Experimentally and mysteriously, the concentration of quasiparticles in a gapped superconductor at low temperatures always by far exceeds its equilibrium value. We study the dynamics of localized quasiparticles in superconductors with a spatially fluctuating gap edge. The competition between phonon-induced quasiparticle recombination and generation by a weak non-equilibrium agent results in an upper bound for the concentration that explains the mystery.PACS numbers: 74.40. Gh, 74.62.En, Naïvely, the superconducting gap ∆ should ensure an exponentially small quasiparticle concentration at low temperatures. However, various experiments indicate that a long-lived, non-equilibrium quasiparticle population persists in the superconductor [1][2][3][4][5][6][7]. The quasiparticle poisoning, whereby an unwanted quasiparticle is trapped in a bound state, is an important factor harming the ideal operation of superconducting devices [8]. Unwanted quasiparticles also forbid tempting perspectives to use Majorana states in superconductors for topologically protected quantum computing [9][10][11]. The poisoning rates have been quantified [12][13][14][15][16] and much experimental work is directed on protection from poisoning, with important advances in this direction [17][18][19][20]. The non-equilibrium quasiparticles are produced by some non-equilibrium agent, which is most likely related to the absorption of electromagnetic irradiation from the high-temperature environment [21] and/or electromagnetic fields applied to the setup in the course of its measurement and operation. Surprisingly, the efforts to reduce the intensity of this non-equilibrium agent are not entirely satisfying: the experiments give a substantial residual quasiparticle concentration, even if all efforts are performed [22,23].In this Letter, we study the dynamics of the annihilation of quasiparticles localized at the spatial fluctuations of the gap edge. Importantly, we find that the average distance between the quasiparticles depends only logarithmically on the intensity of the non-equilibrium agent. In simple terms, the exponential dependence of the annihilation rate on the distance between the two quasiparticles results in the quasiparticle concentration valid at small A Γ /r 6 c . [A more accurate estimate for r is given by Eq. (9).] Here, r c is the relevant radius of the localized quasiparticle state to be estimated in detail below: for practical circumstances, it exceeds the superconducting coherence length ξ 0 by not more than an order of magnitude. Furthermore, A is the rate of nonequilibrium generation of quasiparticles per unit volume, andΓ is a material constant characterizing the inelastic quasiparticle relaxation due to electron-phonon interaction. The packing coefficient, C p ≈ 0.605 ± 0.008, can be derived from a simple bursting bubbles model outlined below. Equation (1) explains both the substantial concentration that is observed, as well as the inefficiency of the efforts to reduce it.Let us outline the derivation of the above relations. ...

In systems combining type-II superconductivity and magnetism the non-stationary magnetic field of moving Abrikosov vortices may excite spin waves, or magnons. This effect leads to the appearance of an additional damping force acting on the vortices. By solving the London and Landau-Lifshitz-Gilbert equations we calculate the magnetic moment induced force acting on vortices in ferromagnetic superconductors and superconductor/ferromagnet superlattices. If the vortices are driven by a dc force, magnon generation due to the Cherenkov resonance starts as the vortex velocity exceeds some threshold value. For an ideal vortex lattice this leads to an anisotropic contribution to the resistivity and to the appearance of resonance peaks on the current voltage characteristics. For a disordered vortex array the current will exhibit a step-like increase at some critical voltage. If the vortices are driven by an ac force with a frequency ω, the interaction with magnetic moments will lead to a frequency-dependent magnetic contribution ηM to the vortex viscosity. If ω is below the ferromagnetic resonance frequency ωF , vortices acquire additional inertia. For ω > ωF dissipation is enhanced due to magnon generation. The viscosity ηM can be extracted from the surface impedance of the ferromagnetic superconductor. Estimates of the magnetic force acting on vortices for the U-based ferromagnetic superconductors and cuprate/manganite superlattices are given.