BCS: 50 Years

The following sections are included:

• PREFACE

• CONTENTS

Memory fades. Is it possible to recreate the events that led to BCS? Can we recapture the great difficulty (even conjectured insolubility) superconductivity presented more than half a century ago? Perhaps not. But yellowed notes, like tea-soaked crumbs of madeleine, have awakened for me, sometimes with startling clarity, images and memories from that somewhat distant past.

This article is based on an interview with Bob Schrieffer. The questions are by Joan N. Warnow. The audio version is available on the AIP website at: http://www.aip.org/history/mod/superconductivity/02.html.

This is an excerpt from a talk that John Bardeen gave on the development of the theory of superconductivity in London, England on September 17, 1962 when he received the Fritz London award for his work developing the BCS theory of superconductivity. The talk was given at the Eighth International Conference on Low Temperature Physics at Queen Mary College in London and was reprinted in Physics Today in January of 1963.

Almost half a century passed between the discovery of superconductivity by Kamerlingh Onnes and the theoretical explanation of the phenomenon by Bardeen, Cooper and Schrieffer. During the intervening years the brightest minds in theoretical physics tried and failed to develop a microscopic understanding of the effect. A summary of some of those unsuccessful attempts to understand superconductivity not only demonstrates the extraordinary achievement made by formulating the BCS theory, but also illustrates that mistakes are a natural and healthy part of scientific discourse, and that inapplicable, even incorrect theories can turn out to be interesting and inspiring.

The author describes the inspiration for the experiment by Hebel and Slichter to measure the nuclear spin–lattice relaxation time in super-conductors, the design considerations for the experiment, the surprising experimental results, their theoretical treatment using the Bardeen–Cooper–Schrieffer theory, and how comparing the nuclear relaxation results with those for ultrasound absorption confirmed the central idea of the BCS theory, the BCS pair wave function.

I present an expanded version of a talk given at the Urbana symposium that celebrated the fiftieth anniversary of the publication of the microscopic theory of superconductivity by Bardeen, Cooper, and Schrieffer — BCS. I recall at some length, the work with my Ph.D. mentor, David Bohm, and my postdoctoral mentor, John Bardeen, on electron interaction in metals during the period 1948–55 that helped pave the way for BCS, describe the immediate impact of BCS on a small segment of the Princeton physics community in the early spring of 1957, and discuss the extent to which the Bardeen–Pines–Frohlich effective electron-electron interaction provided a criterion for superconductivity in the periodic system. I describe my lectures on BCS at Niels Bohr's Institute of Theoretical Physics in June 1957 that led to the proposal of nuclear superfluidity, discuss nuclear and cosmic superfluids briefly, and close with a tribute to John Bardeen, whose birth centennial we celebrated in 2008, and who was my mentor, close colleague, and dear friend.

The essay below is an attempt to re-create the wonderful scientific atmosphere that emerged after the basic BCS ideas first arrived in Russia in 1957. It summarizes the most significant contributions to the microscopic theory of superconductivity by Russian physicists during the next few years that gave the theory its modern form.

After short comments on my early addenda to BCS — gauge invariance and the Anderson–Higgs mechanism, the dirty superconductor “theorem,” and the spinor representation — I focus on the interaction mechanisms which cause electron–electron pairing. These bifurcate into two almost non-overlapping classes. In order to cause electrons to pair in spite of the strong, repulsive, instantaneous Coulomb vertex, the electrons can evade each others' propinquity on the same site at the same time either dynamically, by retaining Г^° (s-wave) relative symmetry, but avoiding each other in time — called “dynamic screening” — or by assuming a non-symmetric relative wave function, avoiding each other in space. All simple metals and alloys, including all the (so far) technically useful superconductors, follow the former scheme. But starting with the first discovery of “heavy-electron” super-conductors in 1979, and continuing with the “organics” and the magnetic transition metal compounds such as the cuprates and the iron pnictides, it appears that the second class may turn out to be numerically superior and theoretically more fascinating. The basic interaction in many of these cases appears to be the “kinetic exchange” or superexchange characteristic of magnetic insulators.

