Switching times in long-overlap Josephson junctions subject to thermal fluctuations and non-Gaussian noise sources

We investigate the superconducting lifetime of long current-biased Josephson junctions, in the presence of Gaussian and non-Gaussian noise sources. In particular, we analyze the dynamics of a Josephson junction as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive state is characterized by nonmonotonic behavior as a function of noise intensity, driving frequency and junction length. We observe that these nonmonotonic behaviours are connected with the dynamics of the junction phase string during the switching towards the resistive state. An important role is played by the formation and propagation of solitons, with two different dynamical regimes characterizing the dynamics of the phase string. Our analysis allows to evidence the effects of different bias current densities, that is a simple spatially homogeneous distribution and a more realistic inhomogeneous distribution with high current values at the junction edges. Stochastic resonant activation, noise enhanced stability and temporary trapping phenomena are observed in the system investigated.Comment: 16 pages, 9 figures, Physical Review B, in pres

Effects of L\'evy noise on the dynamics of sine-Gordon solitons in long Josephson junctions

We numerically investigate the generation of solitons in current-biased long Josephson junctions in relation to the superconducting lifetime and the voltage drop across the device. The dynamics of the junction is modelled with a sine-Gordon equation driven by an oscillating field and subject to an external non-Gaussian noise. A wide range of $\alpha$-stable L\'evy distributions is considered as noise source, with varying stability index $\alpha$ and asymmetry parameter $\beta$. In junctions longer than a critical length, the mean switching time (MST) from superconductive to the resistive state assumes a values independent of the device length. Here, we demonstrate that such a value is directly related to the mean density of solitons which move into or from the washboard potential minimum corresponding to the initial superconductive state. Moreover, we observe: (i) a connection between the total mean soliton density and the mean potential difference across the junction; (ii) an inverse behavior of the mean voltage in comparison with the MST, with varying the junction length; (iii) evidences of non-monotonic behaviors, such as stochastic resonant activation and noise enhanced stability, of MST versus the driving frequency and noise intensity for different values of $\alpha$ and $\beta$; (iv) finally, these non-monotonic behaviors are found to be related to the mean density of solitons formed along the junction.Comment: 24 pages, 8 figures, submitted to J. Stat. Mech.: Theory Exp. arXiv admin note: text overlap with arXiv:1406.481

Sine-Gordon breathers generation in driven long Josephson junctions

We consider a long Josephson junction excited by a suitable external ac-signal, in order to generate control and detect breathers. Studying the nonlinear supratransmission phenomenon in a nonlinear sine-Gordon chain sinusoidally driven, Geniet and Leon explored the bifurcation of the energy transmitted into the chain and calculated a threshold $A (\omega)$ for the external driving signal amplitude, at which the energy flows into the system by breathers modes. I numerically study the continuous sine-Gordon model, describing the dynamics of the phase difference in a long Josephson junction, in order to deeply investigate the "continuous limit" modifications to this threshold. Wherever the energy flows into the system due to the nonlinear supratransmission, a peculiar breather localization areas appear in a $(A, \omega)$ parameters space. The emergence of these areas depends on the damping parameter value, the bias current, and the waveform of driving external signal. The robustness of generated breathers is checked by introducing into the model a thermal noise source to mimic the environmental fluctuations. Presented results allows one to consider a cryogenic experiment for creation and detection of Josephson breathers.Comment: 8 pages, 3 figure

