Simulation of dynamics of the order parameter in superconducting nanostructured materials: Effect of the magnetic field renormalization

The effect of the magnetic field renormalization in superconducting nanostructured materials is quantitatively evaluated. For demonstration purposes, three superconducting structures with various geometric shapes and dimensions and functioning in different resistive regimes are considered. Simulation is based on a set of equations including the time-dependent Ginzburg-Landau equation coupled with the Maxwell equations. An impact of the order parameter on the vector and scalar potentials is taken into account. It is shown that for Nb structures having thicknesses (∼200 nm) less than the magnetic field penetration depth (∼300 nm), the effect of the magnetic field renormalization equivocally affects the spatiotemporal distribution of superconducting vortices. For a slab with the thickness of ∼100 nm, the absolute value of the average voltage generated by moving vortices changes by less than 1%. With increasing the thickness of C-shaped structures up to 500 nm, the renormalization effect leads to the growth of the average voltage by up to 10%.