Two Dimensional Josephson Junction Arrays

Two dimensional Josephson junction arrays (JJAs) offer theopportunity to study a variety of basic physical concepts. Thepresent review focuses on recent experimental work on thedynamics of JJAs, as characterized by ac conductancemeasurements. The review starts with a discussion of basicphysics necessary to describe JJAs. Some experimentalissues, array fabrication and measurement techniques areconsidered next. In a perpendicular magnetic field, a JJA isan experimental realization of the frustrated XY model, withthe frustration parameter f, corresponding to the number offlux quanta in a unit cell of the array, adjusted by themagnetic field. It is thereby possible to investigate thenature of the ground states at arbitrary frustrations. Phasetransitions are the next topic: the vortex unbindingtransition is observed at integer f-values, while, if thejunction coupling energies are appropriately varied across thearray, at half-integer f-values the Ising transition,associated with chiral symmetry breaking, may be observed.Some aspects of vortex dynamics, a subject which is not yetcompletely understood, are then considered. Under certainconditions there is virtually no pinning in JJAs, they aretherefore ideally suited for the study of vortex dynamics. Thenext topic of this review is concerned with the influence ofdisorder on the ground states and on the phase transitions inJJAs. Site percolation in JJAs has provided some insightsinto the physics of disordered systems and allowed to verifysome theoretical predictions on percolation in two dimensions.A quick look at JJAs in the underdamped regime concludesthis review.     

Transverse Voltage in Disordered Josephson Junction Arrays with Diagonal Bias

We study numerically the effect of disorder in the transport properties of square Josephson junction arrays with a dc current applied in the diagonal direction ([11] direction). We obtain a finite transverse voltage in this case when we consider the presence of disorder in the critical currents of the junctions. We show that this behavior is in good agreement with previous experimental, results in square arrays with a diagonal current drive.     

Kinetic Inductance and Coulomb Blockade in One Dimensional Josephson Junction Arrays

One dimensional Josephson junction arrays have been fabricated andcurrent-voltage characteristics (IVC) have been measured at cryogenic temperatures. The arrays were fabricated in a SQUID-geometry which allowed an in situ tuning of the Josephson energy by application of a magnetic field. The IVC of the arrays shows a clear Coulomb blockade state. In the Coulomb blockade regime the IVC are hysteretic. The array is modeled using a serial resistive-inductive-junction model which is able to qualitatively explain the IVC. In this model an inductance of the order of 0.1–10 mH per junction is needed to account for the hysteresis. Kinetic inductance, stemming from the inertia of the Cooper pairs, gives the correct order of magnitude. The problem of self-heating is also discussed as an alternative explanation of the hysteresis.     

用于量子电压基准中约瑟夫森结阵列的CMP平整化工艺研究

化学机械平坦化(chemical mechanical planarization,CMP)工艺处理Si02绝缘层是一种获得高度集成化超导电路的关键技术,尤其适合于多层堆叠约瑟夫森结阵列器件的平整化.设计了应用于热氧化生长的Si02薄膜和化学气象沉积生长的Si02薄膜的CMP工艺,得出两种薄膜的抛光速率分别为2 nm/...     

Cross-Whisker Intrinsic Josephson Junction as a Probe of Symmetry of the Superconducting Order Parameter

As a test of the superconducting order parameter, we have developed an intrinsic Josephson junction by the name of cross-whisker junction. This junction was made using two Bi₂Sr₂CaCu₂O_8+d single crystal whiskers. Two whiskers were connected at their c planes with various cross-angles. Angular dependence of the critical current densities shows d-wave-like fourfold-symmetry. However, the angular dependence is much stronger than that of the conventional d_x ^{2-y 2} wave. The Jc shows its smallest value around 45 deg, which suggests that the Josephson penetration depth becomes longer. We have successfully observed a Fraunhofer pattern in the cross-whisker junction with cross-angle 45 deg.     

Current-Phase Relation in FSIFS Josephson Junction

In the framework of Tsukada-Furusaki formula, we calculate dc josephson current at a ferromagnetic superconductor–insulator–ferromagnetic superconductor (FSIFS) junction as function of phase difference between two ferromagnetic superconductors (FSs). We consider identical FSs which are in three different Cooper pairing states: one singlet S wave pairing and two triplet with parallel and anti parallel spins. We find a sinusoidal form for strong barrier strength for above-mention Cooper pairing states while we find a deviation from sinusoidal form for weak barrier strength. Different behaviors of I(?) in terms of FS exchange field can help us distinguish the type of Cooper pairing state at the FSs which is still a controversial issue in low-temperature physics.     

