Josephson current in nanofabricated V/Cu/V mesoscopic junctions

Courtois H., Meschke M., Peltonen J.T., Pekola J.P.

We investigate hysteresis in the transport properties of superconductor-normal-metal-superconductor (S-N-S) junctions at low temperatures by measuring directly the electron temperature in the normal metal. Our results demonstrate unambiguously that the hysteresis results from an increase of the normal-metal electron temperature once the junction switches to the resistive state. In our geometry, the electron temperature increase is governed by the thermal resistance of the superconducting electrodes of the junction.

le Sueur H., Joyez P., Pothier H., Urbina C., Esteve D.

Using a dual-mode STM-AFM microscope operating below 50 mK we measured the local density of states along small normal wires connected at both ends to superconductors with different phases. We observe that a uniform minigap can develop in the whole normal wire and in the superconductors near the interfaces. The minigap depends periodically on the phase difference. The quasiclassical theory of superconductivity applied to a simplified 1D model geometry accounts well for the data.

Giazotto F., Heikkilä T.T., Pepe G.P., Helistö P., Luukanen A., Pekola J.P.

We propose a mesoscopic kinetic-inductance radiation detector based on a long superconductor-normal metal-superconductor Josephson junction. The operation of this proximity Josephson sensor relies on large kinetic inductance variations under irradiation due to the exponential temperature dependence of the critical current. Coupled with a dc superconducting quantum interference device readout, the PJS is able to provide a signal to noise (S/N) ratio up to ∼103 in the terahertz regime if operated as calorimeter, while electrical noise equivalent power as low as ∼7×10−20W∕Hz at 200mK can be achieved in the bolometer operation. The high performance together with the ease of fabrication make this structure attractive as an ultrasensitive cryogenic detector of terahertz electromagnetic radiation.

Angers L., Chiodi F., Montambaux G., Ferrier M., Guéron S., Bouchiat H., Cuevas J.C.

We report the design and measurement of Superconducting/normal/superconducting (SNS) proximity DC squids in the long junction limit, i.e. superconducting loops interrupted by two normal metal wires roughly a micrometer long. Thanks to the clean interface between the metals, at low temperature a large supercurrent flows through the device. The dc squid-like geometry leads to an almost complete periodic modulation of the critical current through the device by a magnetic flux, with a flux periodicity of a flux quantum h/2e through the SNS loop. In addition, we examine the entire field dependence, notably the low and high field dependence of the maximum switching current. In contrast with the well-known Fraunhoffer-type oscillations typical of short wide junctions, we find a monotonous gaussian extinction of the critical current at high field. As shown in [15], this monotonous dependence is typical of long and narrow diffusive junctions. We also find in some cases a puzzling reentrance at low field. In contrast, the temperature dependence of the critical current is well described by the proximity effect theory, as found by Dubos et al. [16] on SNS wires in the long junction limit. The switching current distributions and hysteretic IV curves also suggest interesting dynamics of long SNS junctions with an important role played by the diffusion time across the junction.

Crosser M.S., Huang J., Pierre F., Virtanen P., Heikkilä T.T., Wilhelm F.K., Birge N.O.

We report the results of several nonequilibrium experiments performed on superconducting/normal/superconducting (S/N/S) Josephson junctions containing either one or two extra terminals that connect to normal reservoirs. Currents injected into the junctions from the normal reservoirs induce changes in the electron energy distribution function, which can change the properties of the junction. A simple experiment performed on a three-terminal sample demonstrates that quasiparticle current and supercurrent can coexist in the normal region of the S/N/S junction. When larger voltages are applied to the normal reservoir, the sign of the current-phase relation of the junction can be reversed, creating a ``$\ensuremath{\pi}$ junction.'' We compare quantitatively the maximum critical currents obtained in four-terminal $\ensuremath{\pi}$ junctions when the voltages on the normal reservoirs have the same or opposite sign with respect to the superconductors. We discuss the challenges involved in creating a ``Zeeman'' $\ensuremath{\pi}$ junction with a parallel applied magnetic field and show in detail how the orbital effect suppresses the critical current. Finally, when normal current and supercurrent are simultaneously present in the junction, the distribution function develops a spatially inhomogeneous component that can be interpreted as an effective temperature gradient across the junction, with a sign that is controllable by the supercurrent. Taken as a whole, these experiments illustrate the richness and complexity of S/N/S Josephson junctions in nonequilibrium situations.

