True Genius: The Life and Science of John Bardeen: The Only Winner of Two Nobel Prizes in Physics (2002)

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11 Cracking the Riddle of Superconductivity T he network of support Bardeen found at the University of Illinois formed the backdrop for his continuing work on superconductivity. A year after Serin’s call in May 1950 with the insight about the lattice vibrations, Bardeen was still struggling to make further progress. In July he complained to Rudolf Peierls that all the methods he had tried for treating superconductivity had failed. Still he sensed the work was moving in the right direc- tion. “I believe that the explanation of the superconducting proper- ties is to be found along the lines suggested by Fritz London.” The hint that bolstered Bardeen’s confidence was small but sig- nificant: “The wave functions for the electrons are not altered very much by a magnetic field.” From this “rigidity” of the super- conducting wave function Bardeen derived his sense of certainty about the nature of the solution. The rigidity followed from the energy gap. Somehow, he believed, it had to do with the long-range ordering. That was, he guessed, why superconductors expel magnetic fields (the Meissner effect). But these were only intui- tions. He could not yet express them in any language, not even that of mathematics. Bardeen’s notes and letters about superconductivity let others follow the painstaking route he now took in approaching the riddle. In 1951 his handwritten notes include the following list of smaller problems he thought would be useful to solve along the way: 190 

Cracking the Riddle of Superconductivity 191 (1) Derivation of London equations for multiply connected body (2) Proof of current and effective mass theories for one-electron wave functions (3) Analysis of diamagnetic properties of gas of electrons with small effective mass (4) Extension of 3 to include high frequencies and scattering of electrons (effect of electric field) (5) Boundary energy for thin films (6) Better calculation of interaction energies (7) Specific heat and other thermal properties. All these “sub-problems” involved situations that were accessible through experimental or theoretical research. The first one deals with experiments in which currents were observed to flow indefinitely around a ring (a multiply connected body). The current and effective mass theories in the second item refer to Bardeen’s wish to fully understand the theory of single- electron wave functions. Diamagnetic properties were critical because of the observation that superconductors expel magnetic fields. Examining the case of high frequencies enabled drawing on experiments offering information about the dynamics of super- conductors. Boundary and interaction energies were important to research, especially for thin-film experiments in which one can study the region near the surface where magnetic fields are not completely excluded, as in the thick sample case. Finally, the spe- cific heat and other thermal properties were measurable properties that could test one’s understanding of the superconducting state. These problems could not be treated using a free-electron model. They resulted, Bardeen knew, from the countless inter- actions between electrons and between electrons and the lattice. Bardeen worried that in using the standard Hartree-Fock approxi- mation method, which assumed that electrons move independently in a self-consistent field, he might be eliminating a crucial—per- haps the most crucial—aspect of the system. As he stated in a talk given later that year, he hoped to draw on the new field theory tools developed shortly after World War II by Richard Feynman, Julian Schwinger, and Sin-itero Tomonaga. “It was becoming clear that field theory might be useful in solving the many-body prob- lems of a Fermi gas with attractive interactions between the particles.” Routinely taught to theory graduate students by 1950, field theory had not been part of Bardeen’s training. The fastest way for 

