Current-driven dynamics in Josephson junction networks with an asymmetric potential

We report a systematic study of barrier-crossing dynamics of self-propelled particles (SPPs) across a periodic ratchet potential U0(x), which is fabricated on a ratchet-microgroove-patterned polydimethylsiloxane substrate. From the measured steady-state probability density function P(x;F0) of the SPPs with different self-propulsion forces F0, we find that the escape dynamics of slow-rotating SPPs over the asymmetric ratchet potential can be well described by an activity-dependent potential, U±(x;F0) ≃ U0(x) ∓ aF0x, for the forward (+) and backward (-) moving particles with aF0 being the amplitude of their self-propulsion force projected along the x axis. By a thorough analysis of a large volume of the SPP trajectories obtained from both the spatially symmetric and asymmetric potentials, we delineate two experimental conditions under which the ratchet effect of SPPs is realized without involving a time-dependent rectification, and directed particle transport with a steady flux is observed. This work thus provides an effective statistical approach to describe the non-equilibrium transport of SPPs across ratchet potentials.

The nonlinear current-voltage characteristics of a three-dimensional tunnel junction with weak (low impurity concentration) structural disorder are obtained for temperature T=0, and a formula is derived for the magnitude of the mesoscopic fluctuations in its resonant static tunnel conductance.

The contribution of inelastic subbarrier impurity scattering of tunneling electrons to the nonresonant transmission of a quasi-one-dimensional tunneling junction with weak (low impurity concentrations) structural disorder at temperature T=0 is determined. It is shown that this contribution leads to an increase in the tunneling transmission and conditions are determined for which this increase may be appreciable.

Ratchet effect in an underdamped periodic potential and its characterisation

We study the ratchet effect of a damped relativistic particle driven by both asymmetric temporal bi-harmonic and time-periodic piecewise constant forces. This system can be formally solved for any external force, providing the ratchet velocity as a nonlinear functional of the driving force. This allows us to explicitly illustrate the functional Taylor expansion formalism recently proposed for this kind of systems. The Taylor expansion reveals particularly useful to obtain the shape of the current when the force is periodic, piecewise constant. We also illustrate the somewhat counterintuitive effect that introducing damping may induce a ratchet effect. When the force is symmetric under time-reversal and the system is undamped, under symmetry principles no ratchet effect is possible. In this situation increasing damping generates a ratchet current which, upon increasing the damping coefficient eventually reaches a maximum and decreases toward zero. We argue that this effect is not specific of this example and should appear in any ratchet system with tunable damping driven by a time-reversible external force.

The Mott insulating state formed from bosons is ubiquitous in solid He-4, cold atom systems, Josephson junction networks and perhaps underdoped high-Tc superconductors. We predict that close to the quantum phase transition to the superconducting state the Mott insulator is not at all as featureless as is commonly believed. In three dimensions there is a phase transition to a low temperature state where, under influence of an external current, a superconducting state consisting of a regular array of 'wires' that each carry a quantized flux of supercurrent is realized. This prediction of the "type-II Mott insulator" follows from a field theoretical weak-strong duality, showing that this 'current lattice' is the dual of the famous Abrikosov lattice of magnetic fluxes in normal superconductors. We argue that this can be exploited to investigate experimentally whether preformed Cooper pairs exist in high-Tc superconductors.

We show that —in the quantum regime— a Josephson junction rhombi chain (i.e. a Josephson junction chain made by rhombi formed by joining 4 Josephson junctions) may be effectively mapped onto a quantum Hamiltonian describing Ising spins in a transverse magnetic field with open boundary conditions. Then, we elucidate how a Y-shaped network fabricated with 3 Josephson junction rhombi chains may be used as a quantum device realizing the two-channel Kondo model recently proposed by Tsvelik in Phys. Rev. Lett., 110 (2013) 147202. We point out that the emergence of a 2-channel Kondo effect in this superconducting network may be probed through the measurement of a pertinent Josephson current.

We study the evolution of cosmological domain walls in models with asymmetric potentials. Our research goes beyond the standard case of spontaneous breaking of an approximate symmetry. When the symmetry is explicitly broken the potential exhibits nearly degenerate minima which can lead to creation of a metastable network of domain walls. The time after which the network will decay depends on the difference of values of the potential in minima, its asymmetry around the maximum separating minima and the bias of the initial distribution of the field. Effect of asymmetry around the maximum separating minima is novel one that we study with a new type of potential. Using numerical lattice simulations we determine relative importance of these factors on decay time of networks for generic potentials. We find that even very small departures from the symmetric initial distribution case lead to rapid decay of the domain wall network. As a result creation of a long lasting network capable of producing observable gravitational wave signals is much more difficult than previously thought. On the other hand details of the shape of the potential turn out to be much less important than was expected and the evolution of network from symmetric distribution is controlled by the difference of values of the potential in the minima.

