Magnetic self-field entry into a current-carrying type-II superconductor

A problem of the irreversible entry of the Abrikosov vortex ring, induced by the self-field of a transport current, into a long type-II superconductor cylinder of arbitrary radius R is solved exactly in the London approximation. The magnetic field and current distribution for the toroidal vortex inside the cylinder are evaluated. The Gibbs free energy of the system is calculated when the transport current is applied. The critical current ${\mathit{j}}_{\mathit{c}}$ of a spontaneous vortex penetration into the superconductor through a surface Bean-Livingston barrier is found to be independent of the radius of the cylinder and close to the depairing current. However, the dependence of the width of edge barrier on the transport current in a thin cylinder is found to differ qualitatively from that in a thick cylinder. As a result of this, in the first case there is no characteristic current but ${\mathit{j}}_{\mathit{c}}$, while in the second case a characteristic current ${\mathit{j}}_{\mathit{c}1}$≃${\mathit{j}}_{\mathit{c}}$/κ arises (κ the Ginzburg-Landau parameter) at which the barrier width drops down to values of the order of the magnetic-field-penetration depth λ, which allows for vortex entry on the surface defects of the size of λ. The latter result is discussed in reference to the high-critical-current observations on the microbridges of high-temperature superconductors.