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.

The photon count rate (PCR) of superconducting single-photon detectors made of ${\mathrm{Mo}}_x{\mathrm{Si}}_{1\text{−}x}$ films shaped as a 2-$\mu \mathrm{m}$-wide strip and a 115-nm-wide meander strip line is studied experimentally as a function of the dc biasing current at different values of the perpendicular magnetic field. For the wide strip, a crossover current $I_{\mathrm{cross}}$ is observed, below which the PCR increases with an increasing magnetic field and above which it decreases. This behavior contrasts with the narrow ${\mathrm{Mo}}_x{\mathrm{Si}}_{1\text{−}x}$ meander, for which no crossover current is observed, thus suggesting different photon-detection mechanisms in the wide and narrow strips. Namely, we argue that in the wide strip the absorbed photon destroys superconductivity locally via the vortex-antivortex mechanism for the emergence of resistance, while in the narrow meander superconductivity is destroyed across the whole strip line, forming a hot belt. Accordingly, the different photon-detection mechanisms associated with vortices and the hot belt determine the qualitative difference in the dependence of the PCR on the magnetic field.

The structure and energy of saddle point (SP) states in a two-dimensional (2D) superconducting film of finite width w with transport current I are found in the framework of the Ginzburg-Landau model. We show that very near the depairing current Idep, a SP state with a vortex does not exist; it transforms to a 2D nucleus state, which is a finite region with partially suppressed order parameter. It is also shown that for slightly lower currents the contribution of the vortex core energy is important for a SP state with a vortex and it cannot be neglected for I$\gtrsim${}0.6Idep. It is demonstrated that in a film with local current concentration near a bend, the energy of the SP state may be much smaller than that in the straight film, and this favors the effect of fluctuations in such samples.

In the framework of the Ginzburg-Landau model, it is shown that narrow superconducting films with width $w\simeq 3–8\xi \left(T\right)$ [$\xi \left(T\right)$ is a temperature-dependent coherence length] exhibit unusual transport properties. In the absence of bulk pinning, its critical current $I_c$ nonmonotonically depends on perpendicular magnetic field $H$ and has one minima (dip) and one maxima (peak) at some magnetic fields. At currents $I\ll I_c\left(H\right)$, the finite magnetoresistance $R\left(H\right)$ of such a sample due to thermoactivated vortex hopping via edge barriers also shows both local maxima (peak) and minima (dip) nearly at the same magnetic fields. In narrower films, such an effect is absent due to absence of the vortices and in wider films the effect is weaker due to increased vortex-vortex interaction. The finite length of the film produces additional periodic variation in both $I_c\left(H\right)$ and $R\left(H\right)$ because of discrete changes in the number of the vortices, which is superimposed on the above-mentioned nonmonotonic dependence. The obtained results are directly related to many experiments on narrow superconducting films/bridges where such nonmonotonic dependencies $I_c\left(H\right)$ and $R\left(H\right)$ were observed. DOI: http://dx.doi.org/10.1103/PhysRevB.88.014525 ©2013 American Physical Society

Ultrafast vortex motion has recently become a subject of extensive investigations, triggered by the fundamental question regarding the ultimate speed limits for magnetic flux quanta and enhancements of single-photon detectors. In this regard, the current-biased quench of a dynamic flux-flow regime—flux-flow instability (FFI)—has turned into a widely used method for the extraction of information about the relaxation of quasiparticles (unpaired electrons) in a superconductor. However, the large relaxation times ${\tau }_{ϵ}$ deduced from FFI for many superconductors are often inconsistent with the fast relaxation processes implied by their single-photon counting capability. Here, we investigate FFI in $15$-nm-thick $182$-$\mu \mathrm{m}$-wide MoSi strips with rough and smooth edges produced by laser etching and milling by a focused ion beam. For the strip with smooth edges we deduce, from current-voltage ($I$-$V$) curve measurements, a factor of 3 larger critical currents $I_c$, a factor of 20 higher maximal vortex velocities of 20 km/s, and a factor of 20 shorter ${\tau }_{ϵ}$. We argue that for the deduction of the intrinsic ${\tau }_{ϵ}$ of the material from the $I$-$V$ curves, utmost care should be taken regarding the edge and sample quality and such a deduction is justified only if the field dependence of $I_c$ points to the dominating edge pinning of vortices.

At sufficiently large transport currents $I_{\mathrm{tr}}$, a defect at the edge of a superconducting strip acts as a gate for the vortices entering into it. These vortices form a jet, which is narrow near the defect and expands due to the repulsion of vortices as they move to the opposite edge of the strip, giving rise to a transverse voltage $V_{\perp }$. Here, relying upon the equation of vortex motion under competing vortex-vortex and $I_{\mathrm{tr}}$-vortex interactions, we derive the vortex jet shapes in narrow ($\xi \ll w\lesssim {\lambda }_{\mathrm{eff}}$) and wide ($w\gg {\lambda }_{\mathrm{eff}}$) strips [$\xi$: coherence length, $w$: strip width, ${\lambda }_{\mathrm{eff}}$: effective penetration depth]. We predict a nonmonotonic dependence $V_{\perp }\left(I_{\mathrm{tr}}\right)$ which can be measured with Hall voltage leads placed on the line $V_1{V}_2$ at a small distance $l$ apart from the edge defect and which changes its sign upon $l\to -l$ reversal. For narrow strips, we compare the theoretical predictions with experiment, by fitting the $V_{\perp }(I_{\mathrm{tr}},l)$ data for $1\text{−}\mu \mathrm{m}$-wide MoSi strips with single edge defects milled by a focused ion beam at distances $l=16\text{–}80$ nm from the line $V_1{V}_2$. For wide strips, the derived magnetic field dependence of the vortex jet shape is in line with the recent experimental observations for vortices moving in Pb bridges with a narrowing. Our findings are augmented with the time-dependent Ginzburg-Landau simulations which reproduce the calculated vortex jet shapes and the $V_{\perp }(I_{\mathrm{tr}},l)$ maxima. Furthermore, with increase of $I_{\mathrm{tr}}$, the numerical modeling unveils the evolution of vortex jets to vortex rivers, complementing the analytical theory in the entire range of $I_{\mathrm{tr}}$.