M. Weides, R. C. Bialczak, M. Lenander, E. Lucero, Matteo Mariantoni, M. Neeley, A. D. O'Connell, D. Sank, H. Wang, J. Wenner, T. Yamamoto, Y. Yin, A. N. Cleland, J. Martinis
We have developed a novel Josephson junction geometry with minimal volume of lossy isolation dielectric, being suitable for higher quality trilayer junctions implemented in qubits. The junctions are based on in-situ deposited trilayers with thermal tunnel oxide, have micron-sized areas and a low subgap current. In qubit spectroscopy only a few avoided level crossings are observed, and the measured relaxation time of $T_1\approx400\;\rm{nsec}$ is in good agreement with the usual phase qubit decay time, indicating low loss due to the additional isolation dielectric.
We studied the anomalous Josephson current appearing at zero phase difference in junctions coupled with a ferromagnetic trilayer which has noncoplanar magnetizations. A $π/2$ junction with an equilibrium phase difference $π/2$ is obtained under suitable conditions. The equilibrium phase difference and the amplitude of the supercurrent are all tunable by the structure parameters. In addition to calculating the anomalous current using the Bogoliubov-de Gennes equation, we also developed a clear physical picture explaining the anomalous Josephson effect in the structure. We show that the triplet …
Josephson junction transistors and 50-junction arrays with linear junction dimensions from 200 nm down to 70 nm were fabricated from standard Nb/AlOx/Nb trilayers. The fabrication process includes electron beam lithography, dry etching, anodization, and planarization by chemical-mechanical polishing. The samples were characterized at temperatures down to 25 mK. In general, all junctions are of high quality and their I-U characteristics show low leakage currents and high superconducting energy gap values of 1.35 meV. The characteristics of the transistors and arrays exhibit some features in the…
We report on the electrical transport properties of Nb based Josephson junctions with Pt/Co$_{68}$B$_{32}$/Pt ferromagnetic barriers. The barriers exhibit perpendicular magnetic anisotropy, which has the main advantage for potential applications over magnetisation in-plane systems of not affecting the Fraunhofer response of the junction. In addition, we report that there is no magnetic dead layer at the Pt/Co$_{68}$B$_{32}$ interfaces, allowing us to study barriers with ultra-thin Co$_{68}$B$_{32}$. In the junctions, we observe that the magnitude of the critical current oscillates with increas…
[100]-tilt grain-boundary YBa2Cu3O7-x (YBCO) junctions are promising for investigation of macroscopic quantum phenomena in high-Tc Josephson junctions. However, fabrication of the [100]-tilt grain-boundary YBCO junctions with a high resistance, which are required to study quantum effects, is difficult because of a high transparency of a tunnel barrier in this type of junctions. Here, we demonstrate a modification of grain-boundary barrier properties with a new approach to an oxygen electromigration in the YBCO grain-boundary junctions when the oxygen diffuses under an applied electric field fr…
DC superconducting quantum interference devices (dc-SQUIDs) were fabricated in Co-doped BaFe2As2 epitaxial films on (La, Sr)(Al, Ta)O3 bicrystal substrates with 30deg misorientation angles. The 18 x 8 micro-meter^2 SQUID loop with an estimated inductance of 13 pH contained two 3 micro-meter wide grain boundary junctions. The voltage-flux characteristics clearly exhibited periodic modulations with deltaV = 1.4 micro-volt at 14 K, while the intrinsic flux noise of dc-SQUIDs was 7.8 x 10^-5 fai0/Hz^1/2 above 20 Hz. The rather high flux noise is mainly attributed to the small voltage modulation de…
Stacks of a few intrinsic tunnel junctions were micro-fabricated on the surface of Bi-2212 single crystals. The number of junctions in a stack was tailored by progressively increasing the height of the stack by ion-beam etching, while its tunneling characteristics were measured in-situ in a vacuum chamber for temperatures down to ~13 K. Using this in-situ etching/measurements technique in a single piece of crystal, we systematically excluded any spurious effects arising from variations in the junction parameters and made clear analysis on the following properties of the surface and inner condu…
Transport measurements in thin film junctions of NbN-$\rm Bi_2Se_3$ exhibit tunneling as well as bound state resonances. The junctions are prepared by pulsed laser deposition of a NbN layer through a 25 $μ$m wide gold wire shadow mask bisecting the wafer into two halves, on a $\rm Bi_2Se_3$ blanket film without further patterning. This results in two independent near-edge junctions connected in series via the 25 $μm$ long and 10 mm wide area of the uncapped $\rm Bi_2Se_3$ layer. Conductance spectra measured across the wire masked trench at different locations on the wafer show that some juncti…
We investigate transport properties of a trilayer made of a d-wave superconductor connected to two ferromagnetic electrodes. Using Keldysh formalism we show that crossed Andreev reflection and elastic cotunneling exist also with d-wave superconductors. Their properties are controlled by the existence of zero energy states due to the anisotropy of the d-wave pair potential.
