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/Sr2RuO4 type junctions.
The transition from the model of a long Josephson junction of variable width to the model of a junction with a coordinate-dependent Josephson current amplitude is effected through a coordinate transformation. This establishes the correspondence between the classes of Josephson junctions of variable width and quasi-one-dimensional junctions with a variable thickness of the barrier layer. It is shown that for a junction of exponentially varying width the barrier layer of the equivalent quasi-one-dimensional junction has a distributed resistive inhomogeneity that acts as an attractor for magnetic…
We combine electron beam lithography and masked anodization of epitaxial aluminium to define tunnel junctions via selective oxidation, alleviating the need for wet-etch processing or direct deposition of dielectric materials. Applying this technique to define Josephson junctions in proximity induced superconducting Al-InAs heterostructures, we observe multiple Andreev reflections in transport experiments, indicative of a high quality junction. We further compare the mobility and density of Hall-bars defined via wet etching and anodization. These results may find utility in uncovering new fabri…
Josephson junctions were fabricated in epitaxial films of cobalt-doped BaFe2As2 on [001]-tilt (La,Sr)(Al,Ta)O3 bicrystal substrates. 10m-wide microbridges spanning a 30-degrees-tilted bicrystal grain boundary (BGB bridge) exhibited resistively-shunted-junction (RSJ)-like current-voltage characteristics up to 17 K, and the critical current was suppressed remarkably by a magnetic field. Microbridges without a BGB did not show the RSJ-like behavior, and their critical current densities were 20 times larger than those of BGB bridges, confirming BGB bridges display a Josephson effect originating fr…
Critical curves "critical current - external magnetic field" of long Josephson junctions with inhomogeneity and variable width are studied. We demonstrate the existence of the regions of magnetic field where some fluxon states are stable only, if the external current through the junction is different from zero. Position and size of such regions depend on length of the junction, its geometry, parameters of inhomogeneity and form of the junction. The noncentral (left and right) pure fluxon states are appeared in the inhomogeneous Josephson junction with increase in the junction length. We demons…
We present a theory for the Josephson effect in an unconventional superconductor / one-dimensional electron gas / unconventional superconductor (s/o/s) junction, where the Josephson current is carried by components injected perpendicular to the interface. When superconductors on both sides have triplet symmetries, the Josephson current is enhanced at low temperature due to the zero-energy states formed near the interface. Measuring Josephson current in this s/o/s junction, we can identify parity of the superconductor.
We present a closed form solution for the self-resonances in a short Josephson tunnel junction. This solution is alternative to the well known textbook result \cite{Barone,Kulik} based on a series expansion. Results are derived for the up-to-date case of a $0 - π$ junction.
We present a theory of the Josephson effect in a twofold-tilted Josephson junction made by d-wave anisotropic layered superconductors. We find the appearance of an intrinsic electrical resistance that arises from the misalignment of the superconductive planes (the CuO_2 planes in YBCO) in the two electrodes. This intrinsic contribution to the tunnel barrier has several non-trivial consequences. The result is relevant for understanding the electric transport properties of [100] tilt and [100] tilt-tilt Josephson junctions based on d-wave superconductors.