Following Brian Josephson's prediction in 1962, Anderson and Rowell observed Josephson tunneling in 1963. The following year, Jaklevic, Lambe, Silver and Mercereau demonstrated quantum interference in a superconducting ring containing two Josephson tunnel junctions. Subsequently, the first practical devices emerged, including the point-contact dc and rf SQUIDs (Superconducting QUantum Interference Devices) of Zimmerman and Silver and Clarke's SLUG (Superconducting Low-inductance Undulatory Galvanometer) — a blob of solder frozen around a length of niobium wire. The return to the tunnel junction as the Josephson element was heralded by the cylindrical SQUID in 1976. The square washer dc SQUID developed by Ketchen and Jaycox in 1982 remains the workhorse design for most applications. Theories for the dc and rf SQUIDs were worked out in the 1970s. Today, SQUIDs (mostly dc) are used in a variety of configurations — for example, as magnetometers, gradiometers, cryogenic current comporators, low-frequency and microwave amplifiers, and susceptometers — in applications including magnetoencephalography, magnetocardiography, geophysics, nondestructive evaluation, precision gyroscopes, standards, cosmology, nuclear magnetic resonance, reading out superconducting quantum bits, and a myriad of one-of-a-kind experiments in basic science. Experiments are described to search for galaxy clusters, hunt for the axion, and perform magnetic resonance imaging in microtesla fields.

In this pedagogical review, we discuss how electrical resistance can arise in superconductors. Starting with the idea of the superconducting order parameter as a condensate wave function, we introduce vortices as topological excitations with quantized phase winding, and we show how phase slips occur when vortices cross the sample. Superconductors exhibit non-zero electrical resistance under circumstances where phase slips occur at a finite rate. For one-dimensional superconductors or Josephson junctions, phase slips can occur at isolated points in space-time. Phase slip rates may be controlled by thermal activation over a free-energy barrier, or in some circumstances, at low temperatures, by quantum tunneling through a barrier. We present an overview of several phenomena involving vortices that have direct implications for the electrical resistance of superconductors, including the Berezinskii-Kosterlitz-Thouless transition for vortex-proliferation in thin films, and the effects of vortex pinning in bulk type II superconductors on the nonlinear resistivity of these materials in an applied magnetic field. We discuss how quantum fluctuations can cause phase slips and review the non-trivial role of dissipation on such fluctuations. We present a basic picture of the superconductor-to-insulator quantum phase transitions in films, wires, and Josephson junctions. We point out related problems in superfluid helium films and systems of ultra-cold trapped atoms. While our emphasis is on theoretical concepts, we also briefly describe experimental results, and we underline some of the open questions.

An overview is given of a number of pair-breaking interactions in superconductors. They have in common that they violate a symmetry of the pair state. In most cases pairs are formed from time reversed singleparticle states, a noticeable exception being antiferromagnetic superconductors. When time reversibility is broken by an interaction acting on the electrons, the time evolution of the time-reversal operator plays an important role. Depending on whether it is nonergodic or ergodic, we deal with pair weakening or pair breaking. Numerous different interactions are analyzed and discussed. Unifying features of different pair-breaking cases are pointed out. Special attention is paid to the Zeeman effect and to scattering centers with low-energy excitations. The Kondo effect and crystalline field split rare-earth ions belong in that category. Modifications caused by strongly anisotropic pair states are pointed out. There is strong evidence that in some cases intra-atomic excitations lead to pair formation rather than pair breaking for which an explanation is provided.

Superconductor-insulator transitions, especially in thin films, can provide the simplest examples of the continuous quantum phase transition paradigm. Quantum phase transitions differ from thermal phase transitions in that they occur at zero temperature when the ground state of a system is changed in response to a variation of an external parameter of the Hamiltonian. In the example of the superconductor-insulator transition, this control parameter could be the parallel or perpendicular magnetic field, disorder, or charge density. Quantum phase transitions are studied through measurements at nonzero temperature of physical behaviors influenced by the quantum fluctuations associated with the transition. This review will focus on experimental aspects of superconductor-insulator transition in disordered films that are effectively two-dimensional. In particular, the evidence for quantum critical behavior in the various types of transitions will be presented. The various theoretical scenarios for the transitions will also be discussed along with the extent to which they are supported by experiment. Open questions relating to the nature of the very puzzling insulating regime and whether there are many different types of superconductor-insulator transitions will be presented. Although this research area is more than 20 years old, rather central issues are not resolved.

An overview is given of the new theories and experiments on the phase diagram of type II superconductors, which in recent years have progressed from the Abrikosov mean field theory to the “vortex matter” picture. We then detail some theoretical tools which allow to describe the melting of the vortex lattice, the collective pinning and creep theory, and the Bragg glass theory. It is followed by a short presentation of other glass phases of vortices, as well as phases of moving vortices.