Giazotto F., Heikkilä T.T., Luukanen A., Savin A.M., Pekola J.P.

This review presents an overview of the thermal properties of mesoscopic structures. The discussion is based on the concept of electron energy distribution, and, in particular, on controlling and probing it. The temperature of an electron gas is determined by this distribution: refrigeration is equivalent to narrowing it, and thermometry is probing its convolution with a function characterizing the measuring device. Temperature exists, strictly speaking, only in quasiequilibrium in which the distribution follows the Fermi-Dirac form. Interesting nonequilibrium deviations can occur due to slow relaxation rates of the electrons, e.g., among themselves or with lattice phonons. Observation and applications of nonequilibrium phenomena are also discussed. The focus in this paper is at low temperatures, primarily below 4 K, where physical phenomena on mesoscopic scales and hybrid combinations of various types of materials, e.g., superconductors, normal metals, insulators, and doped semiconductors, open up a rich variety of device concepts. This review starts with an introduction to theoretical concepts and experimental results on thermal properties of mesoscopic structures. Then thermometry and refrigeration are examined with an emphasis on experiments. An immediate application of solid-state refrigeration and thermometry is in ultrasensitive radiation detection, which is discussed in depth. This review concludes with a summary of pertinent fabrication methods of presented devices.

Doh Y., van Dam J.A., Roest A.L., Bakkers E.P., Kouwenhoven L.P., De Franceschi S.

Nanoscale superconductor/semiconductor hybrid devices are assembled from indium arsenide semiconductor nanowires individually contacted by aluminum-based superconductor electrodes. Below 1 kelvin, the high transparency of the contacts gives rise to proximity-induced superconductivity. The nanowires form superconducting weak links operating as mesoscopic Josephson junctions with electrically tunable coupling. The supercurrent can be switched on/off by a gate voltage acting on the electron density in the nanowire. A variation in gate voltage induces universal fluctuations in the normal-state conductance, which are clearly correlated to critical current fluctuations. The alternating-current Josephson effect gives rise to Shapiro steps in the voltage-current characteristic under microwave irradiation.

Savin A.M., Pekola J.P., Flyktman J.T., Anthore A., Giazotto F.

A superconductor-normal metal-superconductor mesoscopic Josephson junction has been realized in which the critical current is tuned through normal current injection using a symmetric electron cooler directly connected to the weak link. Both enhancement of the critical current by more than a factor of two, and supercurrent suppression have been achieved by varying the cooler bias. Furthermore, this transistor-like device demonstrates large current gain (∼20) and low power dissipation.

Dubos P., Courtois H., Pannetier B., Wilhelm F.K., Zaikin A.D., Schön G.

We carry out an extensive experimental and theoretical study of the Josephson effect in S-N-S junctions made of a diffusive normal metal (N) embedded between two superconducting electrodes (S). Our experiments are performed on Nb-Cu-Nb junctions with highly-transparent interfaces. We give the predictions of the quasiclassical theory in various regimes on a precise and quantitative level. We describe the crossover between the short and the long junction regimes and provide the temperature dependence of the critical current using dimensionless units $eR_{N}I_{c}/\epsilon_{c}$ and $k_{B}T/\epsilon_{c}$ where $\epsilon_{c}$ is the Thouless energy. Experimental and theoretical results are in excellent quantitative agreement.

Hoss T., Strunk C., Nussbaumer T., Huber R., Staufer U., Schönenberger C.

Superconductor/normal-metal (SN) interfaces of high transparency exhibit remarkably different properties for electric charge and energy transfer, respectively. Quasiparticles with energy e below the energy gap D of the superconductor cannot enter the superconductor. This implies a high thermal resistance of the SN boundary since energy is exclusively carried by the quasiparticles. 1 In contrast, charge can be transmitted at e,D via the Andreev reflection process: An electron coming from the normal side is reflected as a hole and a Cooper pair is transferred to the superconductor. 2 This should have important consequences for the energy distribution of quasiparticles in a short normal bridge connected to two superconducting reservoirs. Here we assume that the length L of the bridge is larger than the thermal diffusion length LT5A\D/2pkBT which governs the penetration of Cooper pairs into the normal wire. For L.LT the supercurrent through the structure is exponentially weak.

