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# Pinning effects on self-heating and flux-flow instability in superconducting films near $$T_{c}$$

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### Abstract

The effect of pinning on self-heating triggering the Larkin-Ovchinnikov (LO) flux-flow instability (FFI) in superconducting thin films is theoretically investigated. The problem is considered relying upon the Bezuglyj-Shklovskij (BS) generalization of the LO theory, accounting for a finite heat removal from the quasiparticles at temperature $$T^\ast$$ to the bath at temperature $$T_0$$. The FFI critical parameters, namely the current density $$j^{\ast}$$, the electric field $$E^{\ast}$$, the power density $$P^{\ast}$$, and the vortex velocity $$v^{\ast}$$ are calculated and graphically analyzed as functions of the magnetic field and the pinning strength. With increasing pinning strength at a fixed magnetic field value $$E^{\ast}$$ \emph{decreases}, $$j^{\ast}$$ \emph{increases}, while $$P^{\ast}$$ and $$T^{\ast}$$ \emph{remain practically constant}. Vortex pinning may hence be the cause for eventual discrepancies between experiments on superconductors with \emph{strong pinning} and the generalized LO and BS results.

### Most cited references15

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### Dynamic Melting of the Vortex Lattice

(1994)
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### Rearrangement of the vortex lattice due to instabilities of vortex flow

(2007)
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 $$v_c$$ 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 time-dependent Ginzburg-Landau equations and are strictly valid when the coherence length $$\xi(T)$$ is larger or comparable with the decay length $$L_{in}$$ 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 $$a \gg L_{in} \gg \xi (T)$$. We speculate that a similar instability of the vortex lattice should exist for $$v>v_c$$ even when \(a
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### Flux-flow instability and its anisotropy inBi2Sr2CaCu2O8+δsuperconducting films

(1999)
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### Author and article information

###### Journal
2017-04-30
###### Article
1705.00363