192 TRUE GENIUS him to draw on the new formalism would be to take on a collabora- tor. He was particularly interested in exploring the many-body for- malism that David Bohm, one of Robert Oppenheimer’s doctoral students, had developed in Berkeley. Bohm’s original theory concerned the electron–electron inter- actions in the ionized gases known as electron plasmas, a problem of interest to the Manhattan Project, for plasmas were relevant in separating uranium isotopes electromagnetically. Bohm had con- tinued to work on the problem after he joined the faculty at Princeton in 1946. With his graduate students, Eugene Gross and David Pines, Bohm extended the techniques he had developed to modeling the electron interactions in the electron gas. Learning of Bohm’s work on a visit to Princeton during the spring of 1950, Bardeen became interested in how Bohm’s theory separated the long-range Coulomb interactions from the short- range single-particle excitations. He thought the techniques might also work in treating the electron–electron interactions in super- conductors. He asked Bohm in 1951 whether any of his students might be interested in a postdoctoral position at Illinois. Bohm suggested Pines, who arrived in Urbana in July 1952. Bardeen asked Pines to start by looking at a simpler problem that appeared to involve some of the same physics as super- conductors. The problem of the polaron, which Herbert Fröhlich had studied earlier, dealt with how an electron distorts a crystal lattice as it moves along in it—in analogy with the way that a child distorts the mattress of a soft bed as he or she walks on it. In the polaron problem it is the ions in the crystal that cause distortion of the lattice around the electron that moves along. In employing the technique of “canonical transformations” and writing down a de- scription of the energy in terms of operators that can remove or add particles to the system (the method of “second quantization”), Fröhlich had been among the first to introduce field theory con- cepts into solid-state physics. Bardeen wanted to extend this work to how the electrons couple with the movement of the ions to form waves (“lattice vibrations”). In discussing the problem with Tsung-Dao Lee, a young theorist (and future Nobel laureate) who was spending the summer of 1952 in Urbana as Bardeen’s postdoc, Pines realized that the “intermedi- ate coupling method,” which Lee had recently used in his own field theory studies, could be adapted for the polaron problem. Francis 

Cracking the Riddle of Superconductivity 193 Low, an assistant professor in the Illinois physics department, also joined the discussion. In their subsequent paper, Lee, Low, and Pines formulated the polaron problem in such a way that it could later be applied directly to the ground-state wave function specify- ing the state of lowest energy in a superconductor. Bardeen also worked with Pines to extend the Bohm-Pines for- malism to treat the coupling of electrons to the lattice vibrations. One calculation compared the two kinds of electron–electron interactions: the attractive interaction induced by the lattice vibrations (or “phonons”) and the ordinary repulsive interaction deriving from the fact that like charges repel. Gradually Pines and Bardeen came to understand that the attractive phonon-induced interaction arises in situations like that of the polaron, in which an electron moves along in the crystal pulling the positive lattice in toward it. When the lattice moves in, it pulls along other electrons as well, so that the electrons are in effect attracting one another. They also repel one other in the ordi- nary way because they are like charges. But in their calculations Bardeen and Pines found that in cases where the energy transfer is small, the attractive interaction is actually stronger than the repul- sive one. This exciting result implied that for pairs of electrons near the Fermi surface the net interaction is attractive! Could this be the mechanism behind superconductivity? It would take Bardeen five more years to fully answer this question, in the affir- mative. In 1953 Bardeen undertook an extensive literature study of superconductivity for an article that he agreed to author for the Handbuch der Physik, a major review encyclopedia. Each year the editor, then Sigfried Flügge, selected a research topic that he judged ripe for review and commissioned authors to write on the topic. For the 1956 Handbuch, Flügge selected low-temperature physics as the topic. He asked Bernard Serin to review the experimental situa- tion and Bardeen the theoretical outlook on superconductivity. Bardeen concentrated on the review during 1954, writing almost 100 pages. Trying to identify the missing pieces in the current understanding of superconductivity and the concepts that would be needed to develop a complete theory, he argued for the London notion of an “ordered phase in which quantum effects extend over large distances in space.” He ventured to say that super- conductors are “probably characterized by some sort of order 