Noisy dynamics in long and short Josephson junctions

The study of nonlinear dynamics in long Josephson junctions and the features of a particular kind of junction realized using a graphene layer, are the main topics of this research work. The superconducting state of a Josephson junction is a metastable state, and the switching to the resistive state is directly related to characteristic macroscopic quantities, such as the current the voltage across the junction, and the magnetic field through it. Noise sources can affect the mean lifetime of this superconducting metastable state, so that noise induced effects on the transient dynamics of these systems should be taken into account. The long Josephson junctions are investigated in the sine-Gordon framework, stressing the relations beetwen nonlinear excitations travelling into the medium and switching dynamics towards the resistive state. Nonlinear travelling wave solutions of the sine-Gordon equation are solitons and antisolitons (and their combinations), breathers and plasma waves. The effect of a non-Gaussian noise source is considered, by changing peculiar system parameters, such as the junction length or the frequency and the amplitude of an applied oscillating bias current, and features of the noise sources, such as the amplitude and the statistic of the stochastic signal. Fortran codes are implemented to integrate the nonlinear stochastic differential equations for the order parameter of these systems. Typical noise induced effects, such as the noise enhanced stability and the resonant activation, are evident exploring the mean switching time from the superconducting regime, as a function of the noise amplitude and driving frequency, respectively. Attention is given to the soliton evolution in connection with the escape dynamics from the superconducting metastable state. Moreover, noise induced breathers are detected. Breathers are special solutions of the sine-Gordon equation, composed by a coupled soliton-antisoliton pair, oscillating in an internal frame with a proper frequency. These solutions are highly unstable, and their detection in long Josephon junctions is an open challenge. The possibility to generate only breathers into a junction properly excited is the main focus of the second part of this work. The phenomenon of nonlinear supratransmission in long Josephson junction stimulated by an external signal is analyzed. In correspondence of precise combinations of values of amplitude A and frequency omega of the external sinusoidal pulse, the generation of only breathers emerges. Variations of the pulse durations, both of the applied bias current and of the damping parameter affect the localizations of breathers on a (A,omega) 2D parametric space. The robustness of the generated breathers is tested inserting into the model a thermal noise source to mimic the environmental influence. The last part of this work deals with the characteristics of a Josephson junctions designed suspending over a graphene layer two superconducting electrodes. The resistively and capacitively shunted junction model is used to analyze the dynamics of this system, including the Josephson current affected by the graphene. The mean escape times under the influence of a colored noise source are calculated varying the noise intensity and driving frequency, and setting different values of the mean bias current. Noise enhanced stability characterizes the mean escape times as a function of the noise intensity. Dynamic and stochastic resonant activation effects can be clearly distinguished in different noise amplitude ranges. A complete probability density function analysis shades light on the features and the details of all these noise induced effects. The experimental implications of this work are finally discussed, togheter with its possible future developments.The study of nonlinear dynamics in long Josephson junctions and the features of a particular kind of junction realized using a graphene layer, are the main topics of this research work. The superconducting state of a Josephson junction is a metastable state, and the switching to the resistive state is directly related to characteristic macroscopic quantities, such as the current the voltage across the junction, and the magnetic field through it. Noise sources can affect the mean lifetime of this superconducting metastable state, so that noise induced effects on the transient dynamics of these systems should be taken into account. The long Josephson junctions are investigated in the sine-Gordon framework, stressing the relations beetwen nonlinear excitations travelling into the medium and switching dynamics towards the resistive state. Nonlinear travelling wave solutions of the sine-Gordon equation are solitons and antisolitons (and their combinations), breathers and plasma waves. The effect of a non-Gaussian noise source is considered, by changing peculiar system parameters, such as the junction length or the frequency and the amplitude of an applied oscillating bias current, and features of the noise sources, such as the amplitude and the statistic of the stochastic signal. Fortran codes are implemented to integrate the nonlinear stochastic differential equations for the order parameter of these systems. Typical noise induced effects, such as the noise enhanced stability and the resonant activation, are evident exploring the mean switching time from the superconducting regime, as a function of the noise amplitude and driving frequency, respectively. Attention is given to the soliton evolution in connection with the escape dynamics from the superconducting metastable state. Moreover, noise induced breathers are detected. Breathers are special solutions of the sine-Gordon equation, composed by a coupled soliton-antisoliton pair, oscillating in an internal frame with a proper frequency. These solutions are highly unstable, and their detection in long Josephon junctions is an open challenge. The possibility to generate only breathers into a junction properly excited is the main focus of the second part of this work. The phenomenon of nonlinear supratransmission in long Josephson junction stimulated by an external signal is analyzed. In correspondence of precise combinations of values of amplitude A and frequency omega of the external sinusoidal pulse, the generation of only breathers emerges. Variations of the pulse durations, both of the applied bias current and of the damping parameter affect the localizations of breathers on a (A,omega) 2D parametric space. The robustness of the generated breathers is tested inserting into the model a thermal noise source to mimic the environmental influence. The last part of this work deals with the characteristics of a Josephson junctions designed suspending over a graphene layer two superconducting electrodes. The resistively and capacitively shunted junction model is used to analyze the dynamics of this system, including the Josephson current affected by the graphene. The mean escape times under the influence of a colored noise source are calculated varying the noise intensity and driving frequency, and setting different values of the mean bias current. Noise enhanced stability characterizes the mean escape times as a function of the noise intensity. Dynamic and stochastic resonant activation effects can be clearly distinguished in different noise amplitude ranges. A complete probability density function analysis shades light on the features and the details of all these noise induced effects. The experimental implications of this work are finally discussed, togheter with its possible future developments

Bipolar thermoelectrical SQUIPT (BTSQUIPT)