A technique to induce spatial modulation of critical current density in niobium based Josephson devices by using a selective thermal annealing is reported. By depositing a carbon film onto selected region of the Josephson element it is possible to induce a localized heating, with a spatial resolution less than 1 μm, exploiting the much higher absorbance coefficient of carbon than the niobium one. The effectiveness of such technique is demonstrated by experimental measurement of the critical current vs. magnetic field, measured at T = 4.2 K, showing that the change of critical current density occurs only in the region corresponding to the absorber film area. Furthermore, the theoretical behaviour, by modelling a suitable step-like junction barrier shape, has been carried out to fit the experimental data in order to verify the selective modulation of critical current. This technique can be very useful in view of quantum computing experiments, Majorana fermions detection and superconducting magnetic sensors.

Triangular arrays of Ni nanotriangles embedded in superconducting Nb films exhibit unexpected dynamical vortex effects. Collective pinning with a vortex lattice configuration different from the expected fundamental triangular "Abrikosov state" is found. The vortex motion which prevails against the triangular periodic potential is produced by channelling effects between triangles. Interstitial vortices coexisting with pinned vortices in this asymmetric potential, lead to ratchet reversal, i.e. a DC output voltage which changes sign with the amplitude of an applied alternating drive current. In this landscape, ratchet reversal is always observed at all magnetic fields (all numbers of vortices) and at different temperatures. The ratchet reversal is unambiguously connected to the presence of two locations for the vortices: interstitial and above the artificial pinning sites.

The motion of magnetic flux quanta in superconductors leads to dissipation, making its control crucial for fluxonic devices. Recently, interest has grown in the ratchet (diode) effect, which enables non-reciprocal, dissipationless currents and superconducting rectifiers, with potential applications in energy-efficient computing, memory, and switching systems. However, most approaches to superconducting ratchet systems involve patterning thin films across their entire area, and few studies have examined symmetry breaking from disparities in thin-film edge barriers. Here, non-reciprocal current flow and vortex dynamics are demonstrated in a superconducting NbC strip with periodic edge indentations, which induce current crowding and edge barrier suppression, facilitating vortex entry. Upon reversing the current polarity at a magnetic field of 16mT, a maximum ratchet efficiency of ≈35% is observed based on critical current differences, and ≈60% based on maximal voltage differences preceding the flux-flow instability. Numerical simulations using the time-dependent Ginzburg-Landau equationsupport the findings and reveal the formation of "flux pockets"-regions where vortices become trapped between indentations-as well as diverse vortex configurations, including chains, jets, andrivers.

Transport of the Brownian particles driven by Lévy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination techniques, we obtain the group velocity which can measure the transport. It is found that the group velocity increases monotonically with the subdiffusive index and there exists an optimal value of the Lévy index at which the group velocity takes its maximal value. There is a threshold value of the subdiffusive index below which the ratchet effects will disappear. The nonthermal character of the Lévy flights and the asymmetry of the potential are necessary to obtain the directed transport. Some peculiar phenomena induced by the competition between Lévy flights and subdiffusion are also observed. The pseudonormal diffusion will appear on the level of the median.

Static bifurcation and vibrational resonance in a fractional-order delay Duffing system with asymmetric potential are studied. By utilizing the fast and slow variable separation approach, the static bifurcation is discussed based on the equivalent system. It is found when fractional order and time delay change, the static bifurcation of fractional-order system with asymmetric potential is different from that of system with symmetric potential. In addition, changes in asymmetric parameter can also induce saddle-node bifurcation. Furthermore, according to the approximate analytical expression of response amplitude, the effects of high frequency amplitude, fractional order and asymmetric parameter on vibrational resonance are investigated. The results show that the number of resonance peaks of asymmetric potential system is related to the selection of initial value and the change of asymmetric parameter can also induce vibrational resonance. In the meantime, the good agreement between theoretical prediction and numerical simulation confirms the validity of theoretical analysis.

With both theoretical approximation and numerical simulations, we study steady current of a Brownian particle moving in an asymmetric periodic potential driven by cross-correlation between multiplicative and additive noises. The effects of the asymmetric parameter of the potential, the multiplicative noise intensity, the additive noise intensity and the correlated strength between multiplicative and additive noises are discussed. We find current reversal with respect to a variation of the asymmetric parameter or the correlated strength. It is also shown that the direction of the steady current is controlled by multiplicative or additive noise intensity, but they are not sufficient conditions for current reversal.

Supercurrent rectification, nonreciprocal response of superconducting properties sensitive to the polarity of bias and magnetic field, has attracted growing interest as an ideal diode. While the superconducting rectification effect is a consequence of the asymmetric vortex pinning, the mechanisms to develop its asymmetric potentials have been a subject of ongoing debate, mainly focusing on microscopic breaking of spatial inversion symmetry and macroscopic imbalance of the sample structure. Here, we report on comparative study of the superconducting diode effect and nonreciprocal resistance in a superconducting Fe(Se,Te)/FeTe heterostructure. In normal state, we observe finite nonreciprocal resistance as a hallmark of the spin-orbit interaction with structural inversion asymmetry. In the superconducting state, we find that the strongly enhanced nonreciprocal coefficient in transition regime is directly coupled to the superconducting diode efficiency through a universal scaling law, indicating the role of spin-momentum-locked state on the asymmetric pinning potential. Our findings, providing a unified picture of the superconducting rectification, pave the way for functionalizing superconducting diode devices.