Wave scattering by discrete breathers

We present a theoretical study of linear wave scattering in one-dimensional nonlinear lattices by intrinsic spatially localized dynamic excitations or discrete breathers. These states appear in various nonlinear systems and present a time-periodic localized scattering potential for plane waves. We consider the case of elastic one-channel scattering, when the frequencies of incoming and transmitted waves coincide, but the breather provides with additional spatially localized ac channels whose presence may lead to various interference patterns. The dependence of the transmission coefficient on the wave number q and the breather frequency Omega_b is studied for different types of breathers: acoustic and optical breathers, and rotobreathers. We identify several typical scattering setups where the internal time dependence of the breather is of crucial importance for the observed transmission properties.Comment: 17 pages, 19 figures, submitted to CHAOS (Focus Issue

Nonequilibrium Josephson-like effects in wide mesoscopic S-N-S junctions

Mesoscopic superconducting-normal-metal-superconducting (S-N-S) junctions with a large separation between the superconducting electrodes (i.e. wide junctions) exhibit nonequilibrium supercurrents, even at temperatures for which the equilibrium Josephson effect is exponentially small. The second harmonic of the Josephson frequency dominates these currents, as observed in recent experiments. A simple description of these effects, in the spirit of the Resistively-Shunted-Junction model, is suggested here. It is used to calculate dc I-V characteristics, and to examine the effects of various types of noise and of external microwave radiation (Shapiro steps). It is found that the nonequilibrium supercurrents are excited when the junction is driven by a dc bias or an ac bias, or even by external noise. In the case of junctions which are also long in the direction perpendicular to the current flow, thermodynamic phase fluctuations (thermal noise) alone can drive the quasiparticles out of local equilibrium. Magnetic flux is then predicted to be trapped in units of Phi_0 /2 = hc/4e.Comment: 10 pages, to appear in a special issue of Superlattices & Microstructure

Rearrangement of the vortex lattice due to instabilities of vortex flow

With increasing applied current we show that the moving vortex lattice changes its structure from a triangular one to a set of parallel vortex rows in a pinning free superconductor. This effect originates from the change of the shape of the vortex core due to non-equilibrium effects (similar to the mechanism of vortex motion instability in the Larkin-Ovchinnikov theory). The moving vortex creates a deficit of quasiparticles in front of its motion and an excess of quasiparticles behind the core of the moving vortex. This results in the appearance of a wake (region with suppressed order parameter) behind the vortex which attracts other vortices resulting in an effective direction-dependent interaction between vortices. When the vortex velocity $v$ reaches the critical value $v_c$ quasi-phase slip lines (lines with fast vortex motion) appear which may coexist with slowly moving vortices between such lines. Our results are found within the framework of the time-dependent Ginzburg-Landau equations and are strictly valid when the coherence length $\xi(T)$ is larger or comparable with the decay length $L_{in}$ of the non-equilibrium quasiparticle distribution function. We qualitatively explain experiments on the instability of vortex flow at low magnetic fields when the distance between vortices $a \gg L_{in} \gg \xi (T)$. We speculate that a similar instability of the vortex lattice should exist for $v>v_c$ even when $a<L_{in}$.Comment: 10 pages, 11 figure

AC Josephson effect in the long voltage-biased SINIS junction

Theory of non-stationary coherent effects is developed for superconductor-normal-superconductor (SNS) structures with relatively strong normal scattering on S/N interfaces (interface resistance is large compared to intrinsic resistance of N metal). Analitical expressions are found for the time-dependent anomalous Green functions induced in the N region under the fixed-voltage-bias. The amplitude of the current oscillations is determined in non-equilibrium conditions. Non-stationary correction to the distribution function is calculated in high-temperature limit and found to be slowly decreasing with the temperature, leading to the dominance of the second-harmonic term in the Josepshon current at high temperatures and low voltage.Comment: Final version accepted for publication in JETP Letters. Introduction and discussion in the end of Sec.4 are extended, figure and few references added, some numerical coefficients correcte

Circuit theory of multiple Andreev reflections in diffusive SNS junctions: the incoherent case

The incoherent regime of Multiple Andreev Reflections (MAR) is studied in long diffusive SNS junctions at applied voltages larger than the Thouless energy. Incoherent MAR is treated as a transport problem in energy space by means of a circuit theory for an equivalent electrical network. The current through NS interfaces is explained in terms of diffusion flows of electrons and holes through tunnel and Andreev resistors. These resistors in diffusive junctions play roles analogous to the normal and Andreev reflection coefficients in OTBK theory for ballistic junctions. The theory is applied to the subharmonic gap structure (SGS); simple analytical results are obtained for the distribution function and current spectral density for the limiting cases of resistive and transparent NS interfaces. In the general case, the exact solution is found in terms of chain-fractions, and the current is calculated numerically. SGS shows qualitatively different behavior for even and odd subharmonic numbers, and the maximum slopes of the differential resistance correspond to the gap subharmonics. The influence of inelastic scattering on the subgap anomalies of the differential resistance is analyzed.Comment: 14 pages, 9 figures, title and text revised, to appear in PR

Microscopic nonequilibrium theory of double-barrier Josephson junctions

We study nonequilibrium charge transport in a double-barrier Josephson junction, including nonstationary phenomena, using the time-dependent quasiclassical Keldysh Green's function formalism. We supplement the kinetic equations by appropriate time-dependent boundary conditions and solve the time-dependent problem in a number of regimes. From the solutions, current-voltage characteristics are derived. It is understood why the quasiparticle current can show excess current as well as deficit current and how the subgap conductance behaves as function of junction parameters. A time-dependent nonequilibrium contribution to the distribution function is found to cause a non-zero averaged supercurrent even in the presence of an applied voltage. Energy relaxation due to inelastic scattering in the interlayer has a prominent role in determining the transport properties of double-barrier junctions. Actual inelastic scattering parameters are derived from experiments. It is shown as an application of the microscopic model, how the nature of the intrinsic shunt in double-barrier junctions can be explained in terms of energy relaxation and the opening of Andreev channels.Comment: Accepted for Phys. Rev.

Nonequilibrium Josephson effect in mesoscopic ballistic multiterminal SNS junctions

We present a detailed study of nonequilibrium Josephson currents and conductance in ballistic multiterminal SNS-devices. Nonequilibrium is created by means of quasiparticle injection from a normal reservoir connected to the normal part of the junction. By applying a voltage at the normal reservoir the Josephson current can be suppressed or the direction of the current can be reversed. For a junction longer than the thermal length, $L\gg\xi_T$, the nonequilibrium current increases linearly with applied voltage, saturating at a value equal to the equilibrium current of a short junction. The conductance exhibits a finite bias anomaly around $eV \sim \hbar v_F/L$. For symmetric injection, the conductance oscillates $2\pi$-periodically with the phase difference $\phi$ between the superconductors, with position of the minimum ($\phi=0$ or $\pi$) dependent on applied voltage and temperature. For asymmetric injection, both the nonequilibrium Josephson current and the conductance becomes $\pi$-periodic in phase difference. Inclusion of barriers at the NS-interfaces gives rise to a resonant behavior of the total Josephson current with respect to junction length with a period $\sim \lambda_F$. Both three and four terminal junctions are studied.Comment: 21 pages, 19 figures, submitted to Phys. Rev.