An overview is given of our present understanding of superconductivity with spontaneously broken translation symmetry in polarized Fermi systems. The existence of “crystalline” superconducting phases is considered in a wide range of systems, prominent examples being conduction electrons in metals, ultra-cold atoms in a trap, nuclear matter and dense quark systems. The underlying physics is delineated and theoretical approaches to the inhomogeneous phases and their properties are discussed. From the experimental side, it is argued that superconductivity with imbalance-induced order parameters is realized in layered organic compounds and potentially in heavy-fermion systems.

After providing some history and background material regarding the evolution of research on superconductivity, a description of the use of the BCS theory for the development of approaches for calculations and predictions of superconducting properties will be given. The emphasis is on estimates of T_c raising T_c, and predicting new superconductors. The basic analysis will be based on the BCS formalism with modern extensions. The focus here is on phonon mediated pairing of electrons as described in the original BCS paper augmented by current modifications and the use of modern calculational approaches.

The rise of the superconducting transition temperature T_c has been reviewed in three major superconducting systems: the cuprate, the Fe-pnictide and the heavy fermion. While the first two systems display high T_cs, heavy fermion superconductors show low T_c but embody many crucial features found in the others. The prospect of future superconductors with higher T_c, preferably close to room temperature, is also discussed. Those interested in the detailed physics of high temperature superconductivity are referred to the article by E. Abrahams in the next chapter of this book and reviews published elsewhere.

Theoretical developments concerning the high transition temperature cuprate superconductors are reviewed.

Following the success of the original BCS theory as applied to superconductivity in metals, it was suggested that the phenomenon of Cooper pairing might also occur in liquid 3-He, though unlike the metallic case the pairs would most likely form in an anisotropic state, and would then lead in this neutral system to superfluidity. However, what had not been anticipated was the richness of the phenomena which would be revealed by the experiments of 1972. In the first place, even in a zero magnetic field there is not one but two superfluid phases, and the explanation of this involves ideas concerning “spin fluctuation feedback” which have no obvious analog in metals. Secondly, the anisotropic nature of the pair wave function, which in the case of the B phase is quite subtle, and the fact that the orientation must be the same for all the pairs, leads to a number of qualitatively new effects, in particular to a spectacular amplification of ultra-weak interactions seen most dramatically in the NMR behavior. In this chapter I review the application of BCS theory to superfluid 3-He with emphasis on these novel features.

After an introduction into 100 years of research on superfluidity and the concept of the BCS-BEC crossover, we describe recent experimental studies of a spin-polarized Fermi gas with strong interactions. Tomographically resolving the spatial structure of an inhomogeneous trapped sample, we have mapped out the superfluid phases in the parameter space of temperature, spin polarization, and interaction strength. Phase separation between the superfluid and the normal component occurs at low temperatures, showing spatial discontinuities in the spin polarization. The critical polarization of the normal gas increases with stronger coupling. Beyond a critical interaction strength all minority atoms pair with majority atoms, and the system can be effectively described as a boson-fermion mixture. Pairing correlations have been studied by RF spectroscopy, determining the fermion pair size and the pairing gap energy in a resonantly interacting superfluid.

This article describes extensions of BCS theory to atomic nuclei and neutron stars, to high density quark matter and connections to pairing in ultracold clouds of atomic fermions.

This article is based on a talk given at a Symposium at the University of Illinois on the occasion to commemorate the 50th anniversary of BCS — I gave a historical overview of how BCS theory has come to be transplanted to particle physics and has helped solve its problems.

The BCS theory injected two powerful ideas into the collective consciousness of theoretical physics: pairing and spontaneous symmetry breaking. In the 50 years since the seminal work of Bardeen, Cooper and Schrieffer, those ideas have found important use in areas quite remote from the stem application to metallic superconductivity. This is a brief and eclectic sketch of some highlights, emphasizing relatively recent developments in QCD and in the theory of quantum statistics, and including a few thoughts about future directions. A common theme is the importance of symmetry transmutation, as opposed to the simple breaking of electromagnetic U(1) symmetry in classic metallic superconductors.

This article is based on the talk given by Steven Weinberg at BCS@50, held on 10–13 October 2007 at the University of Illinois at Urbana-Champaign to celebrate the 50th anniversary of the BCS paper. For more about the conference see http://www.conferences.uiuc.edu/bcs50/.

The following sections are included:

• INDEX