A journey in theory

The Theory of Superconductivity in the High-Tech-TC Cuprates

March 13, 1998

Superconductivity was unexpectedly discovered in 1911 in the Leiden laboratory of H. Kamerlingh Onnes. The observation of the sudden total disappearance of electrical resistance as the temperature was lowered below 4.2 kelvin in a mercury wire, in spite of its rather obvious practical implications (such as the creation of high-field electromagnets), did not lead to immediate widespread activity.

The Leiden laboratory was unique in its capability of achieving the extremely low temperatures required to observe the phenomenon, while the major figures of theoretical physics were deeply involved with the development of the old quantum theory. Thus, advances in experiment and theory were slow in coming: it was not until 1925 that superconductivity was observed in a second laboratory. Even a meaningful phenomenological picture could not be made before the crucial discovery in 1933 that magnetic fields were expelled from the interior of a superconductor. On the theoretical side, although there was not even a quantum theory of metallic behaviour until 1928, various eminent theorists proposed more or less fanciful scenarios for superconductivity.

After 1928, in spite of the efforts of the leading theoretical physicists of the time, it became clear that the many successes of the quantum theory of metals were not giving an easy path to the microscopic description of superconductivity. Useful phenomenological theories of superconductivity were not developed until the description of the electrodynamic and magnetic properties due to Fritz and Heinz London in 1935 and the description of superconductivity as a second-order thermodynamic phase transition in 1950 by Vitalii Ginzburg and Lev Landau. It was not until 46 years after Onnes's discovery that the correct microscopic theory was presented by John Bardeen, Leon Cooper and John R. Schrieffer (BCS) in 1957. The elegant BCS theory, while conceptually deep and original, is remarkably simple mathematically. It predicted and accounts for numerous experimental results on a wide variety of simple metals and alloys that are superconducting at low temperatures. The apparently complete picture of superconductivity that developed in the 1960s and 1970s was shattered 11 years ago by the discovery, by J. Georg Bednorz and Karl Muller, of "high-temperature superconductivity (high-Tc)" in a quaternary alloy based on a copper oxide compound. Since the previously studied superconductors appear to be governed by a mechanism with an inherent limitation to increases in the transition temperature below which they would superconduct, the discovery of superconductivity at 33 kelvin and shortly thereafter at 92 kelvin in a related compound generated enormous experimental and theoretical activity. After all, to have superconductivity above the temperature of liquid air (77 kelvin) had immediate profound technological implications that generated renewed hopes of achieving superconductivity at ordinary temperatures. In the three years following the discovery of high-Tc, not fewer than 10,000 papers on the subject were published.

The contrast between the leisurely pace of development of conventional superconductivity and the frantic activity on high-Tc in the past decade is striking. The new materials are not difficult to synthesise and the appropriate temperatures are available everywhere, so an enormous collection of experimental data was soon available. Theorists, armed with the quantum theory of electrons in metals and with the beautiful BCS theory of conventional superconductors, attempted applications of these methods to the new com£. It soon became clear that something very special was going on. Unlike the old superconductivity that appears in many different metals and alloys, high-Tc is found only in a small number of cuprate-based com£ whose crystals contain distinct planes of copper and oxygen ions in a square array and which for certain compositions are insulators rather than superconductors.

Philip W. Anderson, Nobel laureate and professor of physics at Princeton University, has been responsible over the years for a remarkable number of seminal contributions to modern theoretical physics. An expert on superconductivity, he concluded at once that the high-Tc phenomenon requires a new theoretical description for the physics of interacting particles in low dimensions.

In 1987, Anderson published an extremely influential paper in Science. In it, he suggested that the chemistry and quasi-two-dimensional structure of the cuprates would lead to unconventional behaviour dominated by strong repulsion between the electrons of the copper oxide planes. Although some of the conjectures in this paper proved to be incorrect, many of the basic physical ideas it outlined have been followed by the majority of researchers in the field. Anderson's paper was the impetus for a proliferation of theoretical work on "the strong-correlation many-body problem", and that issue has become a central theme of research in condensed-matter physics.

In the years following the discovery of high-Tc, Anderson and a number of colleagues have continued to try to formulate a theory, based on his original insights, for the unusual properties of the cuprates in both their superconducting and normal states. The present book represents a history of these efforts. The main chapters were started over several years from 1989 and last revised between 1993 and 1995; they are supplemented by more recent commentaries ("Notes, Appendices, Epilogues") by the author and by a collection of reprints of some of the more important original papers by Anderson and colleagues. Anderson claims that the main outline of his theory of the cuprates is now complete. Hence, in spite of the fact that most of the details have not been - indeed cannot yet be - worked out, his belief is that it is now appropriate to put the main ideas, if not the detailed calculations that must eventually follow, together in a single volume.

The book is an intensely personal description of Anderson's intellectual journey, over the shifting sands of experimental data and theoretical developments, toward the goal of a theory of high-Tc and the normal state of the cuprate superconductors. It is an important book on those grounds alone. Most of Anderson's insights have been basic to the efforts of many theorists, even if they have often followed them in different directions. He himself has followed several unfruitful trails, and some of these are clearly documented by the commentaries. The meat of the book - that is the evolution of his ideas, including his comprehensive attention to experimental information as it developed over the years - makes for fascinating reading.

There are some especially rewarding sections, not available elsewhere. These include a discussion of the Hubbard model in chapters one and five and an appendix on chemical pseudo-potentials in chapter one. However, a reader who approaches the book with the expectation that he or she will finish it with a more or less satisfying understanding of the bases of Anderson's theory will likely be frustrated. The text of the chapters is often quite technical, replete with idiosyncratic labels and spellings, undefined shorthands and abbreviations. The ideas themselves are often very difficult both in fact and in their expression, and it is somewhat irritating to read sections of difficult argumentation only to find in a subsequent note or appendix that the ideas in the main text are incorrect. The book deserves much better than the inconsistent typesetting of the mathematics and the inadequate proofing.

So who should read this book? Anyone interested in how one of our most original theoretical physicists develops his understanding will learn something about the process. Established workers in the field, few of whom subscribe to the Anderson scenario for high-Tc, will nevertheless find many profound and stimulating ideas. Finally, the discriminating and enterprising graduate student may find wonderful research problems scattered throughout.

Elihu Abrahams is professor of physics, Rutgers University, United States.

The Theory of Superconductivity in the High-Tech-TC Cuprates

Author - P. W. Anderson
ISBN - 0 691 04365 5
Publisher - Princeton University Press
Price - £39.50
Pages - 446

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