We analytically study shock wave in the Josephson transmission line (JTL) in the presence of ohmic dissipation. When ohmic resistors shunt the Josephson junctions (JJ) or are introduced in series with the ground capacitors the shock is broadened. When ohmic resistors are in series with the JJ, the shock remains sharp, same as it was in the absence of dissipation. In all the cases considered, ohmic resistors don't influence the shock propagation velocity. We study an alternative to the shock wave - an expansion fan - in the framework of the simple wave approximation for the dissipationless JTL and formulate the generalization of the approximation for the JTL with ohmic dissipation.
We study the resistive transition in Josephson-junction arrays at $f=1/2$ flux quantum per plaquette by dynamical simulations of the resistively-shunted-junction model. The current-voltage scaling and critical dynamics of the phases are found to be well described by the same critical temperature and static exponents as for the chiral (vortex-lattice) transition. Although this behavior is consistent with a single transition scenario, where phase and chiral variables order simultaneously, two different dynamic exponents result for phase coherence and chiral order.
We use driven Monte Carlo dynamics to study the resistive behavior of superconducting Josephson junction arrays on a honeycomb lattice in a magnetic field corresponding to $f$ flux quantum per plaquette. While for $f=1/3$ the onset of zero resistance is found at nonzero temperature, for $f=1/2$ the results are consistent with a transition scenario where the critical temperature vanishes and the linear resistivity shows thermally activated behavior. We determine the thermal critical exponent of the zero-temperature transition for $f=1/2$, from a dynamic scaling analysis of the nonlinear resisti…
We describe resistive states of the system combining two types of orderings - superconducting and ferromagnetic one. It is shown that in the presence of magnetization dynamics such systems become inherently dissipative and in principle cannot sustain any amount of the superconducting current because of the voltage generated by the magnetization dynamics. We calculate generic current-voltage characteristics of a superconductor/ferromagnet/superconductor Josephson junction with an unpinned domain wall and find the low-current resistance associated with the domain wall motion. We suggest the fini…
In this paper, we present data for two nanocrystalline YBa2Cu3O7-x (YBCO) samples which both exhibit Josephson-like Colossal Resistive Switching (JCRS) in voltage-current (V-I) traces from 4.2 K up to room temperature, in magnetic fields up to 8 T. We report Josephson-like hysteresis for both positive and negative current that has not been observed before in colossal resistive switching materials. Non-zero resistance was measured in transport measurements at all temperatures. At low temperatures (< 90 K), we also observed the usual properties for YBCO including weak superconducting and paramag…
We calculate current-phase relation (CPR) of a SN-S-SN Josephson junction based on a variable thickness SN bilayer composed of highly disordered superconductor (S) and low-resistive normal metal (N) with proximity induced superconductivity. In case when the thickness of S,N layers and length of S constriction is about of superconducting coherence length the CPR is single-valued, could be close to sinusoidal one and the product $I_cR_n$ can reach $Δ(0)/2|e|$ ($I_c$ is the critical current of the junction, $R_n$ is its normal-state resistance, $Δ(0)$ is the superconductor gap of single S layer a…
An array of resistively and capacitively shunted Josephson junctions with nonsinusoidal current-phase relation is considered for modelling the transition in high-T$_c$ superconductors. The emergence of higher harmonics, besides the simple sinusoid $I_{c}\sinϕ$, is expected for dominant \emph{d}-wave symmetry of the Cooper pairs, random distribution of potential drops, dirty grains, or nonstationary conditions. We show that additional cosine and sine terms act respectively by modulating the global resistance and by changing the Josephson coupling of the mixed superconductive-normal states. Firs…
We use a driven Monte Carlo dynamics in the phase representation to determine the linear resistivity and current-voltage scaling of a two-dimensional Josephson-junction array at an irrational flux quantum per plaquette. The results are consistent with a phase-coherence transition scenario where the critical temperature vanishes. The linear resistivity is nonzero at any finite temperatures but nonlinear behavior sets in at a temperature-dependent crossover current determined by the thermal critical exponent. From a dynamic scaling analysis we determine this critical exponent and the thermally a…
Bi$_2$Se$_3$ nanoribbons, grown by catalyst-free Physical Vapour Deposition, have been used to fabricate high quality Josephson junctions with Al superconducting electrodes. The conductance spectra (dI/dV) of the junctions show clear dip-peak structures characteristic of multiple Andreev reflections. The temperature dependence of the dip-peak features reveals a highly transparent Al/Bi$_2$Se$_3$ topological insulator nanoribbon interface and Josephson junction barrier. This is supported by the high values of the Bi$_2$Se$_3$ induced gap and of I$_c$R$_n$ (I$_c$ critical current, R$_n$ normal r…
We present a theoretical study of inhomogeneous dynamic (resistive) states in a single plaquette consisting of three Josephson junctions. Resonant interactions of such a breather state with electromagnetic oscillations manifest themselves by resonant current steps and voltage jumps in the current-voltage characteristics. An externally applied magnetic field leads to a variation of the relative shift between the Josephson current oscillations of two resistive junctions. By making use of the rotation wave approximation analysis and direct numerical simulations we show that this effect allows to …
We investigate by numerical simulations the behavior of the power dissipated in a resistive load capacitively coupled to a Josephson flux flow oscillator and compare the results to those obtained for a d.c. coupled purely resistive load. Assuming realistic values for the parameters R and C, both in the high- and in the low-Tc case the power is large enough to allow the operation of such a device in applications.