194 TRUE GENIUS parameter which goes to zero at the transition,” admitting, how- ever, that “we do not have any understanding at all of what the order parameter represents in physical terms.” Bardeen’s article also explored the nature of the phase transi- tion between the normal and superconducting states. Following Fritz London, he tried to unravel the meaning of the energy gap in the electronic excitation spectrum resulting from the “rigidity” of the wave function. At this stage Bardeen could not yet explain such a gap, but by assuming its existence he could show how to develop both the electrodynamic properties of superconductors and a gen- eralization of the London equations, resembling the empirically based nonlocal formulation of superconductor electrodynamics that Pippard had put forth several years earlier. Another focus of Bardeen’s review was the theoretical machin- ery for computing the interactions between electrons or between electrons and phonons (lattice waves) in the superconductor. Appealing to recently developed field theory techniques, including Tomonaga’s strong-coupling approach and the Bohm-Pines theory, he underscored the importance of considering the electrons as elec- trically screened by the cloud of positive charge surrounding them when they travel through the system. Bardeen’s review concluded: “A framework for an adequate theory of superconductivity exists, but the problem is an exceedingly difficult one. Some radically new ideas are required.” In the period when Bardeen was working on his Handbuch article, J. Robert Schrieffer—the “S” of the BCS (Bardeen-Cooper- Schrieffer) theory of superconductivity—came to Urbana from MIT. He arrived in the fall of 1953, having written an undergraduate thesis under John Slater on the energy-level spacing in the multiplet structure of transition metal atoms. His exposure to the work of Slater’s group had whetted Schrieffer’s appetite for theoretical physics. He developed “a model in my own mind of how creativity takes place and how this structured process of going from the known to the unknown in finite steps is very important.” He also came to realize that “one can’t make the intuitive leap immediately, and there is a heck of a lot of hard tough work that goes in between.” Schrieffer was not completely happy with Slater’s approach. He felt that the people in Slater’s group seemed to be “doing numerical calculations on and on.” Schrieffer decided that he “wanted to have a graduate education which perhaps allowed more 

Cracking the Riddle of Superconductivity 195 flexibility for individual creativity.” Applying to several graduate programs, he was “shocked” to receive a letter from the University of Illinois inviting him to work with Bardeen. He had “heard out- standing things about Professor Bardeen.” On the day Schrieffer came to meet his new advisor, Bardeen’s office appeared to be empty. But while Schrieffer wandered around the building, “I passed a gentleman on the steps three times in a row, and it happened to be Professor Bardeen.” Schrieffer spent the next year and a half taking courses, working out physics problems, and experimenting in Bardeen’s semiconductor laboratory. Schrieffer met with Bardeen “at least weekly and often more fre- quently.” He never felt “any problem of coming and chatting with him. He was sympathetic, always suggesting how to get around difficulties.” In the spring of 1955, after working with Bardeen for a year and a half, Schrieffer approached Bardeen about selecting a thesis topic. Well prepared, Bardeen reached into his bottom drawer and pro- duced a list of about ten problems that he considered suitable. When Schrieffer glanced at the list, he noticed that one question involved explaining why a metal with a magnetic impurity shows a resistance minimum in the electrical resistivity versus tempera- ture curve. Normally the resistivity rises with temperature in a smooth curve. Bardeen and other many-body theorists recognized that explaining this resistance minimum was an important prob- lem years before Jun Kondo solved it in the late 1960s. Schrieffer’s attention fixed on the last item on the list, super- conductivity. “Why don’t you think about it?” said Bardeen. Schrieffer understood that selecting superconductivity for his thesis would be risky. The problem “had been worked on for a long time and workers had met a lot of failures.” He also knew something about the problem already, having helped to proofread Bardeen’s Handbuch article. “The question I had in my mind was: was there something that I might do and that I might contribute? The other question was whether Professor Bardeen himself would be concen- trating on this area, so that we would have in some sense a useful interaction.” Schrieffer sought the advice of Francis Low. “How old are you?” Low asked him. “Twenty-four.” “Well, you can waste a year of your life and see how it goes.” Schrieffer took this answer “as 

