Momentum conservation,time dependent Ginzburg Landau equation and paraconductivity

Superconductors exhibit increasing electrical conductivity as the temperature approachesT _c from above, due to superconducting fluctuations. The functions σ_f1=σ(ω, ?)-σ _n (ω), ?=(T-T _c )/T _c , have been derived by Schmidt phenomenologically using the time dependent Ginzburg-Landau equation (TDGL). These functions fail to vanish in the absolute clean limit τ → ∞ as they must. We have therefore reinvestigated the derivation of the linearized TDGL-equation and the corresponding current expression in the presence of a time dependent vector potential. We find several new terms, which are important for the rather clean superconductor only and are easily interpreted physically in terms of momentum conservation. Applying these corrected equations to the paraconductivity problem, we derive σ_fl(ω, ?) which has an extra factor (1 —iωτ)^?2 compared to Schmidt's result. There is also an additional term, which is connected to the problem of the contribution calculated by Maki. By comparison with the linear response function belowT _c , we show that this term is valid in the limit ¦ω¦?¦Δ¦ only and may not be continued to ω=0. There remains, however, a problem connected with this term, which cannot be solved within the present phenomenological framework.