We study experimentally and theoretically the influence of phase-whirling (resistive) state in one junction of a two-fold Josephson stack on the fluxon motion in the other junction. In experiment, we measure the fluxon velocity versus current in one junction as a function of the state (Meissner or resistive) of the neighboring junction. The analysis, made for the limit of high fluxon density, shows that the interaction with the resistive state results in an increase of the effective damping for the moving fluxon and, therefore, in reduction of its velocity. Numerical simulations confirm this r…
We study the scaling behavior and critical dynamics of the resistive transition in Josephson-junction arrays, at f=1/2 flux quantum per plaquette, by numerical simulation of an on-site dissipation model for the dynamics. The results are compared with recent simulations using the resistively-shunted-junction model. For both models, we find that the resistivity scaling and critical dynamics of the phases are well described by the same critical temperature as for the chiral (vortex-lattice) transition, with a power-law divergent correlation length. The behavior is consistent with the single trans…
Topological features of low dimensional superconductors have caused a lot of excitement recently because of their broad range of applications in quantum information and their potential to reveal novel phases of quantum matter. A potential problem for practical applications is the presence of phase-slips that break phase coherence. Dissipation in non-topological superconductors suppresses phase-slips and can restore long-range order. Here we investigate the role of dissipation in a topological Josephson junction. We show that the combined effects of topology and dissipation keeps phase and anti…
We obtain self-consistent macroscopic equations describing interlayer Josephson effect and intralayer disequilibrium in one-dimensional array of Josephson coupled layers. We show that ``nonequilibrium coupling'' can lead to effective spatial and time synchronization and formation of coherent dynamic resistive state (collective Josephson effect) in Nb-AlO-Nb stacked junctions and HTSC (intrinsic Josephson effect). We propose it to be the origin of collective switching phenomena observed in PbBiSrCaCuO.
Dynamical Reduction of Two Series Josephson Junctions to a Synthetic High-Transparency Josephson Element
University of Salerno（萨莱诺大学）；INFN, Sezione di Napoli, Gruppo Collegato di Salerno（意大利国家核物理研究所，那不勒斯分部，萨莱诺协作组）；CNR-SPIN（意大利国家研究委员会自旋物理中心）；QuantWare（QuantWare公司）；University of Sannio（萨尼奥大学）
Equations describing the resistive state of a layered superconductor with anisotropic pairing are derived. The similarity with a stack of Josephson junctions is found at small voltages only, when current density in the direction perpendicular to the layers can be interpreted as a sum of the Josephson superconducting, the Ohmic dissipative and the interference currents. In the spatially uniform state differential conductivity at higher voltages becomes negative. Nonuniformity of the current distribution generates the branch imbalance and violates the Josephson relation between frequency and vol…
The form of the fluctuation-dissipation theorem for a resistively shunted Josephson juction array is derived with the help of the method which explicitely takes into acoount screening effects. This result is used to express the flux noise power spectrum in terms of frequency dependent sheet impedance of the array. The relation between noise amplitude and parameters of the detection coil is analysed for the simplest case of a single-loop coil.