We theoretically study the quasiparticle current behaviour of a thermally-biased bipolar thermoelectrical superconducting quantum interference proximity transistor, formed by a normal metal wire embedded in a superconducting ring and tunnel-coupled to a superconducting probe. In this configuration, the superconducting gap of the wire can be modified through an applied magnetic flux. We analyse the thermoelectric response as a function of magnetic flux, at fixed temperatures, in the case of a device made of the same superconductor. We demonstrate magnetically controllable, bipolar thermoelectric behaviour and discuss optimal working conditions by looking at the thermoelectric power and other figures of merit of the device.Comment: 6 pages, 4 figure

Hallmarks of non-trivial topology in Josephson junctions based on oxide nanochannels

We investigate the topological properties of a Josephson junction obtained by constraining a two-dimensional electron gas at oxide interface to form a quasi-1D conductor. We reveal an anomalous critical current behaviour with a magnetic field applied perpendicular to the Rashba spin-orbit one. We relate the observed critical current enhancement at small magnetic fields with a non-trivial topology, accompanied by Majorana bound states (MBSs) pinned at the edges of the superconducting leads. Signatures of MBSs also include a sawtooth profile in the current-phase relation. Our findings allow to recognize fingerprints of topological superconductivity in non-centrosymmetric materials and confined systems with Rashba spin-orbit interaction, and to explain recent experimental observations for which a microscopic description is still lacking.Comment: 10 pages, 8 figures, pape

Colossal orbital-Edelstein effect in non-centrosymmetric superconductors

In superconductors that lack inversion symmetry, the flow of supercurrent can induce a non-vanishing magnetization, a phenomenon which is at the heart of non-dissipative magneto-electric effects, also known as Edelstein effects. For electrons carrying spin and orbital moments a question of fundamental relevance deals with the orbital nature of magneto-electric effects in conventional spin-singlet superconductors with Rashba coupling. Remarkably, we find that the supercurrent-induced orbital magnetization is more than one order of magnitude greater than that due to the spin, giving rise to a colossal magneto-electric effect. The induced orbital magnetization is shown to be sign tunable, with the sign change occurring for the Fermi level lying in proximity of avoiding crossing points in the Brillouin zone and in the presence of superconducting phase inhomogeneities, yielding domains with opposite orbital moment orientation. The orbital-dominated magneto-electric phenomena, hence, have clear-cut marks for detection both in the bulk and at the edge of the system and are expected to be a general feature of multi-orbital superconductors without inversion symmetry breaking.Comment: 7 pages, 5 figure

Heat-transfer fingerprint of Josephson breathers

A sine-Gordon breather enhances the heat transfer in a thermally biased long Josephson junction. This solitonic channel allows for the tailoring of the local temperature throughout the system. Furthermore, the phenomenon implies a clear thermal fingerprint for the breather, and thus a 'non-destructive' breather detection strategy is proposed here. Distinct breathing frequencies result in morphologically different local temperature peaks, which can be identified in an experiment.Comment: 8 pages, 5 figure

Comment on "Non-reciprocal topological solitons in active metamaterials"

In the recent work "Non-reciprocal topological solitons in active metamaterials" (see arXiv:2312.03544v1), for an analytical understanding of the system under consideration, the authors derive an ordinary differential equation for the sine-Gordon (anti)soliton velocity, with the perturbation theory in the adiabatic approximation, via the inverse scattering transform formalism, see Eq. (3) in their work. Here we note that the latter equation for the (anti)soliton velocity also follows from an energy balance approach.Comment: 1 page; comment on arXiv:2312.0354

Noise-induced, ac-stabilized sine-Gordon breathers: Emergence and statistics

Noisy and ac forcing can cooperatively lead to the emergence of sine-Gordon breathers robust to dissipation. This phenomenon is studied, for both Neumann and periodic boundary conditions (NBC and PBC, respectively), at different values of the main system parameters, such as the noise intensity and the ac frequency-amplitude pair. In all the considered cases, nonmonotonicities of the probability of generating only breathers versus the noise strength are observed, implying that optimal noise ranges for the breather formation process exist. Within the latter scenarios, the statistics of the breathers' number, position, and amplitude are analyzed. The number of breathers is found to grow, on average, with the noise amplitude. The breathers' spatial distribution is sharply peaked at the system's edges for NBC, whereas it is essentially uniform for PBC. The average breather amplitude is dictated by the ac frequency-amplitude pair. Finally, a size analysis shows that the minimum system length for the generation mechanism is given by the typical breather half-width (width) in NBC (PBC).Comment: 18 pages, 7 figure