Nonlinear kinetic inductance and stability of the superconducting state in superconductors with a nonuniform current...

Within the Ginzburg-Landau model, it is shown that for superconducting slabs with a nonuniform current distribution across the width, the dependence of the kinetic inductance on currentL_k(I) is determined by the superconductor widthw. For widths less than the critical widthw_c,L_kdiverges as the critical currentI_с(the depairing currentI_dep) is approached, which coincides with the case of narrow superconducting slabs/strips with a uniform current distribution across the width. Forw>w_c, the kinetic inductance remains finite atI=I_c. It is found that atw=w_c, the instability mechanism of the superconducting state changes. Forw>w_cthe transition to the resistive state atI=I_cis associated with a modulational instability of the superconducting order parameterwith a finite period, whose evolution over time leads to the entry of chains of vortices and antivortices from opposite edges of the superconductor. Forw<w_c, modulation ofwith a finite period occurs only at later stages of the instability development. Based on the results obtained for slabs, for superconducting strips we assume the existence of a similar critical width at which the mechanism of instability and the behavior of kinetic inductanceL_knearI_сchange.