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

Within the Ginzburg-Landau model, it is shown that for superconducting slabs and strips with a nonuniform current distribution across the width, the dependence of the kinetic inductance on current L k (I) is determined by the superconductor width w. For widths less than the critical width w c , L k diverges as the critical current I с (the depairing current I dep ) is approached, which coincides with the case of narrow superconducting slabs/strips with a uniform current distribution across the width. For w>w c , the kinetic inductance remains finite at I=I c . It is found that at w=w c , the instability mechanism of the superconducting state changes. For w>w c the transition to the resistive state at I=I с is associated with a modulational instability of the superconducting order parameter Ψ with a finite period, whose evolution over time leads to the entry of chains of vortices and antivortices from opposite edges of the superconductor. For w<w c , modulation of Ψ with a finite period occurs only at later stages of the instability development.