Nonlinear Viscous Vortex Motion in Two-Dimensional Josephson-Junction Arrays

When a vortex in a two-dimensional Josephson junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a {\bf nonlinear} viscous force of the form $F_D=\eta(\dot y)\dot y={{A}\over {1+B\dot y}}\dot y$, where $\dot y$ is the vortex velocity, $\eta(\dot y)$ is the velocity dependent viscosity and $A$ and $B$ are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies.Comment: 14 pages RevTex, 9 Postscript figure

Vortex reflection at boundaries of Josephson-junction arrays

We study the propagation properties of a single vortex in square Josephson-junction arrays (JJA) with free boundaries and subject to an applied dc current. We model the dynamics of the JJA by the resistively and capacitively shunted junction (RCSJ) equations. For zero Stewart-McCumber parameter $\beta_c$ we find that the vortex always escapes from the array when it gets to the boundary. For $\beta_c\geq 2.5$ and for low currents we find that the vortex escapes, while for larger currents the vortex is reflected as an antivortex at one edge and the antivortex as a vortex at the other, leading to a stationary oscillatory state and to a non-zero time-averaged voltage. The escape and the reflection of a vortex at the array edges are qualitatively explained in terms of a coarse-grained model of a vortex interacting logarithmically with its image. We also discuss the case when the free boundaries are at $45$ degrees with respect to the direction of the vortex motion. Finally, we discuss the effect of self-induced magnetic fields by taking into account the full-range inductance matrix of the array, and find qualitatively equivalent results.Comment: 14 pages RevTex, 9 Postscript figure

Single-vortex-induced voltage steps in Josephson-junction arrays

We have numerically and analytically studied ac+dc driven Josephson-junction arrays with a single vortex or with a single vortex-antivortex pair present. We find single-vortex steps in the voltage versus current characteristics (I-V) of the array. They correspond microscopically to a single vortex phase-locked to move a fixed number of plaquettes per period of the ac driving current. In underdamped arrays we find vortex motion period doubling on the steps. We observe subharmonic steps in both underdamped and overdamped arrays. We successfully compare these results with a phenomenological model of vortex motion with a nonlinear viscosity. The I-V of an array with a vortex-antivortex pair displays fractional voltage steps. A possible connection of these results to present day experiments is also discussed.Comment: 10 pages double sided with figures included in the text. To appear in Journal of Physics, Condensed Matte

Discreteness-induced resonances and AC voltage amplitudes in long one-dimensional Josephson junction arrays

New resonance steps are found in the experimental current-voltage characteristics of long, discrete, one-dimensional Josephson junction arrays with open boundaries and in an external magnetic field. The junctions are underdamped, connected in parallel, and DC biased. Numerical simulations based on the discrete sine-Gordon model are carried out, and show that the solutions on the steps are periodic trains of fluxons, phase-locked by a finite amplitude radiation. Power spectra of the voltages consist of a small number of harmonic peaks, which may be exploited for possible oscillator applications. The steps form a family that can be numbered by the harmonic content of the radiation, the first member corresponding to the Eck step. Discreteness of the arrays is shown to be essential for appearance of the higher order steps. We use a multi-mode extension of the harmonic balance analysis, and estimate the resonance frequencies, the AC voltage amplitudes, and the theoretical limit on the output power on the first two steps.Comment: REVTeX, 17 pages, 7 figures, psfig; to appear in J. Applied Physic

Phase-transitions in spin-crossover thin films probed by graphene transport measurements

Future multi-functional hybrid devices might combine switchable molecules and 2D material-based devices. Spin-crossover compounds are of particular interest in this context since they exhibit bistability and memory effects at room temperature while responding to numerous external stimuli. Atomically-thin 2D materials such as graphene attract a lot of attention for their fascinating electrical, optical, and mechanical properties, but also for their reliability for room-temperature operations. Here, we demonstrate that thermally-induced spin-state switching of spin-crossover nanoparticle thin films can be monitored through the electrical transport properties of graphene lying underneath the films. Model calculations indicate that the charge carrier scattering mechanism in graphene is sensitive to the spin-state dependence of the relative dielectric constants of the spin-crossover nanoparticles. This graphene sensor approach can be applied to a wide class of (molecular) systems with tunable electronic polarizabilities.Comment: main text: 13 pages, 5 figures ; SI: 14 pages, 12 figure

