the current perpendicular to the FeAs layers, the samples were microfabricated with the focused ion beam(FIB)technique. Details of this process on FIB sample preparation have been reported elsewhere.[39]The samples connected to a puck were mounted on a PPMS horizontal rotator to scanθat a resolution of 0.015°.

3. Results and discussion

3.1. Results

Figure 1(a) shows the x-ray diffraction (XRD) result of the Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5single crystals. All of the indexed peaks identified belong to the Ca10(Pt3As8)(Fe2As2)5triclinic structure phase. The presence of only (00l) reflection peaks indicates that the natural cleavage planes are parallel to the FeAs layers and the stacks of alternating FeAs and PtAs layers are perfect. The calculated interlayer distance isd～10.283 ?A, close to the previous reported value.[37]The temperature-dependent resistivityρab(T) shows that as the temperature is lowered, the metallic behavior is followed by a semiconducting one, and finally superconductivity emerges below 12.8 K as shown in Fig. 1(b). The bulk superconductivity is confirmed by the diamagnetic signal observed in both zero-field-cooling (ZFC) and field-cooling (FC) measurements below 12.4 K, which is consistent with that in the temperature-dependent resistivityρab(T) measurements,as shown in Fig.1(c).

To investigate the possible iJJs behaviors, we have measured the angular and temperature dependent resistance of the micro-fabricated sample with a cross-section of 2.5×1.9μm2fabreicated by FIB technique as shown in Fig. 2(a). Upon cooling, the temperature-dependent resistivityρc?(T) exhibits a semiconducting behavior above 15 K in the normal state, in contrast to that in Fig. 1(b), suggesting a weak coupling between the FeAs layers. From the angular dependent flux-flow resistance in Fig. 2(c), it can be seen that the flux-flow resistance overall decreases with lower temperature, which is consistent with the behaviors of Abrikosov vortices due to the enhanced pinning upon cooling. However, there exists a surprising exception in a narrow angularregion aroundθ=0°. Upon cooling fromTc, nearθ=0°, a broad peak grows gradually in a background. At the crossover temperatureT＊?7 K,the background disappears and a sharp peak centered atθ=0°emerges in a very narrow angular region(less than±0.5°).

Fig.1. The characterization of Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5 single crystals.(a)The typical XRD θ-2θ scan of a Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5 single crystal. (b)The temperature-dependent resistivity ρab(T)with the current I=10μA parallel to the FeAs layers. The inset is the schematic of the crystal structure of Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5. (c) The temperature dependence of magnetic susceptibility measured in the zero field cooling(ZFC)and field cooling(FC)with the magnetic field H =20 Oe parallel to the FeAs layers in order to weaken the demagnetization effect.The inset is the blowup of the temperature-dependent magnetic susceptibility near zero.

Fig. 2. The interlayer dissipation resistance of a typical Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5 sample. (a) False-color scanning electron micrograph of a typical sample microfabricated by FIB technique. The crystal (alternating purple and green) was carved with four electrodes, each of which was connected to the Au electrode (yellow) via FIB-assisted deposited Pt (blue). The interlayer transport measurements were performed by the current flowing along c?normal to the FeAs layers(green)indicated by the red arrow. The scale bar is 5μm. (b)The temperature-dependent resistivity ρc?(T)with the current I=1μA.The inset is the blowup of ρc?(T)from 2 K to 30 K.(c)The flux-flow resistance as a function of θ in a fixed field of H=4 T for several temperatures. The current is I=100μA.(d)The enlarged angular dependent flux-flow resistance of(c)in a narrow angular region(±2°)around the FeAs layers below 10 K.The red and blue arrows correspond to θ =0° and θ =0.5°,respectively.

Figure 2(d)is a finer scan of the flux-flow resistance in a narrow angular region (±2°) around the FeAs layers for several temperatures below 10 K. In contrast to the behavior of the resistance peak aboveT＊, belowT＊the resistance peak atθ=0°first increases with the decreasing temperature and finally reaches saturation at lower temperatures.