We study vortex structure in three different models of long Josephson junctions: exponentially shaped Josephson junction and Josephson junctions with resistor and shunt inhomogeneities in barrier layer. Numerical calculations of the possible magnetic flux distributions and corresponding bifurcation curves have done. For these three models the critical curves ``critical current-magnetic field'' are constructed. We develop an idea of the equivalence of exponentially shaped Josephson junction and rectangular junction with distributed inhomogeneity and demonstrate that at some parameters of shunt …
Josephson junctions were photogenerated in underdoped thin films of the YBa$_2$Cu$_3$O$_{6+x}$ family using a near-field scanning optical microscope. The observation of the Josephson effect for separations as large as 100 nm between two wires indicates the existence of an anomalously large proximity effect and show that the underdoped insulating material in the gap of the junction is readily perturbed into the superconducting state. The critical current of the junctions was found to be consistent with the conventional Josephson relationship. This result constrains the applicability of SO(5) th…
We present the measurement of superconductor / ferromagnetic Josephson junctions, based on an epitaxial Nb bottom electrode and epitaxial Fe20Ni80 barrier. Uniform junctions have been fabricated with a barrier thicknesses in the range 2-12 nm. The maximum critical current density ~ 2.4 \pm 0.2 * 10^9 Am^-2 was found for a devices with a 3 nm thick barrier at 4.2 K, corresponding to an average characteristic voltage I_C R_N ~ 16 \muV. The I_C R_N showed a non-monotonic behavior with Fe20Ni80 thickness. The variation of the resistance of a unit area AR_N, of the junctions with barrier thickness …
We present a fabrication scheme and testing results for epitaxial sub-micrometer Josephson junctions. The junctions are made using a high-temperature (1170 K) "via process" yielding junctions as small as 0.8 mu m in diameter by use of optical lithography. Sapphire (Al2O3) tunnel-barriers are grown on an epitaxial Re/Ti multilayer base-electrode. We have fabricated devices with both Re and Al top electrodes. While room-temperature (295 K) resistance versus area data are favorable for both types of top electrodes, the low-temperature (50 mK) data show that junctions with the Al top electrode hav…
The critical current response to an applied out-of-plane magnetic field in a Josephson junction provides insight into the uniformity of its current distribution. In Josephson junctions with semiconducting weak links, the carrier density and, therefore the overall current distribution could be modified electrostatically via metallic gates. Here, we show local control of the current distribution in an epitaxial Al-InAs Josephson junction equipped with five mini-gates. We demonstrate that not only can the junction width be electrostatically defined but also we can locally adjust the current profi…
Measurement of multiple Andreev reflection (MAR) in a Josephson junction made from an InAs heterostructure with epitaxial aluminum is used to quantify the highly transparent semiconductor-superconductor interface, indicating near-unity transmission. The observed temperature dependence of MAR does not follow a conventional BCS form, but instead agrees with a model in which the density of states in the quantum well acquires an effective induced gap, in our case 180 μeV, close to that of the epitaxial superconductor. Carrier density dependence of MAR is investigated using a depletion gate, reveal…
We report a unique experimental approach to create topological superconductors by inducing superconductivity into epitaxial metallic thin film with strong spin-orbit coupling. Utilizing molecular beam epitaxy technique under ultra-high vacuum condition, we are able to achieve (111) oriented single phase of gold (Au) thin film grown on a well-oriented vanadium (V) s-wave superconductor film with clean interface. We obtained atomically smooth Au thin films with thicknesses even down to below a nanometer showing near-ideal surface quality. The as-grown V/Au bilayer heterostructure exhibits superc…
Operation of a Superconducting Quantum Interference Device (SQUID) made of stacked Josephson junctions is analyzed numerically for a variety of junction parameters. Due to a magnetic coupling of junctions in the stack, such a SQUID has certain advantages as compared to an uncoupled multi-junction SQUID. Namely, metastability of current-flux modulation can be reduced and a voltage-flux modulation can be improved if junctions in the stack are phase-locked. Optimum operation of the SQUID is expected for moderately long, strongly coupled stacked Josephson junctions. A possibility of making a stack…
The properties of Josephson junction including a ferromagnetic insulating layer are studied theoretically. The calculated current shows the anomalous dependence on the magnitude of the exchange interaction at the interface. The Josephson junction changes from 0-junction to $π$-junction with the increase of the magnitude of the exchange interaction.
Magnetotransport measurements were done on $\Nb/\Al_2Ø_3/\Cu/\Ni/\Nb$ superconductor-insulator-ferromagnet-superconductor Josephson tunnel junctions. Depending on ferromagnetic $\Ni$ interlayer thickness and geometry the standard (1d) magnetic field dependence of critical current deviates from the text-book model for Josephson junctions. The results are qualitatively explained by a short Josephson junction model based on anisotropy and 2d remanent magnetization.
