Dynamic transition of vortices into phase slips and generation of vortex-antivortex pairs in thin film Josephson junctions under dc and ac currents

We present theoretical and numerical investigations of vortices driven by strong dc and ac currents in long Josephson junctions described by a nonlinear integro-differential equation which takes into account nonlocal electrodynamics of films, vortex bremsstrahlung and Cherenkov radiation amplified by the attraction of vortices to the edges of the junction. The work focuses on the dynamics of vortices in Josephson junctions in thin films where the effects of Josephson nonlocality dominate but London screening is negligible. We obtained an exact solution for a vortex driven by an arbitrary time-dependent current in an overdamped junction where the vortex turns into a phase slip if the length of the junction is shorter than a critical length which depends on current. Our analytical and numerical results show that the dynamic behavior of vortices depends crucially on the ohmic damping parameter. In overdamped junctions vortices expand as they move faster and turn into phase slips as current increases. In underdamped junctions vortices entering from the edges produce Cherenkov radiation generating cascades of expanding vortex-antivortex pairs, which ultimately drive the entire junction into a resistive phase slip state. Simulations revealed a variety of complex dynamic states of vortices under dc and ac currents which can manifest themselves in hysteretic current-voltage characteristics with jumps and regions with negative differential resistance resulting from transitions from oscillating to ballistic propagation of vortices, their interaction with pinning centers and standing nonlinear waves in the junction.Comment: 19 page

Fragmentation of Fast Josephson Vortices and Breakdown of Ordered States by Moving Topological Defects

Topological defects such as vortices, dislocations or domain walls define many important effects in superconductivity, superfluidity, magnetism, liquid crystals, and plasticity of solids. Here we address the breakdown of the topologically-protected stability of such defects driven by strong external forces. We focus on Josephson vortices that appear at planar weak links of suppressed superconductivity which have attracted much attention for electronic applications, new sources of THz radiation, and low-dissipative computing. Our numerical simulations show that a rapidly moving vortex driven by a constant current becomes unstable with respect to generation of vortex-antivortex pairs caused by Cherenkov radiation. As a result, vortices and antivortices become spatially separated and accumulate continuously on the opposite sides of an expanding dissipative domain. This effect is most pronounced in thin film edge Josephson junctions at low temperatures where a single vortex can switch the whole junction into a resistive state at currents well below the Josephson critical current. Our work gives a new insight into instability of a moving topological defect which destroys global long-range order in a way that is remarkably similar to the crack propagation in solids.Comment: Sci. Rep. 5, 1782

Nonlinear Dynamics of Vortices in Different Types of Grain Boundaries

As a major component of linear particle accelerators, superconducting radio-frequency (SRF) resonator cavities are required to operate with lowest energy dissipation and highest accelerating gradient. SRF cavities are made of polycrystalline materials in which grain boundaries can limit maximum RF currents and produce additional power dissipation sources due to local penetration of Josephson vortices. The essential physics of vortex penetration and mechanisms of dissipation of vortices driven by strong RF currents along networks of grain boundaries and their contribution to the residual surface resistance have not been well understood. To evaluate how GBs can limit the performance of SRF materials, particularly Nb and Nb3Sn, we performed extensive numerical simulations of nonlinear dynamics of Josephson vortices in grain boundaries under strong dc and RF fields. The RF power due to penetration of vortices both in weakly-coupled and strongly-coupled grain boundaries was calculated as functions of the RF field and frequency. The result of this calculation manifested a quadratic dependence of power to field amplitude at strong RF currents, an illustration of resistive behavior of grain boundaries. Our calculations also showed that the surface resistance is a complicated function of field controlled by penetration and annihilation of vortices and antivortices in strong RF fields which ultimately saturates to normal resistivity of grain boundary. We found that Cherenkov radiation of rapidly moving vortices in grain boundaries can produce a new instability causing generation of expanding vortex-antivortex pair which ultimately drives the entire GB in a resistive state. This effect is more pronounced in polycrystalline thin film and multilayer coating structures in which it can cause significant increase in power dissipation and results in hysteresis effects in I-V characteristics, particularly at low temperatures

Fragmentation of Fast Josephson Vortices and Breakdown of Ordered States by Moving Topological Defects