Dubos P., Charlat P., Crozes T., Paniez P., Pannetier B.

We have developed a novel lift-off process for fabrication of high quality superconducting submicron niobium structures. The process makes use of a thermostable polymer with a high transition temperature Tg=235 °C and an excellent chemical stability. The superconducting critical temperature of 150-nm-wide niobium lines is above 7 K. An example of shadow evaporation of a Nb-Cu submicron hybrid structure is given. A potential application of this process is the fabrication of very small single electron devices using refractory metals.

Baselmans J.J., Morpurgo A.F., van Wees B.J., Klapwijk T.M.

When two superconductors are connected by a weak link, a supercurrent flows, the magnitude of which is determined by the difference in the macroscopic quantum phases of the superconductors. This phenomenon was discovered by Josephson1 for the case of a weak link formed by a thin tunnel barrier: the supercurrent, I, is related to the phase difference, π, through the Josephson current–phase relation, I = Icsinπ, with Ic being the critical current which depends on the properties of the weak link. A similar relation holds for weak links consisting of a normal metal, a semiconductor or a constriction2. In all cases, the phase difference is zero when no supercurrent flows through the junction, and increases monotonically with increasing supercurrent until the critical current is reached. Here we use nanolithography techniques to fabricate a Josephson junction with a normal-metal weak link in which we have direct access to the microscopic current-carrying electronic states inside the link. We find that the fundamental Josephson relation can be changed from I = Icsinπ to I = Icsin(π + π)—that is, a π-junction—by controlling the energy distribution of the current-carrying states in the normal metal. This fundamental change in the way these Josephson junctions behave has potential implications for their use in superconducting electronics as well as in (quantum) logic circuits based on superconductors.

Morpurgo A.F., Klapwijk T.M., van Wees B.J.

A Josephson junction has been realized in which the supercurrent flow is regulated by a “normal” control current traversing the normal metal in between the superconducting electrodes. The principle of operation of the devices is based on the existing relation between the magnitude of the supercurrent and the electronic distribution function in the junction. This method for controlling the supercurrent has clear advantages over other known methods and is relevant for superconducting electronics applications.

Noer R.J.

Electron-tunneling measurements have been made in vanadium films containing varying amounts of gaseous impurities. Transition temperatures ${T}_{c}$ vary from near the bulk value to more than 2 K below it. After corrections are made for spurious leakage conductivity, tunneling characteristics are in all cases consistent with a simple BCS superconducting density of states. ${T}_{c}$ and the zero-temperature energy gap $\ensuremath{\epsilon}(0)$ vary in accordance with $\frac{2\ensuremath{\epsilon}(0)}{k{T}_{c}}=3.5\ifmmode\pm\else\textpm\fi{}0.1$. In consequence, it does not appear that gaseous impurities enter the vanadium lattice in a paramagnetic configuration.

Radebaugh R., Keesom P.H.

