Theory of Fluctuations in Superconductors Anatoly Larkin and Andrei Varlamov , Oxford U. Press, New York, 2005. $164.50 (412 pp.). ISBN 0-19-852815-9
The Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity is one of the most successful of all the theoretical models of condensed matter ever developed. This is perhaps surprising, because the theory is in essence a mean-field theory. In principle, it is similar in structure to the Curie–Weiss theory of magnetism or the Hartree–Fock theory of electronic structure. Nowadays, neither of those two theories would be considered accurate enough for normal use in realistic calculations. So why is the BCS theory so exceptional?
The answer was pointed out in the 1960s by Vitaly Ginzburg, who showed that the very large size of the BCS coherence length ξ is the key to why a relatively simple mean-field theory is so accurate. The BCS coherence length corresponds to the radius of the bound Cooper pair; it is so large that within it, each Cooper pair overlaps with many thousands of others—hence the mean-field approximation is nearly exact. For bulk conventional, or type I, metallic superconductors, Ginzburg explained that the fluctuation corrections to BCS theory are only appreciable in a tiny range of temperatures, perhaps within 10–6 K to 10–10 K of the critical temperature T c.
Despite Ginzburg’s findings, it turns out that there are many systems in which the effects of fluctuations are not just observable but also important in the role they play. The regular crystalline lattice of superconducting vortices in type II superconductors, discovered by Alexei Abrikosov, is an example. The phenomena of vortex-lattice melting, flux creep, and other fluctuation effects on the vortex lattice are significant theoretically as examples of emergent order in complex systems and have a massive impact on the prospects of real-life commercial applications of high-temperature superconductivity.
Theory of Fluctuations in Superconductors , by Anatoly Larkin and Andrei Varlamov, is a long-overdue, comprehensive introduction to superconducting fluctuations in general, and to several specific examples in which those fluctuations are especially important. Because most textbooks on superconductivity hardly mention fluctuation effects at all, which gives the misleading impression that BCS theory is exact, Theory of Fluctuations in Superconductors is especially vital. The first part of the text concerns fluctuation phenomena that can be studied within the framework of the Ginzburg–Landau theory of superconductivity. The phenomena include scaling and renormalization effects on specific heat and magnetization near T c and the crossover from two- to three-dimensional behavior in layered superconductors explored within the Lawrence–Doniach model. Fluctuations in the Abrikosov-vortex lattice are also examined; however, the authors do not detail the full range of the problem’s complexity.
Larkin, who died unexpectedly last year, was one of the foremost members of the superb Landau school of theorists dominating the field of superconductivity. He made major contributions to the subject for more than 40 years. Presented in 1968, the Aslamazov–Larkin theory of fluctuation contributions to paraconductivity—the conductivity of a superconductor in its normal state—remains a foundational paper of the field. Along with the contributions of Kazumi Maki and Richard Thompson, Larkin and Alexander Aslamazov’s work laid the foundations of the theory of superconducting fluctuations in the conductivity of normal-state metals.
Varlamov, research director at the Italian National Institute of Condensed Matter Physics, has also made important contributions. Notably, he discovered a third, essential effect of fluctuations on the paraconductivity; it arises from the renormalization of the normal-metal density of states as one approaches the instability toward superconductivity. In modern terms, this is a form of the “pseudogap” effect.
The second part of the book thoroughly explains the microscopic theory of fluctuation phenomena in superconductors and presents the contributions of Aslamazov and Larkin and of Maki and Thompson. The section introduces effects of density of states in paraconductivity, the derivation of the time-dependent Ginzburg–Landau expansion, and the effects of impurities. Although the book, as implied by its title, is concerned mainly with theory, the authors also offer in the second part some comparisons with experimental data on high-temperature superconductors. The third part of the book extends the authors’ fundamental approach to the calculation of other physical observables, including Hall conductivity, tunnel junctions, magnetoresistance, and thermal conductivity. The fourth and final part is more open-ended and deals with granular superconductors, Josephson junctions, such nanoscale materials as nanorings, and fluctuation effects in superconductors—specifically high-T c cuprate materials—near the metal–insulator transition. The difficulty of understating these complex materials is nicely illustrated by the authors’ use of the medieval cartographers’ phrase hic sunt leones, printed in the under-doped region of their cuprate phase diagram.
Theory of Fluctuations in Superconductors is a thorough and timely book aimed at both theorists and experimentalists interested in current topics in superconductivity. There are many vast topics, including flux-lattice melting or unconventional (p- or d-wave) superconductivity, and experimental results, that the authors only briefly mention. Nevertheless, the book will be a useful guide and reference for graduate students and established workers in the field.
