Current–voltage characteristics of Nb–carbon–Nb junctions

We report on properties of Nb(/Ti)–carbon–(Ti/)Nb junctions fabricated on graphite flakes using e-beam lithography. The devices were characterized at temperatures above 1.8 K where a Josephson current was not observed, but the differential conductivity revealed features below the critical temperature of Nb, and overall metallic conductivity, in spite of a high-junctions resistance. Since the conductivity of graphite along the planes is essentially two-dimensional (2D), we use a theoretical model developed for metal/graphene junctions for interpretation of the results. The model involves two very different graphene “access” lengths. The shorter length characterizes ordinary tunneling between the three-dimensional Nb(/Ti) electrode and 2D graphene, while the second, much longer length, is associated with the Andreev reflections (AR) inside the junction and involves also “reflectionless” AR processes. The relevant transmission factors are small in the first case and much larger in the second, which explains the apparent contradiction of the observed behavior

In-plane fluxon in layered superconductors with arbitrary number of layers

I derive an approximate analytic solution for the in-plane vortex (fluxon) in layered superconductors and stacked Josephson junctions (SJJ's) with arbitrary number of layers. The validity of the solution is verified by numerical simulation. It is shown that in SJJ's with large number of thin layers, phase/current and magnetic field of the fluxon are decoupled from each other. The variation of phase/current is confined within the Josephson penetration depth, $\lambda_J$, along the layers, while magnetic field decays at the effective London penetration depth, $\lambda_c \gg \lambda_J$. For comparison with real high-$T_c$ superconducting samples, large scale numerical simulations with up to 600 SJJ's and with in-plane length up to 4000 $\lambda_J$%, are presented. It is shown, that the most striking feature of the fluxon is a Josephson core, manifesting itself as a sharp peak in magnetic induction at the fluxon center.Comment: 4 pages, 4 figures. Was presented in part at the First Euroconference on Vortex Matter in Superconductors (Crete, September 1999

Josephson effect in double-barrier superconductor-ferromagnet junctions

We study the Josephson effect in ballistic double-barrier SIFIS planar junctions, consisting of bulk superconductors (S), a clean metallic ferromagnet (F), and insulating interfaces (I). We solve the scattering problem based on the Bogoliubov--de Gennes equations and derive a general expression for the dc Josephson current, valid for arbitrary interfacial transparency and Fermi wave vectors mismatch (FWVM). We consider the coherent regime in which quasiparticle transmission resonances contribute significantly to the Andreev process. The Josephson current is calculated for various parameters of the junction, and the influence of both interfacial transparency and FWVM is analyzed. For thin layers of strong ferromagnet and finite interfacial transparency, we find that coherent (geometrical) oscillations of the maximum Josephson current are superimposed on the oscillations related to the crossover between 0 and $\pi$ states. For the same case we find that the temperature-induced $0-\pi$ transition occurs if the junction is very close to the crossovers at zero temperature.Comment: 13 pages, 6 figure

Microscopic self-consistent theory of Josephson junctions including dynamical electron correlations

We formulate a fully self-consistent, microscopic model to study the retardation and correlation effects of the barrier within a Josephson junction. The junction is described by a series of planes, with electronic correlation included through a local self energy for each plane. We calculate current-phase relationships for various junctions, which include non-magnetic impurities in the barrier region, or an interfacial scattering potential. Our results indicate that the linear response of the supercurrent to phase across the barrier region is a good, but not exact indicator of the critical current. Our calculations of the local density of states show the current-carrying Andreev bound states and their energy evolution with the phase difference across the junction. We calculate the figure of merit for a Josephson junction, which is the product of the critical current, Ic, and the normal state resistance, R(N), for junctions with different barrier materials. The normal state resistance is calculated using the Kubo formula, for a system with zero current flow and no superconducting order. Semiclassical calculations would predict that these two quantities are determined by the transmission probabilities of electrons in such a way that the product is constant for a given superconductor at fixed temperature. Our self-consistent solutions for different types of barrier indicate that this is not the case. We suggest some forms of barrier which could increase the Ic.R(N) product, and hence improve the frequency response of a Josephson device.Comment: 46 pages, 21 figure

The Putative Liquid-Liquid Transition is a Liquid-Solid Transition in Atomistic Models of Water

We use numerical simulation to examine the possibility of a reversible liquid-liquid transition in supercooled water and related systems. In particular, for two atomistic models of water, we have computed free energies as functions of multiple order parameters, where one is density and another distinguishes crystal from liquid. For a range of temperatures and pressures, separate free energy basins for liquid and crystal are found, conditions of phase coexistence between these phases are demonstrated, and time scales for equilibration are determined. We find that at no range of temperatures and pressures is there more than a single liquid basin, even at conditions where amorphous behavior is unstable with respect to the crystal. We find a similar result for a related model of silicon. This result excludes the possibility of the proposed liquid-liquid critical point for the models we have studied. Further, we argue that behaviors others have attributed to a liquid-liquid transition in water and related systems are in fact reflections of transitions between liquid and crystal

Verification of digital integrated circuits taking into account pad models

The digital integrated circuit is the main part of different sensors. It performs signal processing, controlling of a system and provides interface with external devices. Timing analysis is a basic verification method of digital integrated circuits. A new technique of digital blocks timing analysis taking into account the models of contact pads is proposed. The results of the I2C interface unit development using the proposed technique are presented