Josephson junctions containing ferromagnetic materials exhibit interesting physics and show promise as circuit elements for superconducting logic and memory. For memory applications, the properties of the junction should be controllable by changing the magnetic configuration inside the junction. To achieve good magnetic switching properties, one should choose a soft magnetic material such as NiFe (permalloy); however, NiFe exhibits poor supercurrent transmission in Josephson junctions. In this work we put thin layers of Ni on either side of the NiFe and characterize the magnetic behavior and s…
We explore novel junction configurations as an extension of our established Focused Ion Beam-based low TC SNS Junction fabrication technique. By milling a circular trench (diameter 1 micron, width 50 nm) in a 125 nm Nb 75 nm Cu bilayer we define a superconducting island connected to the bulk of the film by a normal metal barrier and entirely enclosed in-plane by the superconducting film. The circular junction properties can be probed by depositing an insulating layer over the device and drilling a 0.3 micron diameter hole down to the island to allow a Nb via to be deposited. Device behavior ha…
We highlight the reproducibility and level of control over the electrical properties of YBa$_2$Cu$_3$O$_7$ Josephson junctions fabricated with irradiation from a focused helium ion beam. Specifically, we show the results of electrical transport properties for several junctions fabricated using a large range of irradiation doses. At the lower end of this range, junctions exhibit superconductor-normal metal-superconductor (SNS) Josephson junction properties. However, as dose increases there is a transition to electrical characteristics consistent with superconductor-insulator-superconductor (SIS…
We study the thermodynamics of the diffusive SFS trilayer composed of thin superconductor (S) and ferromagnet (F) layers. On the basis the self-consistent solutions of nonlinear Usadel equations in the F and S layers we obtain the Ginzburg--Landau expansion and compute the condensation free energy and entropy of the $0$ (even) and $π$ (odd) order parameter configurations. The first order $0-π$ transition as a function of temperature $T$ occurs, which is responsible for a jump of the averaged magnetic field penetration depth $λ(T)$ recently observed on experiments [N.Pompeo, et. al., Phys. Rev.…
Fabrication and Structural Analysis of Trilayers for Tantalum Josephson Junctions with Ta$_2$O$_5$ Barriers
University of Washington（华盛顿大学）；Colorado School of Mines（科罗拉多矿业学院）；National Laboratory of the Rockies（落基山国家实验室）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；Rigetti Computing, Inc.（里盖蒂计算公司）
We theoretically study the magnetization inside a normal metal induced in an s-wave superconductor/ferromagnetic metal/normal metal/ferromagnetic metal/s-wave superconductor (S/F1/N/F2/S) Josephson junction. Using quasiclassical Green's function method, we show that the magnetization becomes finite inside N. The origin of this magnetization is due to odd-frequency spin-triplet Cooper pairs formed by electrons of equal and opposite spins, which are induced by proximity effect in the S/F1/N/F2/S junction. We find that the magnetization M(d,q) in N can be decomposed into two parts, M(d,q)=MI(d)+M…
We have fabricated and measured Josephson junction defect spectrometers (JJDSs), which are frequency-tunable, nearly-harmonic oscillators that probe strongly-coupled two-level systems (TLSs) in the barrier of a Josephson junction (JJ). The JJDSs accommodate a wide range of junction inductances, $L_{J}$, while maintaining a resonance frequency, $f_{0}$, in the range of 4-8 GHz. By applying a magnetic flux bias to tune $f_{0}$, we detect strongly-coupled TLSs in the junction barrier as splittings in the device spectrum. JJDSs fabricated with a via-style Al/thermal AlOx/Al junction and measured a…
We propose a trilayer $π$-junction that takes advantage of the unconventional $s_{x^2 y^2}=\cos k_x \cos k_y$ pairing symmetry which changes sign between electron and hole Fermi pockets in the iron pnictides. In addition, we also present theoretical results for Andreev bound states in thin superconductor-normal metal (or insulator) iron-pnictide junctions. The presence of nontrivial in-gap states, which uniquely appear in this unconventional pairing state, is a distinct feature in comparison to other singlet pairing states.
