Using kinetic equation approach we study dynamics of electrons and phonons in current-carrying superconducting nanostrips after absorption of single photon of near-infrared or optical range. We find that the larger the ratio Ce/C ph |T c (Tc is a critical temperature of superconductor, Ce and C ph are specific heat capacities of electrons and phonons, respectively) the larger part of photon's energy goes to electrons, they become stronger heated and, hence, could thermalize faster during initial stage of hot spot formation. Thermalization time τ th could be less then one picosecond for superconductors with Ce/C ph |T c ≫ 1 and small diffusion coefficient D ≃ 0.5cm 2 /s when thermalization occurs mainly due to electron-phonon and phonon-electron scattering in relatively small volume ∼ ξ 2 d (ξ is a superconducting coherence length, d < ξ is a thickness of the strip). At larger times because of diffusion of hot electrons effective temperature inside the hot spot decreases, the size of hot spot increases, superconducting state becomes unstable and normal domain spreads in the strip at current larger than so-called detection current. We find dependence of detection current on the photon's energy, place of its absorption in the strip, width of the strip, magnetic field and compare it with existing experiments. Our results demonstrate that materials with Ce/C ph |T c ≪ 1 are bad candidates for single photon detectors due to small transfer of photon's energy to electronic system and large τ th . We also predict that even several microns wide dirty superconducting bridge is able to detect single near-infrared or optical photon if its critical current exceeds 70 % of depairing current and Ce/C ph |T c 1.

We study the dynamics of the order parameter in a superconducting film with transport current after absorption of a single photon. The system from the time-dependent Ginszburg-Landau equation, Poisson's equation for an electrical potential, and the heat-diffusion equation were solved numerically. For each photon energy in the absence of fluctuations there exists a corresponding threshold current below which the superconducting state is stable and no voltage appears between the ends of the film. At larger currents, the superconducting state collapses starting from the appearance of a vortex-antivortex pair in the center of the region with suppressed superconducting order parameter, which has been created by the absorbed photon. Lorentz force causes motion of these vortices that heats the film locally and gives rise to a normal domain. When biased with the fixed current, the film latches in the normal state. In the regime when the current via superconductor may change, which is more relevant for experiments, the normal domain exists only for a short time, resulting in the voltage pulse with the duration controlled by the kinetic inductance of the superconducting film.

Applying a constant voltage to superconducting nanowires we find that its IV-characteristic exhibits an unusual S-behavior. This behavior is the direct consequence of the dynamics of the superconducting condensate and of the existence of two different critical currents: jc2 at which the pure superconducting state becomes unstable and jc1 < jc2 at which the phase slip state is realized in the system. PACS numbers: 74.25. Op, 74.20.De, The majority of the experiments on the resistive state in quasi-one dimensional systems were performed in the constant current regime and at temperatures close to T c . It is extremely difficult to apply voltage to a superconductor because the current density induced by the applied electric field inevitably reaches the critical value and destroys superconductivity in the sample. The decrease of the superconducting current by the appearance of phase slip centers [1,2,3,4,5] is not effective in this case because of the large heating of the sample at low temperatures. At temperatures close to T c the heating can be suppressed due to the low value of the critical currents but in this case the applied electric field does not penetrate deep into the sample because of the existence of regions near the N-S boundary where the drop of the applied voltage occurs [6,7].This situation drastically changes with the appearance of nano-technology and the ability to create long (to allow the appearance of phase slip centers) superconducting wires with a small cross section (to decrease the effect of heating). In this Letter we present results on the behavior of such nanowires in the constant voltage regime. We found that the I-V characterestic in this case has a remarkable S-shape. Our theoretical analysis based on the time-dependent Ginzburg-Landau equations (TDGL) shows that such a behavior is a direct consequence of the dynamics of the superconducting condensate and we predict new unusual features which still need additional experimental study.The superconducting nanowires were prepared by electrodeposition into nanopores of homemade track-etched polycarbonate membranes [8]. For the lead nanowires, a 22 µm thick membrane (with pore diameter ∼ 40 nm and pore density ∼ 4·10 9 cm −2 ) and an aqueous solution of 40.4 g/l Pb(BF 4 ) 2 , 33.6 g/l HBF 4 and 15 g/l H 3 BO 3 were used [9], while in the case of the tin nanowires, a 50 µm thick membrane (with pore diameter ∼ 55 nm and pore density ∼ 2·10 9 cm −2 ) and an electrolyte of 41.8 g/l Sn(BF 4 ) 2 in water solution were applied. Constant potential of -0.5 V versus an Ag/AgCl reference electrode was used in a three-electrode configuration in order to reduce the Pb 2+ or Sn 2+ ions into the nanopores. As shown in Fig. 1, the nanowires are cylindrical and the diameter is uniform along their length. In order to perform elec-