Josephson Junction based Quantum Computing

Among the physical realizations of the elements required for quantum computation nano-scale electronic devices [2, 10, 12, 16] are very promising. They can be easily integrated into electronic circuits and scaled up to large numbers of qubits. Here we describe qubits based on low-capacitance Josephson junctions. In these systems Coulomb blockade effects allow the control of the charge on a superconducting island. They constitute quantum bits, with logical states differing by the charge on one island. Single- and two-bit operations can be performed by manipulating applied gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. In addition to the manipulation of qubits, the resulting quantum state can be read out by coupling a single-electron transistor capacitively to the qubit. Received: October 23, 1998; revised version: September 21, 1999     

The Effect of the External Magnetic Field on the Current-Voltage Characteristic of HTS Josephson Junction Arrays

No Heading The role of the external magnetic field in performance specialty of the high-temperature superconducting (HTS) Josephson junction array (JJA): HTS Y Ba₂Cu₃O_7–0.05 bicrystal JJA with 180 junctions, is considered. The junctions are created on the yttrium-stabilized zirconium (fianite) substrate with the bicrystal grain boundary. The experimental confirmation of the current density changes under the influence of the external DC magnetic field is obtained. The dependence of current density on the penetrated magnetic field is investigated. The optimal shielding factor needed to obtain high supercurrents in considered system is determined.PACS numbers: 73.21.Ac, 73.30.+y, 74.72.Bk, 74.76.Bz, 74.80.Dm     

Microwave Conductivity of Superconducting and Insulating Fullerides

Superconductivity of A₃C₆₀ (A=K and Rb) is destroyed by the intercalation of neutral ammonia molecules, and is replaced by the antiferromagnetic ground state. These properties suggest the importance of the electronic correlation in fullerides, which have been believed to be simple BCS superconductors. By using a microwave cavity perturbation technique, we confirmed that the conductivity of the antiferromagnet (NH₃)K_3–x Rb _x C₆₀ at 200 K is already 3–4 orders of magnitude smaller than those of superconductors, K₃C₆₀ and (NR₃) _x NaRb₂C₆₀, and that the antiferromagnetic compounds are insulators without metal-insulator transition at the Néel temperature. These results indicate that the Mott–Hubbard transition in the A₃C₆₀ systems is driven by a reduction of lattice symmetry from face-centered-cubic (fcc) to face-centered-orthorhombic (fco), rather than by the magnetic ordering.     

Advanced Concepts in Josephson Junction Reflection Amplifiers

Low-noise amplification at microwave frequencies has become increasingly important for the research related to superconducting qubits and nanoelectromechanical systems. The fundamental limit of added noise by a phase-preserving amplifier is the standard quantum limit, often expressed as noise temperature $T_q=\hbar \omega /2k_B$ . Towards the goal of the quantum limit, we have developed an amplifier based on intrinsic negative resistance of a selectively damped Josephson junction. Here we present measurement results on previously proposed wide-band microwave amplification and discuss the challenges for improvements on the existing designs. We have also studied flux-pumped metamaterial-based parametric amplifiers, whose operating frequency can be widely tuned by external DC-flux, and demonstrate operation at $2\omega $ pumping, in contrast to the typical metamaterial amplifiers pumped via signal lines at $\omega $ .     

Anisotropic Supercurrent in Strained Graphene Josephson Junction

The Weyl?CDirac fermions in graphene-based SG/I/SG (SG denoting superconducting graphene; I, an insulator) junctions subjected to strains become highly asymmetric. The effect of the strain-induced symmetry change of the fermions on the supercurrent is studied. The highly anisotropic velocity near the critical deformation causes the critical current parallel to the direction of strain to oscillate as a function of gate voltage at a very high frequency. The same anisotropic velocity destroys the oscillation of the gate-dependent critical current when the current is perpendicular to the direction of strain. The direction-dependent supercurrent is due to the strain turning the two-dimensional massless relativistic electrons into nearly one-dimensional massless relativistic fermions near the critical deformation. This work reveals that a new effect can be induced by applying strain on a graphene-based Josephson junction.     

Josephson Junction with a Magnetic Vortex

We have studied Josephson tunneling through a circularly polarized micron or submicron-size disk of a soft ferromagnetic material. Such a disk contains a vortex that exhibits rich classical dynamics and has recently been proposed as a tool to study quantum dynamics of the nanoscale vortex core. The change in the Josephson current that is related to a tiny displacement of the vortex core has been computed analytically and plotted numerically for disks used in experiments. It is shown that a Josephson junction with a magnetic disk in the vortex state can be an interesting physical system that may be used to measure the nanoscale motion of the magnetic vortex.     

Magnetometry with Low-Resistance Proximity Josephson Junction

We characterize a niobium-based superconducting quantum interference proximity transistor (Nb-SQUIPT) and its key constituent formed by a Nb–Cu–Nb SNS weak link. The Nb-SQUIPT and SNS devices are fabricated simultaneously in two separate lithography and deposition steps, relying on Ar ion cleaning of the Nb contact surfaces. The quality of the Nb–Cu interface is characterized by measuring the temperature-dependent equilibrium critical supercurrent of the SNS junction. In the Nb-SQUIPT device, we observe a maximum flux-to-current transfer function value of about \(55\;\mathrm {nA}/\mathrm {\Phi }_0\) in the sub-gap regime of bias voltages. This results in suppression of power dissipation down to a few fW. Low-bias operation of the device with a relatively low probe junction resistance decreases the dissipation by up to two orders of magnitude compared to a conventional device based on an Al–Cu–Al SNS junction and an Al tunnel probe (Al-SQUIPT).     