Segmental K-Means Learning with Mixture Distribution for HMM Based Handwriting Recognition

This paper investigates the performance of hidden Markov models (HMMs) for handwriting recognition. The Segmental K-Means algorithm is used for updating the transition and observation probabilities, instead of the Baum-Welch algorithm. Observation probabilities are modelled as multi-variate Gaussian mixture distributions. A deterministic clustering technique is used to estimate the initial parameters of an HMM. Bayesian information criterion (BIC) is used to select the topology of the model. The wavelet transform is used to extract features from a grey-scale image, and avoids binarization of the image.</p

Exchange coupling inversion in a high-spin organic triradical molecule

The magnetic properties of a nanoscale system are inextricably linked to its local environment. In ad-atoms on surfaces and inorganic layered structures the exchange interactions result from the relative lattice positions, layer thicknesses and other environmental parameters. Here, we report on a sample-dependent sign inversion of the magnetic exchange coupling between the three unpaired spins of an organic triradical molecule embedded in a three-terminal device. This ferro-to-antiferromagnetic transition is due to structural distortions and results in a high-to-low spin ground state change in a molecule traditionally considered to be a robust high-spin quartet. Moreover, the flexibility of the molecule yields an in-situ electric tunability of the exchange coupling via the gate electrode. These findings open a route to the controlled reversal of the magnetic states in organic molecule-based nanodevices by mechanical means, electrical gating or chemical tailoring

Superconducting molybdenum-rhenium electrodes for single-molecule transport studies

We demonstrate that electronic transport through single molecules or molecular ensembles, commonly based on gold (Au) electrodes, can be extended to superconducting electrodes by combining gold with molybdenum-rhenium (MoRe). This combination induces proximity-effect superconductivity in the gold to temperatures of at least 4.6 Kelvin and magnetic fields of 6 Tesla, improving on previously reported aluminum based superconducting nanojunctions. As a proof of concept, we show three-terminal superconductive transport measurements through an individual Fe$_4$ single-molecule magnet.Comment: 4 pages, 3 figure

Row-switched states in two-dimensional underdamped Josephson junction arrays

When magnetic flux moves across layered or granular superconductor structures, the passage of vortices can take place along channels which develop finite voltage, while the rest of the material remains in the zero-voltage state. We present analytical studies of an example of such mixed dynamics: the row-switched (RS) states in underdamped two-dimensional Josephson arrays, driven by a uniform DC current under external magnetic field but neglecting self-fields. The governing equations are cast into a compact differential-algebraic system which describes the dynamics of an assembly of Josephson oscillators coupled through the mesh current. We carry out a formal perturbation expansion, and obtain the DC and AC spatial distributions of the junction phases and induced circulating currents. We also estimate the interval of the driving current in which a given RS state is stable. All these analytical predictions compare well with our numerics. We then combine these results to deduce the parameter region (in the damping coefficient versus magnetic field plane) where RS states can exist.Comment: latex, 48 pages, 15 figs using psfi

Superinsulator Phase of Two-Dimensional Superconductors

Using path-integral Quantum Monte Carlo we study the low-temperature phase diagram of a two-dimensional superconductor within a phenomenological model, where vortices have a finite mass and move in a dissipative environment modeled by a Caldeira-Leggett term. The quantum vortex liquid at high magnetic fields exhibits superfluidity and thus corresponds to a {\em superinsulating} phase which is characterized by a nonlinear voltage-current law for an infinite system in the absence of pinning. This superinsulating phase is shifted to higher magnetic fields in the presence of dissipation.Comment: 8 pages, 3 figures, to appear in Phys. Rev. Lett. (Oktober 1998