Influence of topological excitations on Shapiro steps and microwave dynamical conductance in bilayer exciton condensates

The quantum Hall state at total filling factor $\nu_T=1$ in bilayer systems realizes an exciton condensate and exhibits a zero-bias tunneling anomaly, similar to the Josephson effect in the presence of fluctuations. In contrast to conventional Josephson junctions, no Fraunhofer diffraction pattern has been observed, due to disorder induced topological defects, so-called merons. We consider interlayer tunneling in the presence of microwave radiation, and find Shapiro steps in the tunneling current-voltage characteristic despite the presence of merons. Moreover, the Josephson oscillations can also be observed as resonant features in the microwave dynamical conductance

Thermal fluctuations in moderately damped Josephson junctions: Multiple escape and retrapping, switching- and return-current distributions and hysteresis

A crossover at a temperature T* in the temperature dependence of the width s of the distribution of switching currents of moderately damped Josephson junctions has been reported in a number of recent publications, with positive ds/dT and IV characteristics associated with underdamped behaviour for lower temperatures T<T*, and negative ds/dT and IV characteristics resembling overdamped behaviour for higher temperatures T>T*. We have investigated in detail the behaviour of Josephson junctions around the temperature T* by using Monte Carlo simulations including retrapping from the running state into the supercurrent state as given by the model of Ben-Jacob et al. We develop discussion of the important role of multiple escape and retrapping events in the moderate-damping regime, in particular considering the behaviour in the region close to T*. We show that the behaviour is more fully understood by considering two crossover temperatures, and that the shape of the distribution and s(T) around T*, as well as at lower T<T*, are largely determined by the shape of the conventional thermally activated switching distribution. We show that the characteristic temperatures T* are not unique for a particular Josephson junction, but have some dependence on the ramp rate of the applied bias current. We also consider hysteresis in moderately damped Josephson junctions and discuss the less commonly measured distribution of return currents for a decreasing current ramp. We find that some hysteresis should be expected to persist above T* and we highlight the importance, even well below T*, of accounting properly for thermal fluctuations when determining the damping parameter Q.Comment: Accepted for publication in PR

Phase diffusion in graphene-based Josephson junctions

We report on graphene-based Josephson junctions with contacts made from lead. The high transition temperature of this superconductor allows us to observe the supercurrent branch at temperatures up to $\sim 2$ K, at which point we can detect a small, but non-zero, resistance. We attribute this resistance to the phase diffusion mechanism, which has not been yet identified in graphene. By measuring the resistance as a function of temperature and gate voltage, we can further characterize the nature of electromagnetic environment and dissipation in our samples.Comment: 4 pages, 3 figures, PR

Local superfluid densities probed via current-induced superconducting phase gradients

We have developed a superconducting phase gradiometer consisting of two parallel DNA-templated nanowires connecting two thin-film leads. We have ramped the cross current flowing perpendicular to the nanowires, and observed oscillations in the lead-to-lead resistance due to cross-current-induced phase differences. By using this gradiometer we have measured the temperature and magnetic field dependence of the superfluid density and observed an amplification of phase gradients caused by elastic vortex displacements. We examine our data in light of Miller-Bardeen theory of dirty superconductors and a microscale version of Campbell's model of field penetration.Comment: 5 pages, 6 figure

Current and universal scaling in anomalous transport

Anomalous transport in tilted periodic potentials is investigated within the framework of the fractional Fokker-Planck dynamics and the underlying continuous time random walk. The analytical solution for the stationary, anomalous current is obtained in closed form. We derive a universal scaling law for anomalous diffusion occurring in tilted periodic potentials. This scaling relation is corroborated with precise numerical studies covering wide parameter regimes and different shapes for the periodic potential, being either symmetric or ratchet-like ones

Probing the superconducting condensate on a nanometer scale

Superconductivity is a rare example of a quantum system in which the wavefunction has a macroscopic quantum effect, due to the unique condensate of electron pairs. The amplitude of the wavefunction is directly related to the pair density, but both amplitude and phase enter the Josephson current : the coherent tunneling of pairs between superconductors. Very sensitive devices exploit the superconducting state, however properties of the {\it condensate} on the {\it local scale} are largely unknown, for instance, in unconventional high-T$_c$ cuprate, multiple gap, and gapless superconductors. The technique of choice would be Josephson STS, based on Scanning Tunneling Spectroscopy (STS), where the condensate is {\it directly} probed by measuring the local Josephson current (JC) between a superconducting tip and sample. However, Josephson STS is an experimental challenge since it requires stable superconducting tips, and tunneling conditions close to atomic contact. We demonstrate how these difficulties can be overcome and present the first spatial mapping of the JC on the nanometer scale. The case of an MgB$_2$ film, subject to a normal magnetic field, is considered.Comment: 7 pages, 6 figure

Evidence of Josephson-coupled superconducting regions at the interfaces of Highly Oriented Pyrolytic Graphite

Transport properties of a few hundreds of nanometers thick (in the graphene plane direction) lamellae of highly oriented pyrolytic graphite (HOPG) have been investigated. Current-Voltage characteristics as well as the temperature dependence of the voltage at different fixed input currents provide evidence for Josephson-coupled superconducting regions embedded in the internal two-dimensional interfaces, reaching zero resistance at low enough temperatures. The overall behavior indicates the existence of superconducting regions with critical temperatures above 100 K at the internal interfaces of oriented pyrolytic graphite.Comment: 6 Figures, 5 page

Phase-charge duality in Josephson junction circuits: Role of inertia and effect of microwave irradiation

We investigate the physics of coherent quantum phase slips in two distinct circuits containing small Josephson junctions: (i) a single junction embedded in an inductive environment and (ii) a long chain of junctions. Starting from the standard Josephson Hamiltonian, the single junction circuit can be analyzed using quasi-classical methods; we formulate the conditions under which the resulting quasi-charge dynamics is exactly dual to the usual phase dynamics associated with Josephson tunneling. For the chain we use the fact that its collective behavior can be characterized by one variable: the number $m$ of quantum phase slips present on it. We conclude that the dynamics of the conjugate quasi-charge is again exactly dual to the standard phase dynamics of a single Josephson junction. In both cases we elucidate the role of the inductance, essential to obtain exact duality. These conclusions have profound consequences for the behavior of single junctions and chains under microwave irradiation. Since both systems are governed by a model exactly dual to the standard resistively and capacitively shunted junction model, we expect the appearance of current-Shapiro steps. We numerically calculate the corresponding current-voltage characteristics in a wide range of parameters. Our results are of interest in view of a metrological current standard

Mechanism for flux guidance by micrometric antidot arrays in superconducting films

A study of magnetic flux penetration in a superconducting film patterned with arrays of micron sized antidots (microholes) is reported. Magneto-optical imaging (MOI) of a YBCO film shaped as a long strip with perpendicular antidot arrays revealed both strong guidance of flux, and at the same time large perturbations of the overall flux penetration and flow of current. These results are compared with a numerical flux creep simulation of a thin superconductor with the same antidot pattern. To perform calculations on such a complex geometry, an efficient numerical scheme for handling the boundary conditions of the antidots and the nonlocal electrodynamics was developed. The simulations reproduce essentially all features of the MOI results. In addition, the numerical results give insight into all other key quantities, e.g., the electrical field, which becomes extremely large in the narrow channels connecting the antidots.Comment: 8 pages, 7 figure

Detection of Complex Networks Modularity by Dynamical Clustering

Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort ${\cal O}(KN)$ on a generic graph with $N$ nodes and $K$ links.Comment: 5 pages, 2 figures. Version accepted for publication on PRE Rapid Communications: figures changed and text adde