We clarify the applicability of the quasistatic approximation used in Ref. [\onlinecite{VE}], where coupled spin and Josephson plasma waves have been predicted to exist in SIFS Josephson junctions. We show, contrary to the claim of the authors of Ref. [\onlinecite{Maekawa}], that this approximation is very accurate in realistic systems studied experimentally.
Josephson radiation is a useful signature for detecting Majorana zero modes in topological superconductors. We study the Josephson radiation of the underdamped topological Josephson junction within the quantum resistively and capacitively shunted junction model. We show that the quantum dynamics of the Majorana two-level system induce oscillatory patterns in the Josephson emission spectra. With the Floquet method, we obtain analytical results for these oscillatory patterns and find that they are well described by Bessel functions. We perform numerical simulations to verify the analytical resul…
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 calculate the current phase relation of a planar Josephson junction with a ferromagnetic weak link located on top of a thin normal metal film. Following experimental observations we assume transparent superconductor-ferromagnet interfaces. This provides the best interlayer coupling and a low suppression of the superconducting correlations penetrating from the superconducting electrodes into the ferromagnetic layer. We show that this Josephson junction is a promising candidate for an experimental ϕ junction realization.
The spontaneous flux generation and magnetic field modulation of the critical current in a 0-pi Josephson junction are calculated for different ratios of the junction length to the Josephson penetration depth, and different ratios of the 0-junction length to the pi-junction length. These calculations apply to a Pb-YBCO c-axis oriented junction with one YBCO twin boundary, as well as other experimental systems. Measurements of such a junction can provide information on the nature of the c-axis Josephson coupling and the symmetry of the order parameter in YBCO. We find spontaneous flux even for …
The effect of microwave irradiation on the phase dynamics of intrinsic Josephson junctions in high temperature superconductors is investigated. We compare the current-voltage characteristics for a stack of coupled Josephson junctions under external irradiation calculated in the framework of CCJJ and CCJJ+DC models.
We observed splitting of the low-bias vortex-flow branch in a dense-Josephson-vortex state into multiple sub-branches in current-voltage characteristics of intrinsic Josephson junctions (IJJs) of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ single crystals in the long-junction limit. Each sub-branch corresponds to a plasma mode in serially coupled Josephson junctions. Splitting into low-bias linear sub-branches with a spread in the slopes and the inter-sub-branch mode-switching character are in good quantitative agreement with the prediction of the weak but finite inter-junction capacitive-coupling mod…
We study magnetization reversal in a $φ_0$ Josephson junction with direct coupling between magnetic moment and Josephson current. Our simulations of magnetic moment dynamics show that by applying an electric current pulse, we can realize the full magnetization reversal. We propose different protocols of full magnetization reversal based on the variation of the Josephson junction and pulse parameters, particularly, electric current pulse amplitude, damping of magnetization and spin-orbit interaction. We discuss experiments which can probe the magnetization reversal in $φ_0$-junctions.
We discuss how to control dc Josephson current by influencing the structure and nonequilibrium population of Andreev levels via external electrostatic gates, external current injection and electromagnetic radiation. In particular we will consider the "giant" Josephson current in "long" SIS tunnel junctions and the regular and anomalous nonequilibrium Josephson currents in three terminal SNS junctions. We will briefly discuss applications to the Josephson field effect transistor (JOFET) and to the newly invented Josephson interference transistor (JOINT).
