Depairing Current at High Magnetic Fields in Vortex-Free High

May 22, 2019 - Superconductors are essential in many present and future technologies, from large-scale devices for medical imaging, accelerators, or f...
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Letter Cite This: Nano Lett. 2019, 19, 4174−4179

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Depairing Current at High Magnetic Fields in Vortex-Free HighTemperature Superconducting Nanowires Victor Rouco,⊥,∥ Carles Navau,‡ Nuria Del-Valle,‡ Davide Massarotti,§ Gian Paolo Papari,⊥ Daniela Stornaiuolo,⊥ Xavier Obradors,† Teresa Puig,† Francesco Tafuri,⊥ Alvaro Sanchez,*,‡ and Anna Palau*,† †

Insitut de Ciencia de Materials de Barcelona, CSIC, Campus de la UAB, 08193 Bellaterra, Catalonia, Spain Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Catalonia, Spain § Dipartimento di Ingegneria Elettrica e delle Tecnologie dell’Informazione, Università degli Studi di Napoli Federico II, 80125 Napoli, Italy ⊥ Dipartimento di Fisica, Universita degli Studi di Napoli Federico II, 80126 Napoli, Italy

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ABSTRACT: Superconductors are essential in many present and future technologies, from large-scale devices for medical imaging, accelerators, or fusion experiments to ultra-lowpower superconducting electronics. However, their potential applicability, and particularly that of high-temperature superconductors (HTS), is severely affected by limited performances at large magnetic fields and high temperatures, where their use is most needed. One of the main reasons for these limitations is the presence of quantized vortices, whose movements result in losses, internal noise, and reduced performances. The conventional strategy to overcome the flow of vortices is to pin them along artificial defects. Here, we theoretically and experimentally demonstrate that critical-current density in high-temperature superconductors can reach unprecedented high values at high fields and temperatures by preventing vortex entry. By tailoring the geometry, that is, reducing the width, W, of nanowire-patterned HTS films, the range of the Meissner state, for which no vortices are present, is extended up to very large applied field values, on the order of ∼1 T. Current densities on the order of the depairing current can be sustained under high fields for a wide range of temperatures. Results may be relevant both for devising new conductors carrying depairing-current values at high temperatures and large magnetic fields and for reducing flux noise in sensors and quantum systems. KEYWORDS: High-temperature superconductors, nanofabrication, nanowires, depairing current, Meissner state

T

could offer more advantages.2 An additional important fact is that most common HTS materials are thin strips (e.g., coated conductors), with very large demagnetizing fields. As a result, in practice, any value however small of applied magnetic field, perpendicular to the plane of the superconductor, results in vortex penetration. Enhancing current-density values in the mixed state has been a long-standing challenge. To reduce the Jc dependence on the magnetic field, artificial vortex pinning sites are added to the superconductors, requiring a difficult optimization of the pinning landscape for the specific operating conditions (temperature, magnetic field value, and orientation).5−7 Moreover, vortex motion leads to flux noise that limits the operation of sensitive superconducting electronics9 and quantum applications.10 Therefore, achieving large currents in the superconductor in a vortex-free regime becomes crucial for cutting-edge applications for both large and small scales.

he discovery of high-temperature superconductors (HTS) holds great promise to revolutionize the applications of superconducting technologies,1 strongly reducing system operating costs. Still, the potential of HTS materials is far from being fully achieved. The fundamental limits of HTS performance are delimited by the depairing critical-current density, Jc,dp, upper critical magnetic field, μ0Hc2, and critical temperature, Tc.2−7 In particular, for YBa2Cu3O7−δ (YBCO) cuprate superconductors, with characteristic coherence length, ξ0 = ξ(0 K) ∼ 1.5−2 nm, and penetration depth, λ0 = λ(0 K) ∼ 150−200 nm, one obtains a Ginzburg−Landau depairing current, Jc,dp(0 K) ∼ 100−300 MA/cm2, μ0Hc2(0 K) > 100 T, and Tc ∼ 92 K.2,8 However, energy dissipation in the mixed state, in which vortices penetrate the superconductor, severely limits their superconducting performance, thus becoming a critical issue in most practical applications. Motion of vortices under the Lorentz force determines the value of Jc, which is specifically reduced at high temperatures, where thermal effects become very relevant, and high applied fields, which are the situations where HTS © 2019 American Chemical Society