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 vc 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 timedependent Ginzburg-Landau equations and are strictly valid when the coherence length ξ(T ) is larger or comparable with the decay length Lin 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 ≫ Lin ≫ ξ(T ). We speculate that a similar instability of the vortex lattice should exist for v > vc even when a < Lin.

We theoretically study the dependence of the intrinsic detection efficiency (IDE) of superconducting single photon detector on the applied current I and magnetic field H. We find that the current, at which the resistive state appears in the superconducting film, depends on the position of the hot spot (region with suppressed superconductivity around the place where the photon has been absorbed) with respect to the edges of the film. It provides inevitable smooth dependence IDE(I) when IDE ∼ 0.05 − 1 even for homogenous straight superconducting film and in the absence of fluctuations. When IDE 0.05 much sharper current dependence comes from the fluctuation assisted vortex entry to the hot spot located near the edge of the film. We find that weak magnetic field strongly affects IDE when the photon detection is connected with fluctuation assisted vortex entry (IDE≪ 1) and it weakly affects IDE when the photon detection is connected with the current induced vortex entry to the hot spot or nucleation of the vortex-antivortex pair inside the hot spot (IDE∼ 0.05 − 1).

The ultra-fast dynamics of superconducting vortices harbors rich physics generic to nonequilibrium collective systems. The phenomenon of flux-flow instability (FFI), however, prevents its exploration and sets practical limits for the use of vortices in various applications. To suppress the FFI, a superconductor should exhibit a rarely achieved combination of properties: weak volume pinning, close-to-depairing critical current, and fast heat removal from heated electrons. Here, we demonstrate experimentally ultra-fast vortex motion at velocities of 10–15 km s−1 in a directly written Nb-C superconductor with a close-to-perfect edge barrier. The spatial evolution of the FFI is described using the edge-controlled FFI model, implying a chain of FFI nucleation points along the sample edge and their development into self-organized Josephson-like junctions (vortex rivers). In addition, our results offer insights into the applicability of widely used FFI models and suggest Nb-C to be a good candidate material for fast single-photon detectors.

We introduce a type of vortex entry edge barrier which controls the critical current in a perpendicular magnetic field in thin-film weak-pinning superconducting strips. Measurements of the critical current in thinfilm amorphous-MoGe strips show a linear decrease with increasing magnetic field strength at low magnetic fields, and a crossover at a well-defined threshold field to an inverse power-law decay that is independent of the strip width. This behavior has not been observed previously due to bulk pinning, which only becomes dominant in our MoGe samples at high magnetic fields. To describe our results, we present calculations of the current distribution in thin superconducting strips with a finite penetration depth and negligible bulk pinning, and show that the measured critical currents in our MoGe samples correspond to a current density at the strip edge which approaches the Ginzburg-Landau depairing limit. Shape variations and defects along the strip edges influence the vortex entry conditions, leading to deviations from the ideal behavior, including offsets in the critical current maximum with respect to zero field.

Experimental results on the phase slip process in superconducting lead nanowires are presented under two different experimental conditions: constant applied current or constant voltage. Based on these experiments we established a simple model which gives us the condition of the appearance of phase slip centers in a quasione-dimensional wire. The competition between two relaxations times ͑relaxation time of the absolute value of the order parameter ͉͉ and relaxation time of the phase of the order parameter in the phase slip center ) governs the phase slip process. Phase slips, as periodic oscillations in time of the order parameter, are only possible if the gradient of the phase grows faster than the value of the order parameter in the phase slip center, or equivalently if Ͻ ͉͉ .