A Josephson junction is made of two superconductors sandwiching an insulator, and a Josephson vortex is a magnetic vortex (flux tube) absorbed into the Josephson junction, whose dynamics can be described by the sine-Gordon equation. In a field theory framework, a flexible Josephson junction was proposed, in which the Josephson junction is represented by a domain wall separating two condensations and a Josephson vortex is a sine-Gordon soliton in the domain wall effective theory. In this paper, we propose a Josephson junction of non-Abelian color superconductors, that is described by a non-Abel…
We show that the time reversal symmetry inevitably breaks in a superconducting Josephson junction formed by two superconductors with different pairing symmetries dubbed as i-Josephson junction. While the leading conventional Josephson coupling vanishes in such an i-Josephson junction, the second order coupling from tunneling always generates chiral superconductivity orders with broken time reversal symmetry. Josephson frequency in the i-junction is doubled, namely $ω= 4eV /h$. The result provides a way to engineer topological superconductivity such as the d + id' -wave superconducting state ch…
Quantum fluctuations in a current biased Josephson junction, described in terms of the RCSJ-model, are considered. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and calculate the widths …
The most important practical characteristic of a Josephson junction is its critical current. The shape of the junction determines the specific form of the magnetic-field dependence of the its Josephson current. Here we address the magnetic diffraction patterns of specially shaped planar Josephson tunnel junctions. We focus on a wide ensemble of generalized ellipses, called superellipses, which retain the second order symmetry. We analyze the implications of this type of isometry and derive the explicit expressions for the threshold curves of superelliptic Josephson junctions. A detailed study …
High quality epitaxial NbN/MgO/NbN Josephson junctions have been realized with MgO barriers up to a thickness of d=1 nm. The junction properties coherently scale with the size of barrier, and low critical current densities down to 3 A/cm$^2$ have been achieved for larger barriers. In this limit, junctions exhibit macroscopic quantum phenomena for temperatures lower than 90 mK. Measurements and junction parameters support the notion of a possible use of these devices for multiphoton quantum experiments, taking advantage of the fast non equilibrium electron-phonon relaxation times of NbN.
We consider theoretically and numerically magnetic field dependencies of the maximum supercurrent across Josephson tunnel junctions with spatially alternating critical current density. We find that two flux-penetration fields and one-splinter-vortex equilibrium state exist in long junctions.
The development of superconducting memory and logic based on magnetic Josephson junctions relies on an understanding of junction properties and, in particular, the dependence of critical current on external magnetic flux (i.e. Fraunhofer patterns). With the rapid development of Josephson junctions with various forms of inhomogeneous barrier magnetism, Fraunhofer patterns are increasingly complex. In this paper we model Fraunhofer patterns for magnetic Josephson junctions in which the barrier magnetic susceptibility is position- and external magnetic field dependent. The model predicts anomalou…
The physics of Josephson tunnel junctions drastically depends on their geometrical configurations. The shape of the junction determines the specific form of the magnetic-field dependence of the its Josephson current. Here we address the magnetic diffraction patterns of specially shaped planar Josephson tunnel junctions in the presence of an in-plane magnetic field of arbitrary orientations. We focus on a wide ensemble of junctions whose shape is invariant under point reflection. We analyze the implications of this type of isometry and derive the threshold curves of junctions whose shape is the…
We investigate stationary charge imbalance effect in the system of coupled overdamped Josephson junctions. We show that coupling between junction and nonzero stationary charge imbalance in the resistive state bring to a decrease of the Josephson frequency in the Josephson junctions of the stack. The formed difference in Josephson frequency leads to the nonuniform switch to the Shapiro step regime in the presence of external electromagnetic radiation and appearance of kinks of voltage on the IV-characteristics of the stack. We also show that stationary charge imbalance brings to the slope of th…
We report systematic measurements of the critical current versus magnetic field patterns of annular Josephson junctions in a wide magnetic field range. A modulation of the envelope of the pattern, which depends on the junction width, is observed. The data are compared with theory and good agreement is found.
We confirmed the existence of the collective transverse plasma modes excited by the motion of the Josephson vortex lattice in stacked intrinsic Josephson junctions of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ by observing the multiple subbranches in the Josephson-vortex-flow current-voltage characteristics. We also observed the symptom of the microwave emission from the resonance between the Josephson vortex lattice and the collective transverse plasma modes, which provides the possibility of developing Josephson-vortex-flow electromagnetic oscillators.
A novel way to realize a pi Josephson junction is proposed, based on a weak link in an unconventional d-wave superconductor with appropriately chosen boundary geometry. The critical current of such a junction is calculated from a fully selfconsistent solution of microscopic Eilenberger theory of superconductivity. The results clearly show, that a transition to a pi Josephson junction occurs for both low temperatures and small sizes of the geometry.