An effective free energy of a two dimensional (i.e. large area) Josephson Junctions is derived, allowing for thermal fluctuations, for random magnetic fields and for external currents. We show by using replica symmetry breaking methods, that the junction has four distinct phases: disordered, Josephson ordered, a glass phase and a coexisting Josephson order with the glass phase. Near the coexistence to glass transition at s=1/2 the critical current is ~ (area)^{-s+1/2} where s is a measure of disorder. Our results may account for junction ordering at temperatures well below the critical tempera…
We have studied the electric transport properties of symmetrical [001] tilt NdCeCuO bicrystal grain boundary Josephson junctions (GBJs) fabricated on SrTiO bicrystal substrates with misorientation angles of 24 and 36.8 degree. The superconducting properties of the NdCeCuO-GBJs are similar to those of GBJs fabricated from the hole doped high temperature superconductors (HTS). The critical current density Jc decreases strongly with increasing misorientation angle. The products of the critical current Ic and the normal resistance Rn (about 0.1 mV at 4.2 K) are small compared to the gap voltage an…
Superconducting junctions are widely used in multitude of applications ranging from quantum information science and sensing to solid-state cooling. Traditionally, such devices must be fabricated on flat substrates using standard lithographic techniques. In this study, we demonstrate a highly versatile method that allows for superconducting junctions to be fabricated on a more complex topography. It is based on maskless direct laser writing (DLW) two-photon lithography, which allows writing in 3D space. We show that high-quality normal metal-insulator-superconductor (NIS) tunnel junctions can b…
We have developed a combined photolithography and electron-beam lithography fabrication process for sub-\mum to \mum-size Nb/Al-AlOx/Nb Josephson junctions. In order to define the junction size and protect its top electrode during anodic oxidation, we developed and used the new concept of an aluminum hard mask. Josephson junctions of sizes down to 0.5 \mum2 have been fabricated and thoroughly characterized. We found that they have a very high quality, which is witnessed by the IV curves with quality parameters Vm > 50 mV and Vgap = 2.8 mV at 4.2 K, as well as IcRN products of 1.75-1.93 mV obta…
Superconducting tunnel junctions are being developed for application as photon detectors in astronomy. We present the latest results on the development of very high quality, very low critical temperature junctions, fabricated out of pure Al electrodes. The detectors are operated at 50 mK in an adiabatic demagnetisation refrigerator. The contacts to the top and base electrodes of these junctions are fabricated either out of Nb or Ta, which has strong implications on the loss time of the quasiparticles. The Nb contacted junctions show quasiparticle loss times varying between 5 and 80 usec, depen…
Superconductor-Ferromagnet-Superconductor (S-F-S) Josephson junctions were fabricated by making a narrow cut through a S-F double layer using direct writing by Focused Ion Beam (FIB). Due to a high resolution (spot size smaller than 10 nm) of FIB, junctions with a small separation between superconducting electrodes ($\leq$ 30 nm) can be made. Such a short distance is sufficient for achieving a considerable proximity coupling through a diluted CuNi ferromagnet. We have successfully fabricated and studied S-F-S (Nb-CuNi-Nb) and S-S'-S (Nb-Nb/CuNi-Nb) junctions. Junctions exhibit clear Fraunhofer…
The most developed integrated receivers for THz radiation nowadays are based on Josephson junction SIS devices. In this kind of devices, the highest receivable frequency is determined by the energy gap of the superconducting electrodes and limited to approximately 700 GHz in case of Nb/AlOx/Nb multilayers. We have developed a technology for NbN/AlN/NbN Josephson junctions on sapphire substrates which allow operation at frequencies above 1 THz. The trilayers are deposited in-situ in a 3-chamber DC-magnetron sputtering system at temperatures as high as 775 °C. Each layer is reactively sputtered …
MgB2 tunnel junctions (MgB2/barrier/MgB2) were fabricated using a native oxide grown on the bottom MgB2 film as the tunnel barrier. Such barriers therefore survive the deposition of the second electrode at 300oC, even over junction areas of ~1 mm2. Studies of such junctions, and those of the type MgB2/native or thermal oxide/metal (Pb, Au, or Ag) show that tunnel barriers grown on MgB2 exhibit a wide range of barrier heights and widths.