The specific heat of vanadium (resistivity ratio = 140) has been measured in the superconducting and normal states between 0.5 and 5.4\ifmmode^\circ\else\textdegree\fi{}K. The normal-state specific heat is given by ${C}_{n}=9.82T+0.035{T}^{3}+{C}_{\mathrm{nuc}}$ mJ ${\mathrm{mole}}^{\ensuremath{-}1}$ ${\mathrm{deg}}^{\ensuremath{-}1}$, where the term ${C}_{\mathrm{nuc}}$ arises from the interaction of the nuclear magnetic moments with the applied magnetic field. The coefficient of the cubic term corresponds to a Debye temperature ${\ensuremath{\bigominus}}_{0}$ at 0\ifmmode^\circ\else\textdegree\fi{}K of (382\ifmmode\pm\else\textpm\fi{}10)\ifmmode^\circ\else\textdegree\fi{}K, which is slightly less than the value 399.3\ifmmode^\circ\else\textdegree\fi{}K obtained from elastic measurements. The superconducting specific heat contains a term linear in $T$ which is 0.52% of the normal-state linear term. This indicates the presence of a very small energy gap at the Fermi surface in addition to the normal gap. At all but the lowest temperatures the specific heat is governed by the normal energy gap and is in fair agreement with the BCS prediction. The agreement becomes excellent if the normal energy gap is assumed to be anisotropic with a maximum value of $3.52k{T}_{c}$ and a minimum of $3.20k{T}_{c}$, which is consistent with ultrasonic measurements. The superconducting transition temperature for this sample is (5.379\ifmmode\pm\else\textpm\fi{}0.004) \ifmmode^\circ\else\textdegree\fi{}K with a total transition width of only about 1 mdeg. The intrinsic transition temperature for vanadium is estimated to be (5.414\ifmmode\pm\else\textpm\fi{}0.010) \ifmmode^\circ\else\textdegree\fi{}K.

Skryabina O.V., Bakurskiy S.V., Ruzhickiy V.I., Shishkin A., Klenov N.V., Soloviev I.I., Kupriyanov M.Y., Stolyarov V.S.

Abstract We study the effect of electrode width on superconducting current transport in Nb–Au–Nb Josephson bridges. The critical current as well as the normal bridge resistance drop with decreasing electrode width on scales of a few μ m , which are orders of magnitude larger than the estimated coherence length of the Au strip. We consider several physical reasons for such an anomalous influence of the width W of the superconducting electrode on the critical current I c (AIWIc) and provide model fits for the resistive and superconducting properties of the bridges. The smooth dependence of the Nb–Au–Nb bridge parameters on the electrode width can be used to optimize the design of superconducting devices for specific applications.

Bakurskiy Sergey, Ruzhickiy Vsevolod, Neilo Alexey, Klenov Nikolay, Soloviev Igor, Elistratova Anna, Shishkin Andrey, Stolyarov Vasily, Kupriyanov Mikhail

We have studied the Thouless energy in Josephson superconductor – normal metal – superconductor (SN-N-NS) bridges analytically and numerically, considering the influence of the sub-electrode regions. We have discovered a significant suppression of the Thouless energy with increasing interfacial resistance, consistent with experimental results. The analysis of the temperature dependence of the critical current in Josephson junctions in comparison with the expressions for the Thouless energy may allow the determination of the interface parameters of S and N-layers.

Sotnichuk S.V., Skryabina O.V., Shishkin A.G., Bakurskiy S.V., Kupriyanov M.Y., Stolyarov V.S., Napolskii K.S.

Puglia C., De Simoni G., Giazotto F.

The effect of electrostatic gating on metallic elemental superconductors was recently demonstrated in terms of modulation of the switching current and control of the current phase relation in superconducting quantum interferometers. The latter suggests the existence of a direct connection between the macroscopic quantum phase in a superconductor and the applied gate voltage. The measurement of the switching current cumulative probability distributions (SCCPD) is a convenient and powerful tool to analyze such relation. In particular, the comparison between the conventional Kurkijarvi-Fulton-Dunkleberger model and the gate-driven distributions give useful insights into the microscopic origin of the gating effect. In this review, we summarize the main results obtained in the analysis of the phase slip events in elemental gated superconducting weak-links in a wide range of temperatures between 20 mK and 3.5 K. Such a large temperature range demonstrates both that the gating effect is robust as the temperature increases, and that fluctuations induced by the electric field are not negligible in a wide temperature range.

Kemppinen A., Ronzani A., Mykkänen E., Hätinen J., Lehtinen J.S., Prunnila M.

We demonstrate highly transparent silicon–vanadium and silicon–aluminum tunnel junctions with relatively low sub-gap leakage current and discuss how a trade-off typically encountered between transparency and leakage affects their refrigeration performance. We theoretically investigate cascaded superconducting tunnel junction refrigerators with two or more refrigeration stages. In particular, we develop an approximate method that takes into account self-heating effects but still allows us to optimize the cascade a single stage at a time. We design a cascade consisting of energy-efficient refrigeration stages, which makes cooling of, e.g., quantum devices from above 1 K to below 100 mK a realistic experimental target.