Received: April 24, 2019 Published: May 22, 2019 4174

DOI: 10.1021/acs.nanolett.9b01693 Nano Lett. 2019, 19, 4174−4179

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Nano Letters

However, up to now, the simultaneous accomplishment of both effects, that is, the vortex-free state in a wide range of the H−T phase diagram in nanowires sustaining large depairing critical-current densities, has not been achieved yet. Realizing such possibility in a technologically relevant material such as YBCO can establish a new strategy for achieving large currents at high fields in high-temperature superconductors, other than the widely explored modification of the pinning landscape. In this work, we provide experimental evidence that, by an appropriate combination of these two effects, unprecedented Jc(H) performances may be achieved in YBCO nanowires with tailored geometry. Nanowires with widths of W ∼ 80−100 nm and thickness of t = 150 nm show a basically temperatureindependent Jc(H) plateau, with critical-current density values approaching the YBCO depairing limit in the applied field as large as μ0Ha ∼ 1 T. Such values of current at high fields are above those achieved using conventional flux-pinning strategies. It is worth noting that the obtained results are not limited to a thin film geometry as they offer enhanced flexibility in the device design. We first present the theoretical basis of how a tailored geometry at the nanoscale leads to vortex exclusion up to high fields and then experimentally confirm the validity of the proposed strategy in actual superconducting YBCO nanowires. We consider a superconducting slab extending in the y direction, occupying the region −W/2 < x < W/2, with thickness t ≫ W along the z-axis. A uniform external magnetic field, μ0Ha, is applied along the z-direction. We use κ = λ/ξ, with λ and ξ being the superconductor London penetration and coherence lengths, respectively. We assume W ≫ ξ and λ ≫ ξ (κ ≫ 1). In this geometry, for which demagnetizing effects are negligible (t ≫ W), it is energetically favorable to have vortices in the superconductor when the applied field reaches the first critical field μ0Hc1, given by32

Reduction of the dimensionality in oxide functional materials has received growing scientific and technological interest due to the range of new properties and obtained functionalites, as compared with those of the bulk.11−13 Thanks to advances in high-resolution lithography techniques, it is now possible to fabricate complex nanostructures in epitaxial functional oxides, without damaging their physical properties.14 When a superconducting film is shrunk to mesoscopic length scales, both the supercurrent distribution and the properties of vortex matter are strongly influenced by the sample topology and size.15−17 In particular, there are two effects that may be specially relevant for technological applications. On the one hand, the critical current density may be enhanced up to the depairing limit, by reducing the cross section to the characteristic lengths ξ and λ. This effect has been theoretically predicted in several studies18−20 and experimentally observed in both conventional type II superconductors and high-temperature superconductors. Some examples in conventional superconductors include Al,21 Nb, or Mo0.7Ge0.322 thin films, with thicknesses of t ∼ 20−50 nm, patterned with micrometric wires, W ∼ 1−2 μm. Moreover, robust values of self-field Jc,dp, over the full superconducting temperature range, could also be achieved in complex structures consisting of two-dimensional Nb thin films (t = 11 nm) patterned with nanomeshes (34 nm spatial periodicity).23 Although being a more challenging task, theoretical depairing currents at zero applied field have also been obtained in high-temperature superconductors.24 For example, in YBCO nanowires with cross sections of 50 × 50 nm2, this is ascribed to current crowding effects25 or (Ba,K)Fe2As2 microbridges (t = 2 μm) with nanoscale thickness (t ∼ 90 nm).26 On the other hand, geometry constraints are known to be responsible for vortex exclusion and rearrangement processes. It is theoretically predicted that vortices are completely expelled from a thin superconducting strip, of width W larger than the in-plane penetration depth, below a critical field B0 ∼ 1/W2, which only depends on the width of the strip with a prefactor that slightly depends on the model considered.27−29 This effect has been experimentally proven in micrometric Nb and YBCO thin strips through vortex imaging techniques. In the first case, by reducing the width of the strip down to W = 1.6 μm, the first vortex penetration was observed at ∼2 mT,28 whereas in the latter vortex expulsion until ∼0.1 mT, it was obtained in strips of t = 6 μm.29 In both cases, vortex arrangement in a single row at the center of the strip was observed when the applied field reached B 0 . These experimental and theoretical works anticipated the potential of nanometric structures to eliminate noise linked to vortex motion up to high magnetic fields. First, vortex penetration at fields of ∼1 T was experimentally demonstrated on W-based nanowires of t = 30 nm and W = 50 nm,30 by means of magnetoresistance measurements. In the same work, recovery of the superconducting state at even larger fields was reported due to vortex self-arresting processes, opening the path for the design of loss-less superconducting devices at high fields and temperatures. Magnetoresistance measurements were also used to study geometrical effects on the vortex lattice in hightemperature superconducting nanowires.31 All of these studies were performed close to the irreversibility line by using low applied currents.