We have observed a dissipative phase diffusion branch in arrays of hysteretic high-Tc intrinsic Josephson junctions. By comparing the data with a thermal activation model we extract the impedance seen by the junction in which phase diffusion is occurring. At the plasma frequency this junction is isolated from its environment and it sees its own large (~ kilo Ohm) impedance. Our results suggest that stacks of Josephson junctions may be used for isolation purposes in the development of a solid state quantum computer.
Charge formations on superconducting layers and creation of the longitudinal plasma wave in the stack of intrinsic Josephson junctions change crucially the superconducting current through the stack. Investigation of the correlations of superconducting currents in neighboring Josephson junctions and the charge correlations in neighboring superconducting layers allows us to predict the additional features in the current--voltage characteristics. The charge autocorrelation functions clearly demonstrate the difference between harmonic and chaotic behavior in the breakpoint region. Use of the corre…
We have developed a novel fabrication process for ultra-small, full-epitaxial NbN Josephson junctions on a silicon (Si) substrate. A full-epitaxial NbN/AlN/NbN tri-layer was grown on a Si (100) wafer with a (200)-oriented TiN buffer layer. It was patterned into Josephson junctions by an electron beam lithography (EBL) for junction definition followed by a reactive ion etch (RIE). A chemical mechanical polishing (CMP) process and an additional RIE by using CHF$_3$ gas formed reliable electrical contacts between the junction counter electrodes and the wiring layer. All fabricated junctions, with…
Tunnel junction between two superconductors is considered in the vicinity of the critical temperature. Superconductive fluctuations above Tc give rise to the noise of the ac Josephson current although the current itself is zero in average. As a result of fluctuations, current noise spectrum is peaked at the Josephson frequency, which may be considered as precursor of superconductivity in the normal state. Temperature dependence and shape of the Josephson current noise resonance line is calculated for various junction configurations.
Josephson vortices in naturally stacked Bi-2212 tunneling junctions display rich dynamic behavior that derives from the coexistence of three basic states: static Josephson vortex lattice, coherently moving lattice, and incoherent quasiparticle tunneling state. Rich structure of hysteretic branches observed in the current-voltage characteristics can be understood as combinatorial combinations of these three states which are realized in different junctions and evolve separately with magnetic field and bias current. In particular, the multiple Josephson-vortex-flow branches at low bias currents a…
We use a tight-binding Bogoliubov-de Gennes (BdG) formalism to self-consistently calculate the proximity effect, Josephson current, and local density of states in ballistic graphene SNS Josephson junctions. Both short and long junctions, with respect to the superconducting coherence length, are considered, as well as different doping levels of the graphene. We show that self-consistency does not notably change the current-phase relationship derived earlier for short junctions using the non-selfconsistent Dirac-BdG formalism but predict a significantly increased critical current with a stronger…
We examine the magnetic interference patterns of Josephson junctions with a region of 0- and of pi-phase shift. Such junctions have recently been realized as c-axis YBCO-Pb junctions with a single twin boundary in YBCO. We show that in general the junction generates self-fields which introduces an asymmetry in the critical current under reversal of the magnetic field. Numerical calculations of these asymmetries indicate they account well for the unexplained features observed in single twin boundary junctions.
Transport properties of high quality Nb/semiconductor/Nb long Josephson junctions based on metamorphic In_0.75Ga_0.25As epitaxial layers are reported. Different junction geometries and fabrication procedures are presented that allow a systematic comparison with quasiclassical theory predictions. The impact of junction transparency is highlighted and a procedure capable of yielding a high junction quality factor is identified.