We present experimental results on a Josephson parametric amplifier tailored for readout of ultra-sensitive thermal microwave detectors. In particular, we discuss the impact of fabrication details on the performance. We show that the small volume of deposited dielectric materials enabled by the side-wall passivated spacer niobium junction technology leads to robust operation across a wide range of operating temperatures up to 1.5 K. The flux-pumped amplifier has gain in excess of 20 dB in three-wave mixing and its center frequency is tunable between 540 MHz and 640 MHz. At 600 MHz, the amplifi…
Superconductor-insulator-superconductor tunnel junctions have been fabricated on MgB2 that display Josephson and quasiparticle currents. These junctions exhibit a gap magnitude, Delta~2.5 meV, that is considerably smaller than the BCS value, but which clearly and reproducibly closes near the bulk Tc. In conjunction with fits of the conductance spectra, these results are interpreted as direct evidence of two-band superconductivity.
We have performed a detailed study of the time stability and reproducibility of sub-micron $Al/AlO_{x}/Al$ tunnel junctions, fabricated using standard double angle shadow evaporations. We have found that by aggressively cleaning the substrate before the evaporations, thus preventing any contamination of the junction, we obtained perfectly stable oxide barriers. We also present measurements on large ensembles of junctions which prove the reproducibility of the fabrication process. The measured tunnel resistance variance in large ensembles of identically fabricated junctions is in the range of o…
The magnetic and transport properties of $Pd_{0.99}Fe_{0.01}$ thin films have been studied. We have found that the Curie temperature of the films is about 20 K and the magnetic properties strongly depend on temperature below $T_{Curie}$. We have also fabricated the set of superconductor-ferromagnet-superconductor josephson junctions $Nb-PdFe-Nb$. The temperature dependence of the junctions with the ferromagnet layer thickness of about 36 nm shows the reentrant behaviour that is the evidence of the transition of the junction into the $π$-state.
We have measured the depinning of trapped kinks in a ratchet potential using a fabricated circular array of Josephson junctions. Our ratchet system consists of a parallel array of junctions with alternating cell inductances and junctions areas. We have compared this ratchet array with other circular arrays. We find experimentally and numerically that the depinning current depends on the direction of the applied current in our ratchet ring. We also find other properties of the depinning current versus applied field, such as a long period and a lack of reflection symmetry, which we can explain a…
We have observed the zero-crossing steps in a surface junction of a mesa structure micro-fabricated on the surface of a Bi-2212 single crystal. With the application of microwave of frequencies 76 and 94 GHz, the current-voltage characteristics show clear voltage steps satisfying the ac Josephson relation. Increasing the microwave power, the heights of the steps show the Bessel-function behavior up to step number n=4. We confirm that the intrinsic surface junction meets the criterion for the observation of zero-crossing steps.
We fabricated high quality Nb/Al_2O_3/Ni_{0.6}Cu_{0.4}/Nb superconductor-insulator-ferromagnet-superconductor Josephson tunnel junctions. Using a ferromagnetic layer with a step-like thickness, we obtain a 0-pi junction, with equal lengths and critical currents of 0 and pi parts. The ground state of our 330 microns (1.3 lambda_J) long junction corresponds to a spontaneous vortex of supercurrent pinned at the 0-pi step and carrying ~6.7% of the magnetic flux quantum Phi_0. The dependence of the critical current on the applied magnetic field shows a clear minimum in the vicinity of zero field.