μ0 Hc1 =

∞ yz Φ0 ijj jjlog κ + 0.081 − 2 ∑ ( −1)n + 1K 0ijjj Wn yzzzzzz 4πλ 2 jjk k λ {zz{ n=1 −1 ij W y jj1 − sechijjj yzzzzzz j z (1) k 2λ {{ k

where Φ0 is the flux quantum, μ0 is the vacuum permeability, and K0 is the zero-order modified Bessel function of the second kind. The expression for μ0Hc1 has the limits ÅÄ ÑÉÑ 2Φ0 ÅÅÅ ji Ñ W zyz j Å logjj1.78 zz + 0.081ÑÑÑÑ μ0 Hc1(W ≪ λ) = 2Å Å Å ÑÑÖ πξ πW ÅÇ k (2) { μ0 Hc1(W ≫ λ) =

Φ0 4πλ 2

(2e−W /2λ + 1)(log κ + 0.081) (3)

We plot in Figure 1 as a solid line the dependence of μ0Hc1 and the limiting expressions upon the superconductor width W (normalized to λ0), given by the above analytic expressions, considering typical ξ0 and λ0 values for YBCO. Interestingly, eq 2 shows that for widths W much smaller than λ the field μ0Hc1 for vortex penetration depends basically on Φ0/W2, which can reach values on the order of 1 T for nanowires with sizes of tens of nanometers. Theory also indicates that μ0Hc1 depends very little upon the temperature (only through the factor ξ inside the logarithm in eq 2). To experimentally confirm the theoretical predictions, we fabricate YBCO nanowires of different widths ranging from W 4175

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with reducing W, with a plateau extended up to μ0Hcrit ∼ 1 T for nanowires with W = 80−100 nm. In macroscopic systems, the Jc plateau is associated with a single-vortex pinning regime dominated by vortex-defect interactions, crossing over to a collective regime above μ0Hcrit when vortex−vortex interactions become important.34,35 In those samples, μ0Hcrit decreases with increasing the temperature due to thermally activated processes.36 However, in our nanowires, the plateau can unambiguously be associated with the absence of vortices in the superconductor. A first evidence can be seen in Figure 1, where we plot the experimental values of μ0Hcrit for the nanowires with different widths W together with the theoretical prediction for the field of vortex penetration. The experimental values match very well the theoretical μ0Hc1 dependence; remarkably, this is a zero-parameter fit as theoretical values only depend upon experimentally determined quantities. Only some of the experimental point at W/ λ0 ∼ 5 (W = 700 nm) departs from the expected line because in this case the original assumption of t ≫ W does not hold. A further confirmation that vortices are absent in our nanowires comes from confirming the temperature independence of μ0Hcrit predicted by the theory. In Figure 3b, it is seen that μ0Hcrit for a nanowire with W = 100 nm remains basically constant in a large temperature window from 5 to 77 K. It is worth noting that the Jc(Ha) curves are reversible when the applied field is decreased from the maximum value, indicating that the Jc plateau can be correlated with the lower critical field Hc1, and that extra possible surface barrier effects for entering or leaving vortices are small. The temperature independence of μ0Hcrit predicted in eq 2 is also evidenced in Figure 4a, where μ0Hcrit(T) obtained for nanowires of different widths and a microwire with W = 30 μm is plotted as a function of temperature. μ0Hcrit remains essentially constant throughout all temperature range for all nanowires, whereas for the microwire, μ0Hcrit monotonically drops with the temperature, as expected considering thermally activated vortex motion.34,35 Here, again the nanowire with W = 700 nm deviates from the expected temperature-independent behavior, with a nonzero slope that may be attributed to the fact that the assumption t ≫ W not hold in this case. Figure 4b shows the self-field Jc, normalized to its value at 5 K, for two nanowires with W = 80 and 100 nm and, for comparison, a microwire with W = 30 μm. The experimentally observed temperature dependence of both nanowires can be