Vortex Excitations and Dynamics in Disordered Josephson Junction Networks

The current-driven dynamics of disordered Josephson junction networks (JJN) in a magnetic field is studied numerically. It is found that the depinning of vortices is caused by the elastic deformation of vortex lattices or by the excitation of vortex-antivortex pairs, depending on the strength of the disorder. The vortex depinning mechanisms and the driven vortex dynamics after depinning are discussed in detail.     

Radiation from Flux Flow in Josephson Junction Structures

We derive the radiation power from a single Josephson junction (JJ) and from layered superconductors in the flux-flow regime. For JJ case, we formulate the boundary conditions for the electric and magnetic fields at the edges of the superconducting leads using the Maxwell equations in the dielectric media and find dynamic boundary conditions for the phase difference in JJ which account for the radiation. We derive the fraction of the power fed into JJ transformed into the radiation. In a finite-length JJ this fraction is determined by the dissipation inside JJ and it tends to unity as dissipation vanishes independently of mismatch of the junction and dielectric media impedances. We formulate also the dynamic boundary conditions for the phase difference in intrinsic JJs in highly anisotropic layered superconductors of the Bi₂Sr₂CaCu₂O₈ type at the boundary with free space. Using these boundary conditions, we solve equations for the phase difference in the linear regime of Josephson oscillations for rectangular and triangular lattices of Josephson vortices. In the case of rectangular lattice for crystals with the thickness along the c-axis much larger than the radiation wavelength, we estimate the radiation power per unit length in the direction of magnetic field at the frequency 1 THz as ∼N μW/cm for Tl₂Ba₂CaCu₂O₈ and ∼0.04 N μW/cm for Bi₂Sr₂CaCu₂O₈. For crystals with thickness smaller than the radiation wavelength, we found that the radiation power in the resonance is independent on number of layers and can be estimated at 1 THz as 0.5 W/cm (Tl₂Ba₂CaCu₂O₈) and 24 mW/cm (Bi₂Sr₂CaCu₂O₈). For rectangular lattice, due to superradiation regime, up to half of power fed into the crystal may be converted into the radiation. In the case of triangular or random lattice in the direction perpendicular to the layers, the fraction of power converted into the radiation depends on the dissipation rate and is much lower than for rectangular lattice in the case of high-temperature superconductors with nodes in the gap.     

Development and Investigation of SNS Josephson Arrays for the Josephson Arbitrary Waveform Synthesizer

Superconductor–normalmetal–superconductor(SNS) Josephson junction series arrays are developed and investigated for applications in the Josephson arbitrary waveform synthesizer (JAWS). The series arrays contain up to about 10 000 junctions arranged in a meanderlike design. AC voltages and arbitrary waveforms are synthesized by operation of the Josephson junctions by short current pulses. Higher harmonics are at least 110 dB below the fundamental. To verify the generated waveforms, a spectrum analyzer that has initially been calibrated using a binary-divided programmable Josephson voltage standard is used.      

Coherence Between Superconducting Edge States in Superconducting Periodic Arrays of Artificial Defects

The transition line of superconducting arrays of holes exhibits a rich field structure due to the interference of superconducting states nucleated at the holes edges. We studied by means of resistance measurements their effect on the T* _c (H) line as a function of transverse magnetic field using regular arrays of nanofabricated micron size holes. The arrays transition fields are higher than for the bulk. Moreover we found a nontrivial field modulation of the T* _c (H) line with an inversion, with increasing field, of the modulation concavity which we assigned to a crossover from a collective to an isolated edge state regime. The high field regime is well described by the nucleation at a single hole in an infinite film. The modulation at low fields was found to be dominated by the interference of neighbor edge states when the inter-hole distance w becomes comparable to the coherence length (T* _c ). A comparison between arrays of different hole shape shows the influence of geometry on the type of interaction established, which can described either as a superconducting wire network or as a weak link array.     

Inherent Thermometry in a Hybrid Superconducting Tunnel Junction

We discuss inherent thermometry in a Superconductor-Normal metal-Superconductor tunnel junction. In this configuration, the energy selectivity of single-particle tunneling can provide a significant electron cooling, depending on the bias voltage. The usual approach for measuring the electron temperature consists in using an additional pair of superconducting tunnel junctions as probes. In this paper, we discuss our experiment performed on a different design with no such thermometer. The quasi-equilibrium in the central metallic island is discussed in terms of a kinetic equation including injection and relaxation terms. We determine the electron temperature by comparing the micro-cooler experimental current-voltage characteristic with isothermal theoretical predictions. The limits of validity of this approach, due to the junctions asymmetry, the Andreev reflection or the presence of sub-gap states are discussed.