196 TRUE GENIUS reasonable evidence that he felt there might be some chance of doing something.” “OK, fine,” said Bardeen when Schrieffer told him he would work on superconductivity. Bardeen mentioned that Leon Cooper, a young theorist trained at Columbia University would be joining them. He explained that Cooper “had a field theory background and that this might be useful.” Cooper had studied nuclear theory under James Rainwater, who, in 1975, would share a Nobel Prize with Aage Bohr and Ben Mottelson for developing a theory of nuclear structure based on connecting ideas of collective motion and particle motion in the nucleus. The addition of Cooper—the “C” of BCS—had been another consequence of Bardeen’s creative use of teamwork. Pines was scheduled to leave Urbana at the end of the 1954–1955 academic year to take a teaching post at Princeton. Still concerned about his own limited training in field theory and Feynman’s and Fröhlich’s considerable advantage in this area, Bardeen had looked for some- one else “versed in field theory who might be willing to work on superconductivity.” In the spring of 1955, Bardeen telephoned the theorist Chen Ning Yang, then at the Princeton Institute for Ad- vanced Study, and asked for a recommendation. Bardeen recalled that “one of the active many-body problems at that time was the structure of the nucleus—many neutrons and protons making up a nucleus. I thought that someone with a back- ground in that field could provide useful information to the problem of the interaction of the electrons and the vibrations of the crystal lattice of the metal and what made it superconducting.” Yang recommended Cooper, who was spending a postdoctoral year at the institute. Cooper was up-to-date in “the latest and most fash- ionable theoretical techniques” (at that time, Feynman diagrams, renormalization methods, and functional integrals). When Bardeen stopped by the institute to meet Cooper, the younger physicist began by saying he didn’t know anything about superconductivity. Bardeen told him “that didn’t matter, that he’d teach me everything and that he was looking for someone who was familiar with current field theoretic techniques.” Cooper also told Bardeen that he doubted field theory would be of any use in ex- plaining superconductivity. But he added that he was ready to leave Princeton. By then, “progress in field theory seemed rather discour- aging.” Although most of the theorists at the institute were still 

Cracking the Riddle of Superconductivity 197 working on the consequences of the great breakthroughs in field theory, the “first flush had already passed.” Reflecting on the work of Schwinger, Feynman, and Tomonaga, they “used to sit around saying, ‘These guys solved all the easy problems and left the hard ones for us.’” Einstein’s death that spring also cast a shadow over the institute. Cooper pondered Bardeen’s offer for a few months. Then early in the summer, while in Sicily, he decided that superconductivity would be “my problem I was going to solve.” He returned to Princeton and drove to Urbana. When Cooper arrived, he found he “really didn’t like the geography” of this “corn-field place.” But he soon discovered that “the department was wonderful. The people were wonderful. It was a fantastic environment.” He vividly recalled the “parties and comradery. And we were always together.” Bardeen asked Cooper to offer a series of informal seminars on field theory as it was used in electrodynamics and to speculate on how it might possibly inform problems of many-body theory. Cooper talked about Feynman diagrams that corresponded to virtual excitations of the Fermi gas. He included a discussion of Feynman’s notion that a positron (antielectron) or a hole are equiva- lent to an electron going backwards in time. Cooper said that the diagrammatic methods were “by and large perturbative techniques rather than techniques which would lead to phase transitions or a qualitative change of the nature of the matter in question.” Schrieffer found Cooper’s talks “very clear,” but he was bothered by his pessimism about whether the techniques could help with superconductivity. Cooper did think that Schwinger’s work on coupled Green’s function methods might be useful, as they were not necessarily perturbative methods. But “we didn’t want to use totally unfamil- iar mathematics,” Schrieffer recalled, so that line was dropped. It was later taken up successfully by Lev Gor’kov in the Soviet Union. To help Cooper educate himself about superconductivity, Bardeen suggested he read two recent texts, one by Fritz London, the other by David Shoenberg. London’s book, published in 1950, offered a reformulation of his earlier ideas about electrons ordered in a system over large distances in a macroscopic quantum state. London called superconductivity a “quantum structure on a mac- roscopic scale.” The state resulted from “a kind of solidification or 