We investigated current-voltage characteristics of unshunted and externally shunted Josephson junctions (JJs) with high critical current densities, Jc, in order to extract their basic parameters and statistical characteristics for JJ modeling in superconducting integrated circuits and to assess their potential for future technology nodes. Nb/AlOx-Al/Nb JJs with diameters from 0.5 μm to 6 μm were fabricated using a fully planarized process with Mo or MoNx thin-film shunt resistors with sheet resistance Rsq = 2 Ω/sq and Rsq = 6 Ω/sq, respectively. We used our standard MIT LL process SFQ5ee to fa…
We consider voltage and current responses formation in DC SQUID with overdamped Josephson junctions in resistive and superconducting state in the frame of resistively shunted junction (RSJ) model. For simplicity we neglect the junction capacitance and the noise effect. Explicit expressions for the responses in resistive state were obtained for a SQUID which is symmetrical with respect to bias current injection point. Normalized SQUID inductance $l = 2 e I_c L/\hbar$ (where $I_c$ is the critical current of Josephson junction, $L$ is the SQUID inductance, $e$ is the electron charge and $\hbar$ i…
The effect of quantum fluctuations on the current-voltage characteristics of Josephson junctions and superconducting nanowires is studied in the underdamped limit. Quantum fluctuations induce transitions between a Coulomb--blockade and a supercurrent branch, and can significantly modify the shape of current-voltage characteristics in the case of a highly resistive environment. Owing to the phase-charge duality, our results can be directly extended to the opposite overdamped limit.
We study the response of high-critical current proximity Josephson junctions to a microwave excitation. Electron over-heating in such devices is known to create hysteretic dc voltage-current characteristics. Here we demonstrate that it also strongly influences the ac response. The interplay of electron over-heating and ac Josephson dynamics is revealed by the evolution of the Shapiro steps with the microwave drive amplitude. Extending the resistively shunted Josephson junction model by including a thermal balance for the electronic bath coupled to phonons, a strong electron over-heating is obt…
In recent years many groups have used Fisher, Fisher, and Huse (FFH) dynamical scaling to investigate and demonstrate details of the superconducting phase transition. Some attention has been focused on two dimensions where the phase transition is of the Kosterlitz-Thouless-Berezinskii (KTB) type. Pierson et al. used FFH dynamical scaling almost exclusively to suggest that the dynamics of the two-dimensional superconducting phase transition may be other than KTB-like. In this work we investigate the ability of scaling behavior by itself to yield useful information on the nature of the transitio…
Wide mesoscopic superconducting - normal-metal - superconducting (S-N-S) junctions exhibit Andreev bound states which carry substantial supercurrents, even at temperatures for which the equilibrium Josephson effect is exponentially small --- the currents carried by different states can cancel each other. This cancellation is incomplete whenever the junctions are driven out of equilibrium, e.g., by a dc voltage. This leads to phenomena similar to the usual dc and ac Josephson effects, but dominated by the second harmonic of the Josephson frequency, which may explain some striking recent experim…
We report on an experimental and theoretical study of the high-frequency mixing properties of ion-irradiated YBa2Cu3O7 Josephson junctions embedded in THz antennas. We investigated the influence of the local oscillator power and frequency on the device performances. The experimental data are compared with theoretical predictions of the general three-port model for mixers, in which the junction is described by the resistively shunted junction model. A good agreement is obtained for the conversion efficiency in different frequency ranges, spanning above and below the characteristic frequencies f…
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…
Anomalous resistive peaks below the superconducting transition temperature in heavily boron doped nanocrystalline diamond films could have potential application in switching devices, however the exact origin is still under study. We establish a temperature dependence of this resistive phase similar to what has been reported for in Josephson junction arrays and other granular superconductors where the charge duel of the Berezinskii-Kosterlitz-Thouless (BKT) transition has been observed. Non-linear magnetoresistance with a temperature dependent peak feature below the critical field are also pres…
We report large-scale simulations of the resistively-shunted Josephson junction array in strip geometry. As the strip width increases, the voltage first decreases following the dynamic scaling ansatz proposed by Minnhagen {\it et al.} [Phys. Rev. Lett. {\bf 74}, 3672 (1995)], and then rises towards the asymptotic value predicted by Ambegaokar {\it et al.} [Phys. Rev. Lett. {\bf 40}, 783 (1978)]. The nonmonotonic size-dependence is attributed to shortened life time of free vortices in narrow strips, and points to the danger of single-scale analysis applied to a charge-neutral superfluid state.