Topological defects such as vortices, dislocations or domain walls define many important effects in superconductivity, superfluidity, magnetism, liquid crystals, and plasticity of solids. Here we address the breakdown of the topologically-protected stability of such defects driven by strong external forces. We focus on Josephson vortices that appear at planar weak links of suppressed superconductivity which have attracted much attention for electronic applications, new sources of THz radiation, and low-dissipative computing. Our numerical simulations show that a rapidly moving vortex driven by a constant current becomes unstable with respect to generation of vortex-antivortex pairs caused by Cherenkov radiation. As a result, vortices and antivortices become spatially separated and accumulate continuously on the opposite sides of an expanding dissipative domain. This effect is most pronounced in thin film edge Josephson junctions at low temperatures where a single vortex can switch the whole junction into a resistive state at currents well below the Josephson critical current. Our work gives a new insight into instability of a moving topological defect which destroys global long-range order in a way that is remarkably similar to the crack propagation in solids

Dynamic pair-breaking current, critical superfluid velocity and nonlinear electromagnetic response of nonequilibrium superconductors

We report numerical calculations of a dynamic pairbreaking current density $J_d$ and a critical superfluid velocity $v_d$ in a nonequilibrium superconductor carrying a uniform, large-amplitude ac current density $J(t)=J_a\sin\Omega t$ with $\Omega$ well below the gap frequency $\Omega\ll \Delta_0/\hbar$. The dependencies $J_d(\Omega,T)$ and $v_d(\Omega,T)$ near the critical temperature $T_c$ were calculated from either the full time-dependent nonequilibrium equations for a dirty s-wave superconductor and the time-dependent Ginzburg-Landau (TDGL) equations for a gapped superconductor, taking into account the GL relaxation time of the order parameter $\tau_{GL}$ and the inelastic electron-phonon relaxation time of quasiparticles $\tau_E$. We show that both approaches give similar frequency dependencies of $J_d(\Omega)$ and $v_d(\Omega)$ which gradually increase from their static pairbreaking GL values $J_c$ and $v_c$ at $\Omega\tau_E\ll 1$ to $\sqrt{2}J_c$ and $\sqrt{2}v_c$ at $\Omega\tau_E\gg 1$. Here $J_d$, $v_d$ and a dynamic superheating field at which the Meissner state becomes unstable were calculated in two different regimes of a fixed ac current and a fixed ac superfluid velocity induced by the applied ac magnetic field $H=H_a\sin\Omega t$ in a thin superconducting filament or a type-II superconductor with a large GL parameter. We also calculated a nonlinear electromagnetic response of a nonequilibrium superconducting state, particularly a dynamic kinetic inductance and a dissipative quasiparticle conductivity, taking into account the oscillatory dynamics of superconducting condensate and the kinetics of quasiparticles driven by a strong ac current. It is shown that an ac current density produces multiple harmonics of the electric field, the amplitudes of the higher-order harmonics diminishing as $\tau_E$ increases

Instability of Flux Flow and Production of Vortex-Antivortex Pairs by Current-Driven Josephson Vortices in Layered Superconductors

We report numerical simulations of the nonlinear dynamics of Josephson vortices driven by strong dc currents in layered superconductors. Dynamic equations for interlayer phase differences in a stack of coupled superconducting layers were solved to calculate a drag coefficient η(J) of the vortex as a function of the perpendicular dc current density J. It is shown that Cherenkov radiation produced by a moving vortex causes significant radiation drag increasing η(v) at high vortex velocities v and striking instabilities of driven Josephson vortices moving faster than a terminal vc. The steady-state flux flow breaks down at ν \u3e vc as the vortex starts producing a cascade of expanding vortex-antivortex pairs evolving into either planar macrovortex structures or branching flux patterns propagating both along and across the layers. This vortex-antivortex pair production triggered by a rapidly moving vortex is most pronounced in a stack of underdamped planar junctions where it can occur at J \u3e Js well below the interlayer Josephson critical current density. Both vc and Js were calculated as functions of the quasiparticle damping parameter, and the dc magnetic field was applied parallel to the layers. The effects of vortex interaction on the Cherenkov instability of moving vortex chains and lattices in annular stacks of Josephson junctions were considered. It is shown that a vortex driven by a current density J \u3e Js in a multilayer of finite length excites self-sustained large-amplitude standing waves of magnetic flux, resulting in temporal oscillations of the total magnetic moment. We evaluated a contribution of this effect to the power W radiated by the sample and showed that W increases strongly as the number of layers increases. These mechanisms can result in nonlinearity of the c-axis electromagnetic response and contribute to THz radiation from the layered cuprates at high dc current densities flowing perpendicular to the ab planes