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By Anatoly Larkin, Andrei Varlamov
This publication provides an entire encyclopedia of superconducting fluctuations, summarizing the final thirty-five years of labor within the box. the 1st a part of the ebook is dedicated to a longer dialogue of the Ginzburg-Landau phenomenology of fluctuations in its thermodynamical and time-dependent types and its quite a few purposes. the second one half bargains with microscopic justification of the Ginzburg-Landau strategy and offers the diagrammatic thought of fluctuations. The 3rd half is dedicated to a less-detailed assessment of the manifestation of fluctuations in observables: diamagnetism, magnetoconductivity, quite a few tunneling features, thermoelectricity, and NMR rest. the ultimate chapters flip to the manifestation of fluctuations in unconventional superconducting platforms: nanodrops, nanorings, Berezinsky-Kosterlitz-Thouless kingdom, quantum part transition among superconductor and insulator, and thermal and quantum fluctuations in vulnerable superconducting structures. The publication ends with a short dialogue on theories of extreme temperature superconductivity, the place fluctuations seem because the attainable protagonist of this interesting phenomenon.
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Example text
This, strong in comparison with the expected scale of Hc2 (0), manifestation of the nonlinear regime in fluctuation magnetization and hence, field dependent fluctuation susceptibility, was the subject of the intensive debates in early 1970s [53–62] (see also the old but excellent review of Scokpol and Tinkham [63]) and after the discovery of HTS [64–67]. We will mainly follow here the recent essay of Mishonov and Penev [48] and the paper of Buzdin et al. [68], dealing with the fluctuation magnetization of a layered superconductor, which allows observing in a unique way all variety of the crossover phenomena in temperature and magnetic field.
27), multiplied by their number N(D) = V ξ −D (T ): π . 29) α This formula gives the correct temperature dependence of the free energy not too close to Tc for the specimens of the even dimensionalities. As we will demonstrate below, a more accurate treatment removes the ln dependence from it in the case of the odd dimensions. Let us restrict ourselves to the region of temperatures beyond the immediate vicinity of transition, where this correction is still small. In this region one can omit the fourth-order term in Ψ(r) with respect to the quadratic one and write down the GL functional, expanding the order parameter in a Fourier series: F(D) = −T V ξ −D (T ) ln F [Ψk ] = FN + [a + k k2 ]|Ψk |2 = FN + αTc 4m + ξ 2 k2 |Ψk |2 .
This problem does not appear at all in the consistent microscopic theory which correctly accounts for the short wavelength fluctuations and does not requires any renormalization procedure. 53) we, following [48], will express the 2D free energy in terms of the Euler gamma function (see Appendix A). 2) one can transform the sum in Eq. 53) to the product and find nc ∼ T /ωc = F(2) ( , h) = − =− TS h ln 2 2πξxy nc −1 n=0 π/2hα n + 1/2 + 2h /2h−1/2 n c ! nc TS π . 57) The natural dimensionless argument of the gamma function appearing here can be expressed in terms of the dimensional variables as 1 +h 1 + = = (T − Tc2 (H)) 2 2h 2h 2H − ∂Hc2 (T ) ∂T .