Figure 1. First penetration field μ0Hc1 (solid line) with the limiting expressions (dashed lines). Red dots correspond to the experimental values of μ0Hcrit. Figures depict the aspect ratio of different nanowires.

= 80 to 700 nm, with a fixed length of 1 μm and thickness of 150 nm (see Figure 2a and Methods). All patterned nanowires presented a sharp critical temperature transition with values of Tc ∼ 87−92. Although no significant degradation of the bulk superconducting properties was observed in any case, it has to be noted that the narrower nanowires were the ones with lower Tc, which are, in any case, far from those values that can lead to weak link behavior.33 Figure 2b shows the self-field criticalcurrent density, Jc,sf, at 5 K for several micro- and nanowires of different widths. A systematic enhancement of Jc,sf is observed when reducing W, reaching values that approach the Ginzburg−Landau depairing current, Jc,dp, in the limit of W < 2λ0. Although many of narrow nanowires show very high values of Jc,sf(5 K) ∼ 40−60 MA/cm2, the reproducibility of samples sustaining critical-current density values close to the depairing is low. At these small dimensions, sample inhomogeneities (porosity, nanoprecipitates, or amorphization during the patterning process) may damage some of the properties and reduce the effective nanowire cross section. Mastering all of these issues would require further research efforts in the nanofabrication technique. The magnetic field dependence of Jc/Jc,sf at 65 K for nanowires of different widths is presented in Figure 3a. Results for a wider microwire of W = 30 μm are added for comparison. For all nanowires, Jc is constant up to a critical magnetic field value, μ0Hcrit. There is a systematic enhancement of μ0Hcrit

Figure 2. (a) False color top-view (top) and cross-sectional (bottom) SEM image of a 80 nm wide, 150 nm thick nanowire. Labels in the cross section indicate the YBCO film, LAO substrate, and Au protective layer. (b) Jc,sf at 5 K for several YBCO micro- and nanowires of different width. 4176

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Figure 3. (a) Normalized critical-current density as a function of the applied magnetic field for nanowires of different widths and a microwire at 65 K. Dashed line shows the criteria used to determine μ0Hcrit (depicted with an arrow for the nanowire of 80 nm). (b) Magnetic field dependence of Jc(Ha), obtained by increasing and decreasing the applied magnetic field (closed and open symbols, respectively), for a nanowire of W = 100 nm at different temperatures.

