I. Aranson et V. Vinokur, SURFACE INSTABILITIES AND VORTEX TRANSPORT IN CURRENT-CARRYING SUPERCONDUCTORS, Physical review. B, Condensed matter, 57(5), 1998, pp. 3073-3083
We investigate the stability of the vortex configuration in thin super
conducting films and layered Josephson-coupled superconductors under a
n applied current analytically and by numerical simulations of the tim
e-dependent Ginzburg-Landau equation. We show that the stationary vort
ex lattice becomes unstable with re spect to long-wavelength perturbat
ions above some critical current I-c. We find that at currents slightl
y exceeding I-c the vortex phase develops plastic flow, where large co
herent pieces of the lattice are separated by Lines of defects and sli
de with respect to each other. At elevated currents a transition to el
astic flow is observed. We obtained the effective one-dimensional Ginz
burg-Landau equation for a description of the vortex penetration from
the edges. We discuss this transition in terms of a one-dimensional ph
ase-slip phenomenon in superconducting wires with a periodically modul
ated temperature. We found several distinct dynamic vortex phases in t
he layered current-carrying superconductors. We show that for some int
ermediate range of the current, depending on the coupling between the
layers, the coherent motion of the pancake vortices in different layer
s becomes unstable leading to dynamic decoupling.