We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase ψ=\pmϕ. The value of ϕ can be chosen by design in the interval 0<ϕ<π. The junctions used in our experiments are fabricated as 0-π Josephson junctions of moderate normalized length with asymmetric 0 and π regions. We show that (a) these ϕ Josephson junctions have two critical currents, corresponding to the escape of the phase ψ from -ϕ and +ϕ states; (b) the phase ψ can be set to a particular state by tuning an external magnetic field or (c) by using a prope…
We demonstrate that shunting of Superconductor-Insulator-Superconductor Josephson junctions by Superconductor-Insulator-Normal metal (S-I-N) structures having pronounced non-linear I-V characteristics can remarkably modify the Josephson dynamics. In the regime of Josephson generation the phase behaves as an overdamped coordinate, while in the superconducting state the damping and current noise are strikingly small, that is vitally important for application of such junctions for readout and control of Josephson qubits. Superconducting Nb/AlO${_x}$/Nb junction shunted by Nb/AlO${_x}$/AuPd juncti…
Nb/Al_2O_3/Ni_{0.6}Cu_{0.4}/Nb based superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson tunnel junctions with a thickness step in the metallic ferromagnetic \Ni_{0.6}\Cu_{0.4} interlayer were fabricated. The step was defined by optical lithography and controlled etching. The step height is on the scale of a few angstroms. Experimentally determined junction parameters by current-voltage characteristics and Fraunhofer pattern indicate an uniform F-layer thickness and the same interface transparencies for etched and non-etched F-layers. This technique could be used to tailor low…
We have fabricated superconductor-normal metal side-junctions with different barrier transparencies out of PdTe$_2$ crystalline flakes and measured the differential conductance spectra. Modeling our measurements using a modified Blonder Tinkham Klapwijk (BTK) formalism confirms that the superconductivity is mostly comprised of the conventional $s$-wave symmetry. We have found that for junctions with very low barrier transparencies, the junctions can enter a thermal regime, where the critical current becomes important. Adding this to the BTK-model allows us to accurately fit the experimental da…
We demonstrate that Josephson devices with nontrivial phase difference $% 0<φ_g <π$ in the ground state can be realized in structures composed from longitudinally oriented normal metal (N) and ferromagnet (F) films in the weak link region. Oscillatory coupling across F-layer makes the first harmonic in the current-phase relation relatively small, while coupling across N-layer provides negative sign of the second harmonic. To derive quantitative criteria for a $φ$-junction, we have solved two-dimensional boundary-value problem in the frame of Usadel equations for overlap and ramp geometries of …
We describe fabrication and testing of composite flux qubits combining Nb- and Al-based superconducting circuit technology. This hybrid approach to making qubits allows for employing pi-phase shifters fabricated using well-established Nb-based technology of superconductor-ferromagnet-superconductor Josephson junctions. The important feature here is to obtain high interface transparency between Nb and Al layers without degrading sub-micron shadow mask. We achieve this by in-situ Ar etching using e-beam gun. Shadow-evaporated Al/AlOx/Al Josephson junctions with Nb bias pads show the expected cur…
We present a structure and a fabrication method for superconducting tunnel junctions down to the dimensions of 200 nm using i-line UV lithography. The key element is a side-wall-passivating spacer structure (SWAPS) which is shaped for smooth crossline contacting and low parasitic capacitance. The SWAPS structure enables formation of junctions with dimensions at or below the lithography-limited linewidth. An additional benefit is avoiding the excessive use of amorphous dielectric materials which is favorable in sub-Kelvin microwave applications often plagued by nonlinear and lossy dielectrics. …
Self-shunted aluminum Josephson junctions with high-transparency barriers were fabricated using the shadow-evaporation technique and measured at low temperatures, T=25 mK. Due to high junction transparency, the IV-characteristics were found to be of only small hysteresis with retrapping-to-switching current ratio of up to 80%. The observed critical currents were close to the Ambegaokar-Baratoff values (up to 80-100%). Good barrier quality was confirmed by the low subgap leakage currents in the quasiparticle branches, which makes the self-shunted Al junctions promising for application in integr…
We have fabricated superconductor-quantum dot-superconductor (SC-QD-SC) junctions by using SC aluminum electrodes with narrow gaps laterally contacting a single self-assembled InAs QD. The fabricated junctions exhibited clear Coulomb staircases and Coulomb oscillations at 40 mK. Furthermore, clear suppression in conductance was observed for the source-drain voltage $|V_{\rm SD}| < 2Δ/e$, where $Δ$ is the SC energy gap of Al. The absence of Josephson current that flows through QDs is due to the strong Coulomb interaction and non-negligible thermal fluctuation in our measurement system.