To further clarify the difference of the vortex dynamics in the two temperature regions below and aboveT＊, we have measured the current-voltage (I-V) characteristics atθ=0°andθ=0.5°.Atθ=0°,as shown in Fig.3(a),aboveT＊upon cooling,theI-Vcurves shift to the right(higher bias current)due to the increase of the critical current. However,upon further cooling belowT＊,the temperature dependence of theI-Vcurves is reversed from that aboveT＊,i.e.,the lower the temperature,the smaller the critical current. On the other hand,atθ=0.5°shown in Fig.3(b),upon cooling acrossT＊,no such a reversal is observed. Accordingly,theI-Vcurves always shift to the right(higher bias current),indicating the continuous increase of the critical current. In addition, theI-Vcurves at 0.5°are similar to those at 0°aboveT＊. The critical current extracted from Figs.3(a)and 3(b)is shown in Fig.3(c). It can be seen in Fig.3(c)that atθ=0°,the critical current first increases with the decreasing temperature,then decreases atT＊and finally reaches saturation at lower temperatures, while atθ=0.5°,the critical current continuously increases. From the flux-flow resistance atθ=0°in Fig.3(d),it is confirmed that increase (decrease) of the flux-flow resistance corresponds to decrease(increase)of the critical current and a same crossover temperatureT＊can be obtained.

3.2. Discussion

As the magnetic field is aligned parallel to the FeAs layers, the increase (decrease) of the critical current (flux-flow resistance)aboveT＊upon cooling, is consistent with what is expected for Abrikosov vortices under enhanced pinning as the temperature is lowered. However,the anomalous decrease(increase) of the critical current (flux-flow resistance) belowT＊upon cooling,contradicts behaviors of Abrikosov vortices.These behaviors can be understood in terms of the change of superconducting order parameter perpendicular to the FeAs layers as the temperature is lowered. AboveT＊, owing to the largerξ⊥thand/2, the superconducting order parameter is continuous and Abrikosov vortices are formed as shown in Fig. 4(a), which can be described by anisotropic Ginzburg-Landau model. However,belowT＊,ξ⊥gets shorter thand/2,resulting in the discrete superconducting order parameter perpendicular to the FeAs layers and Josephson vortices with phase cores, as shown in Fig. 4(b). In addition, as the magnetic field is deviated at a certain angle from the FeAs layers,the composite vortex structures are formed by connecting Josephson vortices to Abrikosov vortices belowT＊,as shown in Fig.4(c). Therefore,due to the strong pinning of Abrikosov vortices, no anomaly of the flux-flow resistance and the critical current is found acrossT＊. In Bi2Sr2CaCu2O8+δ,such an increase in the angular dependent flux-flow resistance is identified as the behavior of the lock-in Josephson vortices,[29,30]which arises from iJJs formed inside Bi2Sr2CaCu2O8+δdue to the extremely shortξ⊥. Therefore, the anomalous behaviors belowT＊atθ=0°can be a result of the formation of Josephson vortices in Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5,which is associated with iJJs formed between the FeAs layers.

Fig.4. The change in the intrinsic structures of the vortices. (a)and(b)correspond to Abrikosov vortices above T＊ and Josephson vortices below T＊ with the magnetic field aligned well along the FeAs layers and the current perpendicular to the FeAs layers,respectively.(c)The structures connecting Josephson vortices to Abrikosov vortices below T＊,as the magnetic field is deviated at certain angle from the FeAs layers.

There are two distinct physical origins for the flux-flow resistance and critical current above and blowT＊upon cooling. AboveT＊, vortices exist in the form of Abrikosov vortices. The increase(decrease)of the critical current(flux-flow resistance)originates from the enhanced pinning with the decreasing temperature. BelowT＊, the shorterξ⊥with lower temperature results in the thinner superconducting layerssand the thicker non-superconducting layerst. In order to determine the critical current (maximum supercurrent) carried by iJJs withNJosephson junctions in the magnetic fieldH, the spatial dependence of the gauge-invariant phase differencesγnin the junctionnneed be derived. In the following, the junction length,the magnetic fieldHand the tunneling current are alongx,yandzdirections, respectively. The second spatial derivative equations[29,41,42]describingγnare

4. Conclusion

In summary, a crossover from Abrikosov vortices to Josephson vortices atT＊ ?7 K has been observed in the interlayer transport measurements in Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5withTc?12 K. BelowT＊,Josephson vortices are associated with the intrinsic Josephson junctions in Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5. Our results demonstrate that the superconductivity is of quasi-2D nature in Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5. It is of great interest to further explore the quasi-2D superconductivity in the ironbased superconductors from both fundamental and application points of view.

Acknowledgements

Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0302903)and the National Natural Science Foundation of China(Grant No.11974412).