Figure 4. (a) Temperature dependence of μ0Hcrit for different nanowires and a microwire. Dashed lines are guide for the eye, illustrating the μ0Hcrit(T) dependence. (b) Temperature dependence of self-field current density Jc,sf normalized to its value at 5 K, for two nanowires with W = 80 nm (pink stars) and 100 nm (green open circles), and a microwire with W = 30 μm (black squares). Solid red line shows the temperature dependence of the depairing current density, Jc,dp. Dashed black line is a guide for the eye.

well fitted with the Ginzburg−Landau depairing current temperature dependence, Jc,dp ∼ 1/(λ2(T)ξ(T)), providing further indication that critical-current density is achieving the theoretical depairing values. In contrast, the Jc temperature dependence for the microwire, governed by vortex pinning, displays a slightly different pattern. Our results may have important consequences in practical applications. On the one hand, the fact that no vortices are present in our nanowires makes them excellent candidates to use them in noise-sensitive devices such as SQUIDs, superconducting qubits, or sensors.9,10 On the other hand, the very large values of current density achieved at high applied fields and temperatures may be also relevant at large scale, with potential to improve the performance of actual thin strips (e.g., coated conductors). Large currents could eventually be obtained by densely packing such nanowires, which may have large thickness, with barely any magnetic interaction among them. In conclusion, we have provided a novel avenue toward achieving unprecedentedly high values of currents at high field and temperatures in superconductivity applications, by tailoring the geometry to prevent vortex penetration rather than the conventional strategy of pinning vortices by defects. Methods. Superconducting nanowires were fabricated by a top-down approach. The initial system consists of a c-axis oriented YBa2Cu3O7−δ (YBCO) 150 nm thick film grown on

LaAlO3 (LAO) substrate via chemical solution deposition methodology.37 Silver contact pads were sputtered on the thin films and annealed under oxygen atmosphere at 450 °C for 1 h to ensure good electrical contacts with resistances below 10 μΩ. Photolithography and chemical etching were used to define microwires of width W = 25 μm and length L = 100 μm, allowing current−voltage, I−V, characteristic measurements with the standard four-point method. Patterned microwires were protected with a 50 nm gold layer grown by sputtering. The width of the microwires was finally reduced to the nanoscale by using focused ion beam (Zeiss 1560XB Cross Beam) lithography, following the process described in ref 38, enabling one to obtain nanowires with good superconducting performances. In field transport, measurements were conducted in a commercial 9T physical property measurement system. The magnetic field was always applied parallel to the caxis of the superconductor in a maximum Lorentz force configuration. Critical temperature, Tc, was measured by recording the voltage under 10 μA current. Critical-current density, Jc, was obtained by means of current bias transport measurements and using a 200 nV criteria. The critical magnetic field value μ0Hcrit discussed below was determined at 0.9Jc,sf. The theoretical formulas for the penetration fields in a typeII superconducting slab used in the text have been derived 4177

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Nano Letters following procedures analogous to those by Abrikosov32 and Shmidt,39 which dealt with the case of the slab in an applied magnetic field. In our case of transport currents, because the experimental values of currents have been on the order of ∼10 mA, they generate a self-field of ∼2 mT, much less than the involved μ0Hc1 or μ0Hs values. For this reason, the field relevant for studying penetration has been considered to be the applied field and not the self-field of the transport currents.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Carles Navau: 0000-0003-4763-5305 Xavier Obradors: 0000-0003-4592-7718 Anna Palau: 0000-0002-2217-164X Present Address ∥

GFMC, Universidad Complutense de Madrid 28040 Madrid Spain. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

We acknowledge financial support from Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa” Programme for Centres of Excellence (SEV-2015-0496), COACHSUPENERGY project (MAT2014-51778-C2-1-R), and SuMaTe (RTI2018-095853-B-C21) cofinanced by the European Regional Development Fund, and project MAT2016-79426-P (Agencia Estatal de Investigación/Fondo Europeo de Desarrollo Regional). We also thank support from the European Union for NANOCOHYBRI project (Cost Action CA 16218) and from the Catalan Government projects SGR-2017-1519 and 2017-SGR-105. A.S. acknowledges a grant from ICREA Academia, funded by the Generalitat de Catalunya. V.R. Acknowledges EU H2020 research and innovation programme (Marie Sklodowska-Curie IF grant agreement OXWALD 838693). We acknowledge the use of ICTS-CNM facilities and ICMAB scientific and technical services. We thank Alexey V. Pan for fruitful discussions.

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