Theory of Dissipative Current-Carrying States in Superconducting Filaments

Abstract

A simple generalized time-dependent Ginzburg-Landau equation valid for dirty superconductors in the vicinity of T c is derived. For thin homogeneous filaments it exhibits oscillatory phase-slip solutions below and above the critical depairing current. The results are compared with I-V curves observed in whiskers and microbridges.

Finite Element Treatment of Vortex States in 3D Mesoscopic Cylindrical Superconductors in a Tilted Magnetic Field

“…3b). We find the multi-vortex states with vorticity L = 2, 3, 4, 5, 6, 7 and 8 for 0.39H c2 < H < 0.95H c2 , and the gi- ant vortex states [3,25,26] with vorticity L = 9−13 for H > 0.95H c2 . It is clear that the L = 0, 2-13 state is a ground state.…”

“…A recent review [25] warns us of the fact that for gapped superconductors TDGL is not strictly valid even above T c , while below T c it becomes totally wrong; nevertheless TDGL remains popular because of its simplicity and its ability to reproduce observed phenomena. Kramer and Watts-Tobin [26] generalized TDGL equation so that it should be applicable to gapped superconductors as long as there is local equilibrium, while still retaining some of the simplifying features of the TDGL formalism. The simulations of the vortex states are conducted in (i) field sweep up: we started from the |ψ| = 1 and slowly increased the magnetic field, after reaching the stationary state, (ii) field sweep down: we started simulation with |ψ| = 0 and H > H c and decreased the field with small steps.…”

The Stationary SQUID

“…We note that L 2 ϕ, Φ and Lǫ 1/2 /ξ(0) = L/ξ(T ) are invariant under this scaling. This scaling breaks down if L is not large in comparison to the average diffusion distance between inelastic collisions [26,27].…”

“…A model that can be justified as long as there is local equilibrium is the Kramer-WattsTobin model [25][26][27], which takes into account the different relaxation times of the absolute value and of the phase of the order parameter. In our units, the evolution equations can be written as…”

Time-dependent Ginzburg-Landau equations for mixedd−ands-wave superconductors

“…Also note that the normal-state Green function can in turn be written as an integral equatioñ 12) with G 0 as the normal-state single-particle Green function in the absence of the electromagnetic field but including the effect due to impurity scatterings. To write down the above integral equation, the squared term of the vector potential has been neglected and the Coulomb gauge is chosen.…”