We present a theoretical study of inhomogeneous dynamic (resistive) states in a single plaquette consisting of three Josephson junctions. These breather states are found to exist in a large range of control parameters (dc bias, anisotropy and self inductance). We perform an analytical analysis of these states, and their stability and resonance behaviour. Numerical calculations confirm our results and show that instabilities arise due to resonant interactions between the breather and electromagnetic oscillations mediated by the breather state. These instabilities manifest themselves by various …
We propose the phase dynamics induced by spin waves in a superconductor/ferromagnet/superconductor (SC/FM/SC) Josephson junction. The resistively shunted junction (RSJ) model, which describes the dynamics of superconducting phase difference, is extended to include the spin wave excitation by ferromagnetic resonance (FMR) using the gauge invariant phase difference between two s-wave superconductors. The current-voltage characteristics show step structures when the magnetization in FM is driven by tuning the microwave frequency to FMR in the SC/FM/SC junction. The result presents a new route to …
A general phenomenological theory describing dynamics of Josephson vortices coupled to wide class of linear waves in layered high-T$_c$ superconductors is developed. The theory is based on hydrodynamic long wave approximation and describes interaction of vortices with electromagnetic, electronic and phonon degrees of freedom on an equal footing. In the limiting cases the proposed theory degenerates to simple models considered earlier. In the framework of the suggested model we undertook the numerical simulation of resistive state in layered superconductors placed in external magnetic field and…
Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$π$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evid…
Current steps in the current-voltage characteristics of wide superconducting Sn films exposed to a microwave irradiation were observed in the resistive state with phase slip lines. The behaviour of the magnitude of the steps on the applied irradiation power was found to be similar to that for the current steps in narrow superconducting channels with phase slip centers and, to some extent, for the Shapiro steps in Josephson junctions. This provides evidence for the Josephson properties of the phase slip lines in wide superconducting films and supports the assumption about similarity between the…
We analyze the interplay of dissipative and quantum effects in the proximity of a quantum phase transition. The prototypical system is a resistively shunted two-dimensional Josephson junction array, studied by means of an advanced Fourier path-integral Monte Carlo algorithm. The reentrant superconducting-to-normal phase transition driven by quantum fluctuations, recently discovered in the limit of infinite shunt resistance, persists for moderate dissipation strength but disappears in the limit of small resistance. For large quantum coupling our numerical results show that, beyond a critical di…
The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control …
We present a quantitative analysis of an escape rate for switching from the superconducting state to a resistive one in series arrays of globally coupled Josephson junctions. A global coupling is provided by an external shunting impedance. Such an impedance can strongly suppress both the crossover temperature from the thermal fluctuation to quantum regimes, and the macroscopic quantum tunneling (MQT) in short Josephson junction series arrays. However, in large series arrays we obtain an enhancement of the crossover temperature, and a giant increase of the MQT escape rate. The effect is explain…
We have observed the Josephson effect in junctions formed between single crystals of SrFe1.74Co0.26As2 and Ba0.23K0.77Fe2As2. I-V curves showed resistively-shunted junction characteristics, and the ac Josephson effect was observed under microwave irradiation. By applying an in-plane magnetic field, the critical current is completely modulated and shows a relatively symmetric diffraction pattern, consistent with the intermediate junction limit. The observation of the Josephson effect in the p-n bicrystal structure not only has significant implications for designing phase-sensitive junctions to …
We investigate the collective phase dynamics in conventional long Josephson junction (LJJ) stacks and in layered superconductors, exhibiting intrinsic LJJ behaviors. Using a theoretical model which accounts for both the magnetic induction effect and the breakdown of local charge neutrality (i.e., charging effect), we show that the collective motion of Josephson vortices, including the dispersion of Josephson plasma mode and the Swihart-type velocity, in an intrinsic LJJ stack such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$ (BSCCO) is significantly modified from those in a conventional LJJ stack. In BSCC…
The quality of a superconductor-normal metal-superconductor Josephson junction (JJ) depends crucially on the transparency of the superconductor-normal metal (S/N) interface. We demonstrate a technique for fabricating planar JJs with perfect S/N interfaces. The technique utilizes a strong inverse proximity effect discovered in Al/V$_5$S$_8$ bilayers, by which the Al layer is driven into the resistive state. The highly transparent S/N homointerface and the peculiar normal metal enable the flow of Josephson supercurrent across a 2.9 $μ$m long weak link. Moreover, our JJ exhibits a giant critical …
It is well known that copper-based perovskite oxides rightly enjoy consensus as high-temperature superconductors on the basis of two signatures: the resistive transition and the Meissner effect. We show that the resistive transitions in carbon nanotubes agree quantitatively with the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory for quasi-1D superconductors although the superconducting transition temperatures can vary from 0.4 K to 750 K for different samples. We have also identified the Meissner effect in the field parallel to the tube axis up to room temperature for aligned and physically…