We have studied both theoretically and experimentally how an LC series circuit connected in parallel to a Josephson junction influences the Josephson dynamics. The presence of the shell circuit introduces two energy scales, which in specific cases can strongly differ from the plasma frequency of the isolated junction. Josephson junctions were manufactured using Nb/Al-AlOx/Nb fabrication technology with various on-chip LC shunt circuits. Spectroscopic measurements in the quantum limit show an excellent agreement with theory taking into account the shunt inductance and capacitance in the Resisti…
The $φ$ Josephson junction has a doubly degenerate ground state with the Josephson phases $\pmφ$. We demonstrate the use of such a $φ$ Josephson junction as a memory cell (classical bit), where writing is done by applying a magnetic field and reading by applying a bias current. In the "store" state, the junction does not require any bias or magnetic field, but just needs to stay cooled for permanent storage of the logical bit. Straightforward integration with Rapid Single Flux Quantum logic is possible.
We reply to the comment [arXiv:0903.5110] on our paper "Mechanism of Terahertz Electromagnetic Emission from Intrinsic Josephson Junctions" [arXiv:0810.5268].
We report on the noise properties of ion-irradiated YBa$_2$Cu$_3$O$_7$ Josephson junctions. This work aims at investigating the linewidth of the Josephson oscillation with a detector response experiment at $\simeq$132 GHz. Experimental results are compared with a simple analytical model based on the Likharev-Semenov equation and the de Gennes dirty limit approximation. We show that the main source of low-frequency fluctuations in these junctions is the broadband Johnson noise and that the excess ($\frac{1}{f}$) noise contribution does not prevail in the temperature range of interest, as report…
A magnetic field induced electric polarization and the corresponding change of an effective junction capacitance are considered within a 3D model of disordered Josephson junction arrays. At some threshold field (near the Josephson network critical field), the effective junction charge and the related capacitance are shown to reach a maximum and to change a sign, respectively. A possibility to observe the predicted effects in artificially prepared arrays of superconducting grains is discussed.
We derive a generic phenomenological model of a Majorana Josephson junction that accounts for avoided crossing of Andreev states, and investigate its dynamics at constant bias voltage to reveal an unexpected pattern of any-π Josephson effect in the limit of slow decoherence.
The Josephson effect in p-wave superconductor / diffusive normal metal / p-wave superconductor junctions is studied theoretically. Amplitudes of Josephson currents are several orders of magnitude larger than those in s-wave junctions. Current-phase (J-ϕ) relations in low temperatures are close to those in ballistic junctions such as J\propto\sin(ϕ/2) and J\proptoϕeven in the presence of random impurity potentials. A cooperative effect between the midgap Andreev resonant states and the proximity effect causes such anomalous properties and is a character of the spin-triplet superconductor juncti…
We derive the qualitative behavior of superconductor-antiferromagnet- superconductor (SAS) Josephson junctions described by Zhang's SO(5) theory. The main differences between these junctions and conventional SIS junctions arise from the non-sinusoidal current-phase relation derived by Demler et al. for thin SAS junctions. Using a simple approximation to this non-sinusoidal function, the current voltage relation, Shapiro steps, thermal fluctuation effects and the diffraction pattern in a magnetic field are obtained.
I consider a Josephson junction crossing the middle of a thin rectangular superconducting strip of length L and width W subjected to a perpendicular magnetic induction B. I calculate the spatial dependence of the gauge-invariant phase difference across the junction and the resulting B dependence of the critical current Ic(B).
We investigate the dynamics of a resistively shunted Josephson junction. We compute the Josephson frequency and the generalized impedances for a variety of the parameters, particularly with relevance to predicting the measurable effects of zero-temperature current noise in the resistor.
Many experiments on high-temperature superconductors have shown paramagnetic behavior when the sample is field cooled. The paramagnetism was first attributed to a d-wave order parameter creating pi-junctions in the samples. However, the same effect was later discovered in traditional low-temperature superconductors and conventional Josephson-junction arrays which are s-wave. By simulating both conventional and mixed pi/conventional Josephson-junction arrays we determine that differences exist which may be sufficient to clearly identify the presence (or absence) of pi-junctions. In particular t…
We present a unified description of a junction between $s$-wave (BCS) superconductors and a junction between $p$-wave superconductors in a topologically nontrivial phase, which relies on a scattering state expansion. We compute Josephson current and thermal noise in the two kinds of junction and exhibit some characteristic features for a junction of two topological superconductors hosting Majorana zero-energy modes.