Skryabina O.V., Bakurskiy S.V., Shishkin A.G., Klimenko A.A., Napolskii K.S., Klenov N.V., Soloviev I.I., Ryazanov V.V., Golubov A.A., Roditchev D., Kupriyanov M.Y., Stolyarov V.S.

AbstractUnlike conventional planar Josephson junctions, nanowire-based devices have a bridge geometry with a peculiar coupling to environment that can favor non-equilibrium electronic phenomena. Here we measure the influence of the electron bath overheating on critical current of several bridge-like junctions built on a single Au-nanowire. Using the Usadel theory and applying the two-fluid description for the normal and superconducting components of the flowing currents, we reveal and explain the mutual influence of the neighbouring junctions on their characteristics through various processes of the electron gas overheating. Our results provide additional ways to control nanowire-based superconducting devices.

Puglia C., De Simoni G., Ligato N., Giazotto F.

Recently, the possibility to tune the critical current of conventional metallic superconductors via electrostatic gating was shown in wires, Josephson weak-links, and superconductor-normal metal–superconductor junctions. Here, we exploit such a technique to demonstrate a gate-controlled vanadium-based Dayem nano-bridge operated as a half-wave rectifier at 3 K. Our devices exploit the gate-driven modulation of the critical current of the Josephson junction and the resulting steep variation of its normal-state resistance, to convert an AC signal applied to the gate electrode into a DC one across the junction. All-metallic superconducting gated rectifiers could provide the enabling technology to realize tunable photon detectors and diodes useful for superconducting electronics circuitry.

De Simoni G., Paolucci F., Puglia C., Giazotto F.

We demonstrate the first \textit{all-metallic} mesoscopic superconductor-normal metal-superconductor (SNS) field-effect controlled Josephson transistors (SNS-FETs) and show their full characterization from the critical temperature $T_c$ down to 50 mK in the presence of both electric and magnetic field. The ability of a static electric field -applied by mean of a lateral gate electrode- to suppress the critical current $I_s$ in a proximity-induced superconductor is proven for both positive and negative gate voltage values. $I_s$ suppression reached typically about one third of its initial value, saturating at high gate voltages. The transconductance of our SNS-FETs obtains values as high as 100 nA/V at 100 mK. On the fundamental physics side, our results suggest that the mechanism at the basis of the observed phenomenon is quite general and does not rely on the existence of a true pairing potential, but rather the presence of superconducting correlations is enough for the effect to occur. On the technological side, our findings widen the family of materials available for the implementation of all-metallic field-effect transistors to \textit{synthetic} proximity-induced superconductors.

Amato G., Greco A., Vittone E.

Thanks to its excellent mechanical properties, graphene is particularly suited for the realization of suspended membranes. The present paper deals with one possible application of such membranes that is the realization of suspended lithographic masks for shadow evaporation onto a substrate. This technique, which is largely used for realizing mesoscopic devices, where the quality requirements for the junctions prevent the exposure to ambient air and the occurrence of quantum phenomena requires highly defined structures, can be improved by the use of pure 2-dimensional masks, like graphene ones. Advantages and differences of this material with respect to commonly employed polymers are presented and discussed.

Skryabina O.V., Egorov S.V., Goncharova A.S., Klimenko A.A., Kozlov S.N., Ryazanov V.V., Bakurskiy S.V., Kupriyanov M.Y., Golubov A.A., Napolskii K.S., Stolyarov V.S.

We report on a fabrication method and electron-transport measurements for submicron Josephson junctions formed by Cu nanowires coupling to superconducting planar Nb electrodes. The Cu nanowires with a resistivity of ρCu≃1 μΩ cm at low temperatures consisting of single-crystalline segments have been obtained by templated electrodeposition using anodic aluminum oxide as a porous matrix. The current-voltage characteristics of the devices have been studied as a function of temperature and magnetic field. For all junctions, the critical current monotonically decreases with a magnetic field. The measured temperature and magnetic field dependencies are consistent with the model for one-dimensional diffusive superconductor/normal metal/superconductor (SNS) Josephson junctions within the quasiclassical theory of superconductivity.

