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The maximal speed $v^\ast$ for magnetic flux quanta is determined by the energy relaxation of unpaired electrons and is thus essential for superconducting microstrip single-photon detectors (SMSPDs). However, the deduction of $v^\ast$ from the current-voltage ($I$-$V$) curves at zero magnetic field is hindered by the unknown number of vortices, $n_\mathrm{v}$, as a small number of fast-moving vortices can induce the same voltage as a large number of slow-moving ones. Here, we introduce an approach for the quantitative determination of $n_\mathrm{v}$ and $v^\ast$. The idea is based on the Aslamazov and Larkin prediction of kinks in the $I$-$V$ curves of wide and short superconducting constrictions when the number of fluxons crossing the constriction is increased by one. We realize such conditions in wide MoSi thin strips with slits milled by a focused ion beam and reveal quantum effects in a macroscopic system. By observing kinks in the $I$-$V$ curves with increase of the transport current, we evidence a crossover from a single- to multi-fluxon dynamics and deduce $v^\ast\simeq12\,$km/s. Our experimental observations are augmented with numerical modeling results which reveal a transition from a vortex chain over a vortex jet to a vortex river with increase of $n_\mathrm{v}$ and the vortex velocity. Our findings are essential for the development of 1D and 2D few-fluxon devices and provide a demanded approach for the deduction of $v^\ast$ at the SMSPD operation conditions., Comment: 10 pages, 4 figures

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 $V_\perp(I_\mathrm{tr})$ which can be measured with Hall voltage leads placed on the line $V_1V_2$ at a small distance $l$ apart from the edge defect and which changes its sign upon $l\rightarrow -l$ reversal. For narrow strips, we compare the theoretical predictions with experiment, by fitting the $V_\perp(I_\mathrm{tr},l)$ data for $1\,\mu$m-wide MoSi strips with single edge defects milled by a focused ion beam at distances $l = 16$-$80$\,nm from the line $V_1V_2$. 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 $I_\mathrm{tr}$., Comment: 12 pages, 6 figures

Ultra-fast 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 the superconductor. However, the large relaxation times $\tau_\epsilon$ 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 $182$ $\mu$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 the current-voltage ($I$-$V$) curve measurements, a factor of 3 larger critical currents $I_\mathrm{c}$, a factor of 20 higher maximal vortex velocities of 20 km/s, and a factor of 40 shorter $\tau_\epsilon$. We argue that for the deduction of the intrinsic $\tau_\epsilon$ 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 $I_\mathrm{c}$ points to the dominating edge pinning of vortices., Comment: 10 pages, 5 figures

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 in a directly written Nb-C superconductor in which a close-to-perfect edge barrier orders the vortex motion at large current values. 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., Comment: 12 pages, 7 pages

The photon count rate of superconducting single photon detectors made of MoSi films shaped as a $2\,\mu$m-wide strip and a 115 nm-wide meander stripline 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 $I_\textrm{cross}$ is observed, below which the photon count rate increases with increasing magnetic field and above which it decreases. This behavior contrasts with the narrow MoSi 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 stripline, forming a hot belt. Accordingly, the different photon detection mechanisms associated with vortices and the hot belt stipulate the qualitative difference in the dependence of the photon count rate on the magnetic field.

Most of superconductors in a magnetic field are penetrated by a lattice of quantized flux vortices. In the presence of a transport current causing the vortices to cross sample edges, emission of electromagnetic waves is expected due to the continuity of tangential components of the fields at the surface. Yet, such a radiation has not been observed so far due to low radiated power levels and lacking coherence in the vortex motion. Here, we report emission of electromagnetic waves from vortices crossing the layers of a superconductor/insulator Mo/Si superlattice. The emission spectra consist of narrow harmonically related peaks which can be finely tuned in the GHz range by the dc bias current and, coarsely, by the in-plane magnetic field value. Our findings show that superconductor/insulator superlattices can act as dc-tunable microwave generators bridging the frequency gap between conventional radiofrequency oscillators and (sub-)terahertz generators relying upon the Josephson effect., Comment: 9 pages, 5 figures

We developed the model of the internal phonon bottleneck to describe the energy exchange between the acoustically soft ultrathin metal film and acoustically rigid substrate. Discriminating phonons in the film into two groups, escaping and nonescaping, we show that electrons and nonescaping phonons may form a unified subsystem, which is cooled down only due to interactions with escaping phonons, either due to direct phonon conversion or indirect sequential interaction with an electronic system. Using an amplitude-modulated absorption of the sub-THz radiation technique, we studied electron-phonon relaxation in ultrathin disordered films of tungsten silicide. We found an experimental proof of the internal phonon bottleneck. The experiment and simulation based on the proposed model agree well, resulting in tau_{e-ph} = 140-190 ps at T_C = 3.4 K, supporting the results of earlier measurements by independent techniques., Comment: 13 pages, 9 figures, 2 table