Electrical conductivity beyond a linear response in layered superconductors under a magnetic field

Complex conductivity in strongly fluctuating layered superconductors

“…where g (ε, τ) = e −(2ε−b+2/d 2 )τ I 0 2τd −2 with I 0 (x) = (1/2π) 2π 0 e x cos θ dθ being the modified Bessel function, τ = τ − τ ′ , t = T /T c , and γ E = 0.577 is Euler constant. As was discussed in [23] there are UV divergences in the intermediate steps, equation (3.2), that are regularized by a cutoff. There is a degree of arbitrariness in its choice and it was shown that in the TDGL theory, the cutoff having a dimension of time, τ c , rather than energy, is most convenient.…”

“…Let us first assume that the vortex liquid is not driven by the electric field. As mentioned above, the cubic term in the TDGL equation (2.7) can be treated in the self-consistent gaussian approximation (explained in detail in [23]) by replacing |ψ n | 2 ψ n with a linear one 2 |ψ n | 2 ψ n…”

“…The thermal average of the density of Cooper pairs can be expressed via the Green's functions: 2) and after renormalization [23], the latter takes the form…”

Fluctuations in superconducting rings with two order parameters

“…Comparison of Eqs. (26) and (27) with the values of | 1,2 | 2 in the absence of fluctuations enables us to estimate the range of temperatures for which fluctuations are important. Figure 1 shows the values of Finally, it should be mentioned that, although the Hartree approximation becomes exact both in the limit of high and of low temperature, it has several limitations, and near T c the variational Gaussian approximation is expected to be more accurate.…”

“…Figure 1 shows the values of Finally, it should be mentioned that, although the Hartree approximation becomes exact both in the limit of high and of low temperature, it has several limitations, and near T c the variational Gaussian approximation is expected to be more accurate. 2,26 …”