We present measurements of the current-phase relation (CPR) of Superconductor-Ferromagnet-Superconductor (SFS) Josephson junctions as a function of temperature. The CPR is determined by incorporating the junction into a superconducting loop coupled to a dc SQUID, allowing measurement of the junction phase difference. Junctions fabricated with a thin (~ 22 nm) barrier of Cu0.47Ni0.53 sandwiched between Nb electrodes exhibit a re-entrant critical current with temperature, vanishing at T =T_pi ~ 2-4 K. We find that the critical current is negative for T < T_pi, indicating that the junction is a p…
Arrays of Vortex Transitional (VT) memory cells with functional density up to $1 Mbit/cm^2$ have been designed, fabricated, and successfully demonstrated. This progress is due to recent advances in design optimization and in superconductor electronics fabrication achieved at MIT Lincoln Laboratory. As a starting point, we developed a demo array of VT cells for the 100-$μA/μm^2$ MIT LL fabrication process SFQ5ee with 8 niobium layers. The studied two-junction memory cell with a two-junction nondestructive readout occupied $168 μm^2$, resulting in an over $0.5 Mbit/cm^2$ functional density. Then…
We have studied fundamental properties of weak-link Sr2RuO4/Sr2RuO4 Josephson junctions fabricated by making a narrow constriction on superconducting Sr2RuO4 films through laser micro-patterning. The junctions show a typical overdamped behavior with much higher critical current density, compared with those previously reported for bulk Sr2RuO4/s-wave superconductor junctions. Observed magnetic field and temperature dependences of the Josephson critical current suggest that the chiral p-wave is unlikely for the superconducting symmetry, encouraging further theoretical calculations of the Sr2RuO4…
We demonstrate topological insulator (Bi$_2$Te$_3$) dc SQUIDs, based on superconducting Nb leads coupled to nano-fabricated Nb-Bi$_2$Te$_3$-Nb Josephson junctions. The high reproducibility and controllability of the fabrication process allows the creation of dc SQUIDs with parameters that are in agreement with design values. Clear critical current modulation of both the junctions and the SQUID with applied magnetic fields have been observed. We show that the SQUIDs have a periodicity in the voltage-flux characteristic of $Φ_0$, of relevance to the ongoing pursuit of realizing interferometers f…
We consider a Josephson junction with ${\rm F_1 F_2 F_3}$ ferromagnetic trilayers in the ballistic regime, where the magnetization in each ferromagnet ${\rm F}_i (i=1,2,3)$, can have arbitrary orientations and magnetization strengths. The trilayers are sandwiched between two $s$-wave superconductors with a macroscopic phase difference $Δφ$. A broad range of magnetization strengths of the central $\rm F_2$ layer are considered, from an unpolarized normal metal (N) to a half-metallic phase, supporting only one spin species. Our results reveal that when the magnetization configuration in ${\rm F_…
We have fabricated c-axis Josephson junctions on single crystals of (Ba,K)Fe2As2 by using Pb as the counter electrode in two geometries, planar and point contact. Junctions in both geometries show resistively shunted junction I-V curves below the Tc of the counter electrode. Microwave induced steps were observed in the I-V curves, and the critical currents are suppressed with an in-plane magnetic field in a manner consistent with the small junction limit. ICRN products of up to 0.3 mV have been observed in these junctions at 4.2 K. The observation of Josephson coupling along the c-axis between…
We investigate analytically long Josephson junctions with phase pi-discontinuity points. Such junctions are usually fabricated as a ramp between a superconductor like YBCO with d-wave symmetry of the order parameter and an s-wave superconductor like Nb. From the top, they look like zigzags with pi-jumps of the Josephson phase at the corners. These pi-jumps, at certain conditions, lead to the formation of half-integer flux quanta, which we call semi-fluxons, pinned at the corners. We derive a version of sine-Gordon equation which describes the dynamics of the Josephson phase in such structures,…
A comparative study of the magnetic remanence exhibited by tridimensional Josephson junction arrays in response to an excitation with an AC magnetic field is presented. The observed temperature behavior of the remanence curves for disordered arrays fabricated from three different materials (Nb, YBa_2Cu_3O_7 and La_{1.85}Sr_{0.15}CuO_4) is found to follow the same universal law (based on the explicit temperature expressions for the activation energy and the inductance-dominated contribution to the magnetization of the array within the framework of the phase-slip model) regardless of the origin …
