Time-Dependent Ginzburg–Landau Simulations of the Critical Current in Superconducting Films and Junctions in Magnetic Fields

Critical Current Densities Through Josephson Junctions in Low Magnetic Fields

“…The starting point for all the simulations presented in this work are the normalized TDGL equations [7], [8], [9], [10]. In Manuscript receipt and acceptance dates will be inserted here.…”

“…III. COMPUTATIONAL METHODOLOGY The computational algorithm used in these simulations solves the TDGL equations in the zero electric potential gauge [7], [17], [20] and has been discussed extensively in previous publications [9], [13], [19]. In brief, the TDGL equations are solved using a finite-difference method based on the method of link variables [21], which ensures gauge invariance of the system.…”

Time-dependent Ginzburg-Landau treatment of rf magnetic vortices in superconductors: Vortex semiloops in a spatially nonuniform magnetic field

“…The normal state conductivity is scaled with its zero temperature value σ → σ n σ and since it is nearly constant in the temperature range of interest for Nb, it is set to σ = 1. The "normalized friction coefficient" is defined as the ratio between the two characteristic time scales τ Ψ and τ 0 , η ≡ τ Ψ τ 0 [64,68] and is proportional to γ defined in Eq.4 η = γ |α|τ 0 . For cases when the source of externally applied magnetic field is outside of the superconducting domain, the B a term in Eq.…”

“…On the other hand materials with a higher density of impurities (dirty limit) will have lower mean free path, thus higher friction coefficient. According to Schmid, in the dirty limit, the friction coefficient has the limiting value of η = 5.78 [34,68].…”

“…Here n is unit vector normal to the boundary, and since we expect Eq. ( 13) to be true even when A = 0 and Ψ = 0 the first boundary condition is [49,62,64,68]:…”