Unstable Flux Flow due to Heated Electrons in Superconducting Films

Abstract

A flux instability occurs in superconductors at low temperatures, where ee scattering is more rapid than ep, whereby the dissipation significantly elevates the electronic temperature while maintaining a thermal-like distribution function. The reduction in condensate and rise in resistivity produce a non-monotonic current-voltage response. In contrast to the Larkin-Ovchinnikov instability where the vortex shrinks, in this scenario the vortex expands and the quasiparticle population rises. Measurements in Y1Ba2Cu3O 7−δ agree quantitatively with the distinct predictions of this mechanism.PACS numbers: 74.60. Ge, 74.72.Bk, 71.10.Ca, 72.10.Di, 72.15.Lh, 73.50.Fq Keywords: Flux, fluxon, vortex, superconductivity, critical, current, instability, unstable, YBCO In a type II superconductor, magnetic fields between the lower critical value H c1 and upper critical field H c2 introduce flux vortices containing a quantum of flux Φ o = h/2e. Here we have superconducting films in a perpendicular applied flux density B, with a transport electric current density j in the plane of the film, which exerts a Lorentz driving force F L = jΦ o . The vortex motion generates an electric field E = vB and is opposed by a viscous drag ηv (η is the coefficient of viscosity and v the vortex velocity), so that in steady state jΦ o = ηv and the response is Ohmic. Larkin and Ovchinnikov (1986) have shown that a dirty superconductor at low temperatures has a free-flux-flow resistivity related to the normalstate value ρ n by [1]Approximately the same result, without the precise 0.9 prefactor, can be obtained by considering the Ohmic dissipation in the core and temporal changes in the order parameter leading to irreversible entropy transfer [2]; the result is also valid for d-wave superconductors that are not superclean [3]. Eq. 1 is equivalent to η ≈ Φ 0 H c2 /ρ n . At low levels of j and E, in the assumed dirty limit l ≪ ξE F /kT c (l is the mean free path and E F is the Fermi energy), η is a constant that is proportional to the order parameter ∆ and inversely proportional to the size ∼ ξ 2 (where ξ is the coherence length) of the vortex [4]. (The Hall effect and transverse component of E are negligible for this discussion, as is vortex pinning because of the large driving forces [5].)At high electric fields and dissipation levels sufficient to alter the electronic distribution function and/or the electronic temperature, j(E) becomes non-linear and can develop an unstable region (dj/dE < 0) above some critical vortex velocity v * . For the regime near T c , such an instability has been predicted by Larkin and Ovchinnikov (LO) [6], and has been experimentally well established [7,8,9,10]. At high temperatures, the electron-phonon (ep) scattering time τ ep can be shorter than the electronelectron (ee) scattering time τ ee , preventing internal equilibration of the electronic system and producing a peculiar non-thermal distribution function. Since the order parameter ∆ is especially sensitive to the distribution function when close to T c , even ...

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