We reveal that topological Josephson junctions provide a natural platform for the interplay between the Josephson effect and the Landau-Zener effect through a two-level system formed by coupled Majorana modes. We build a quantum resistively shunted junction (RSJ) model by modifying the standard textbook RSJ model to take account of the two-level system from the Majorana modes at the junction. We show that the dynamics of the two-level system is governed by a nonlinear Schrödinger equation and solve the equations analytically via a mapping to a classical dynamical problem. This nonlinear dynami…
We study non-equilibrium Josephson effect and phase-dependent conductance in three-terminal diffusive interferometers with short arms. We consider strong proximity effect and investigate an interplay of dissipative and Josephson currents co-existing within the same proximity region. In junctions with transparent interfaces, the suppression of the Josephson current appears at rather large voltage, $eV\sim Δ$, and the current vanishes at $eV\geqΔ$. Josephson current inversion becomes possible in junctions with resistive interfaces, where the inversion occurs within a finite interval of the appli…
Superconducting weak-link (WL), behaving like a Josephson junction (JJ), is fundamental to many superconducting devices such as nanoSQUIDs, single-photon detectors, and bolometers. The interplay between unique nonlinear dynamics and inevitable Joule heating in a JJ leads to new characteristics. Here, we report a time-dependent model incorporating thermal effect in the AC Josephson regime for a Josephson WL shunted by a resistor together with an inductor to investigate the dynamics as well as the resulting current-voltage characteristics. We find that the dynamic regime where phase and temperat…
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…
The boundary effects on the current-voltage characteristics in two-dimensional arrays of resistively shunted Josephson junctions are examined. In particular, we consider both the conventional boundary conditions (CBC) and the fluctuating twist boundary conditions (FTBC), and make comparison of the obtained results. It is observed that the CBC, which have been widely adopted in existing simulations, may give a problem in scaling, arising from rather large boundary effects; the FTBC in general turn out to be effective in reducing the finite-size effects, yielding results with good scaling behavi…
The superconductor-to-insulator quantum phase transition in resistively shunted Josephson junctions is investigated by means of path-integral Monte Carlo simulations. This numerical technique allows us to directly access the (previously unexplored) regime of the Josephson-to-charging energy ratios E_J/E_C of order one. Our results unambiguously support an earlier theoretical conjecture, based on renormalization-group calculations, that at T -> 0 the dissipative phase transition occurs at a universal value of the shunt resistance R_S = h/4e^2 for all values E_J/E_C. On the other hand, finite-te…
We report the experimental evidence of the ac Josephson effect in a transition edge sensor (TES) operating in a frequency domain multiplexer and biased by ac voltage at MHz frequencies. The effect is observed by measuring the non-linear impedance of the sensor. The TES is treated as a weakly linked superconducting system and within the resistively shunted junction model framework. We provide a full theoretical explanation of the results by finding the analytic solution of the non-inertial Langevian equation of the system and calculating the non-linear response of the detector to a large ac bia…
Topological Josephson junctions designed on the surface of a 3D-topological insulator (TI) harbor Majorana bound states (MBS's) among a continuum of conventional Andreev bound states. The distinct feature of these MBS's lies in the $4π$-periodicity of their energy-phase relation that yields a fractional ac Josephson effect and a suppression of odd Shapiro steps under $r\!f$ irradiation. Yet, recent experiments showed that a few, or only the first, odd Shapiro steps are missing, casting doubts on the interpretation. Here, we show that Josephson junctions tailored on the large bandgap 3D TI Bi$_…
A bulk polycrystalline sample of YBa_(2)Cu_(3)O_(7-δ) (δ\approx 0.1) has been irradiated by γ-rays with ^{60}Co source. Non-monotonic behavior of T_{c} with increasing irradiation dose Φ(up to 220 MR) is observed: T_{c} decreases at low doses (Φ< 50 MR) from initial value (\approx 93 K) by about 2 K and then rises, forming a minimum. At higher doses (Φ> 120 MR) T_{c} goes down again. The temperature width of resistive transition increases rather sharply with dose below 75 MR and drops somewhat at higher dose. The results observed are discussed, taking into account the granular structure of sam…
We study the influence of dissipation on the switching current statistics of moderately damped Josephson junctions. Different types of both low- and high- $T_c$ junctions with controlled damping are studied. The damping parameter of the junctions is tuned in a wide range by changing temperature, magnetic field, gate voltage, introducing a ferromagnetic layer or in-situ capacitive shunting. A paradoxical collapse of switching current fluctuations occurs with increasing $T$ in all studied junctions. The phenomenon critically depends on dissipation in the junction and is explained by interplay of…
Exact Duality at Low Energy in a Josephson Tunnel Junction Coupled to a Transmission Line
Université Paris Cité, CNRS, Matériaux et Phénomènes Quantiques（巴黎西岱大学，法国国家科学研究中心，物质与量子现象）；Physics Department, University of California Santa Barbara（加州大学圣塔芭芭拉分校物理系）；Google Quantum AI（谷歌量子AI）