Jabdaraghi R.N., Peltonen J.T., Saira O.-., Pekola J.P.

We characterize niobium-based lateral Superconductor (S)–Normal metal (N)–Superconductor (SNS) weak links through low-temperature switching current measurements and tunnel spectroscopy. We fabricate the SNS devices in two separate lithography and deposition steps, combined with strong argon ion cleaning before the normal metal deposition in the last step. Our SNS weak link consists of high-quality sputtered Nb electrodes that have contacted with evaporated Cu. The two-step fabrication flow enables more flexibility in the choice of materials and pattern design. A comparison of the temperature-dependent equilibrium critical supercurrent with theoretical predictions indicates that the quality of the Nb-Cu interface is similar to that of evaporated Al-Cu weak links. We further demonstrate a hybrid magnetic flux sensor based on an Nb-Cu-Nb SNS junction, where the phase-dependent normal metal density of states is probed with an Al tunnel junction.

Shimada H., Miyawaki K., Hagiwara A., Takeda K., Mizugaki Y.

Superconducting single-electron transistors (SSETs) composed of small Al/AlO/V junctions were fabricated, and their transport properties were investigated. The device with an Al island exhibited a supercurrent that was 2e-periodic in the gate charge while that with a V island showed a periodicity of e, where e is an elementary charge. The Josephson-quasiparticle (JQP)-cycle current appeared at the bias voltage V in the range , where is the superconducting gap of Al and is the charging energy of an elementary charge. This is different from the commonly accepted range for the JQP current such as that in the case of an all Al SSET. There also appeared a large leakage current at , where is the superconducting gap of V. All these properties are accounted for by considering the finite subgap quasiparticle density of states in the V electrode.

Ronzani A., Altimiras C., Giazotto F.

We report the design and implementation of a high-performance superconducting quantum interference proximity transistor (SQUIPT) based on aluminum-copper (Al-Cu) technology. With the adoption of a thin and short copper nanowire we demostrate full phase-driven modulation of the proximity-induced minigap in the normal metal density of states. Under optimal bias we record unprecedently high flux-to-voltage (up to 3 mV/$\Phi_0$) and flux-to-current (exceeding 100 nA/$\Phi_0$) transfer function values at sub-Kelvin temperatures, where $\Phi_0$ is the flux quantum. The best magnetic flux resolution (as low as 500 n$\Phi_0/\sqrt{Hz}$ at 240 mK, being limited by the room temperature pre-amplification stage) is reached under fixed current bias. These figures of merit combined with ultra-low power dissipation and micrometer-size dimensions make this mesoscopic interferometer attractive for low-temperature applications such as the investigation of the magnetization of small spin populations.

Ronzani A., Altimiras C., Giazotto F.

We report on the fabrication and characterization of a two-terminal mesoscopic interferometer based on three V/Cu/V Josephson junctions having nanoscale cross-section. The junctions have been arranged in a double-ring geometry realized by metallic thin film deposition through a suspended mask defined by electron beam lithography. Although a significant amount of asymmetry between the critical current of each junction is observed, we show that the interferometer is able to suppress the supercurrent to a level lower than 6 parts per thousand, being here limited by measurement resolution. The present nano-device is suitable for low-temperature magnetometric and gradiometric measurements over the micrometric scale.

Giazotto F., Bergeret F.S.

We theoretically investigate heat transport in hybrid normal metal-superconductor (NS) nanojunctions focusing on the effect of thermal rectification. We show that the heat diode effect in the junction strongly depends on the transmissivity and the nature of the NS contact. Thermal rectification efficiency can reach up to ∼123% for a fully transmissive ballistic junction and up to 84% in diffusive NS contacts. Both values exceed the rectification efficiency of a NIS tunnel junction (I stands for an insulator) by a factor close to ∼5 and ∼3, respectively. Furthermore, we show that for NS point-contacts with low transmissivity, inversion of the heat diode effect can take place. Our results could prove useful for tailoring heat management at the nanoscale, and for mastering thermal flux propagation in low-temperature caloritronic nanocircuitry.