198 TRUE GENIUS condensation” of the average momentum distribution of the elec- trons. Cooper, who also took his turn proofreading Bardeen’s Handbuch article, agreed that “if we got something like London’s long-range order then we’d get superconductivity.” The mathemati- cal problem was to fill in the intermediate steps. The notion of broken symmetry proved a fertile framework for conceptualizing superconductivity. It describes, for example, the case of a spherical magnet in which the magnetic field is free to point in any direction. But any given spherical magnet always has a north and south pole: the fact that it chooses a certain direction for its axis breaks the system’s symmetry. A more familiar example of broken symmetry is found at the bottom of an ordinary wine bottle, one in which the center of the bottom edge curves upwards. If the bottle were symmetrical, the residue particles would all sit just at the center, on top of the bump. But for any real bottle, things are not symmetrical, so most or all the particles roll down and come to rest at one of the infinite number of places around the edge, which have lower elevation. By choosing any one place to roll down to, the particle breaks the symmetry. Cooper focused on the energy gap. For the case of a normal metal, “you sort of knew what that was like.” But for the super- conductor, it “was qualitatively different. The question was how does that come about?” He argued that if there was “such a radical difference as a single particle energy gap, chances are everything else is going to come out.” It seemed to Cooper “that this was really a very simple problem,” one that should be soluble by “just elementary quantum mechanics. And why am I throwing all of this apparatus at it?” In later years, Cooper described his own approach to problem solving as first examining the simplest possible version of the prob- lem that retained the essential features. “I think one of the ways people delude themselves is to try to solve the more complicated problem before trying to solve the simpler problem that’s along the way.” The approach was a version of the one Bardeen claimed to have learned from Wagner. In the last months of 1955 Cooper turned to “what happens if you have a highly degenerate system with an attractive inter- action.” He examined the simple case of two electrons just outside the Fermi surface, spinning in opposite directions. He tried “to see 

Cracking the Riddle of Superconductivity 199 how, under what assumptions could you get a Meissner effect.” Making certain assumptions, he showed that if the net force between the two electrons is attractive, they will form a bound state lying below the normal continuum of states and separated from the continuum by an energy gap. By late February or early March of 1956, “it seemed clear that if somehow the entire ground state could be composed of such pairs, one would have a ground state with qualitatively different properties from the normal state.” And this ground state—the state of superconductivity—would be separated from the excited states by an energy gap. Cooper “was very excited,” said Schrieffer, who remembered the day Cooper discovered the bound state. It “was there regardless of how weak was the coupling.” Cooper recalled, “I was reasonably excited by these results. But I became aware, painfully, in the months that followed how long the road still was.” For at this stage, Cooper’s communication with Bardeen temporarily broke down. “We went through a period where he thought I was out of my mind.” It was not that Bardeen did not recognize the importance of the Cooper pairs, but rather that he did not want to let the enthusiasm of this step obscure the need, and difficulty, of developing a detailed solution that would consolidate all the known facts. He recognized the vast amount of work that still needed to be done before the problem could be considered solved. As Cooper saw it, “Bardeen couldn’t figure out what I was doing.” Despite the tension that now ensued, Cooper still felt that all three formed a remarkable team in which “each contributed parts that were so essential.” Years later he said, “I can’t imagine any more cooperative feeling. The advance of one was the advance of another.” The team’s interplay recalled the collaborative atmo- sphere of the Bell Labs semiconductor team before the invention of the transistor. Bardeen structured the BCS team on his favorite social model, the family. He was the patriarch and the children were expected to pitch in. In making assignments, motivating members, and plant- ing theoretical seeds, he tried to use the unique talents of each member. Like his own father, Bardeen treated his students as fellow explorers, giving them latitude and allowing them to suffer consequences of their actions. He shared with them his deep under- standing of the quantum theory of solids, which went “all the way back to the very beginning, back to the 1930s,” said John Miller. 

200 TRUE GENIUS When discussing a problem, Bardeen often impressed his students and younger colleagues with his ability to cite specific steps from particular sections of a work he had read. Breaking down the problem of superconductivity into smaller parts, he asked Schrieffer to look into the “t-matrix methods” that Keith Brueckner had recently developed in studying nuclei. He asked Cooper to examine the Bohm-Pines theory and the Bardeen- Pines work in 1954 on the electron–electron interaction. Mean- while he sought other leads. Schrieffer emphasized “the enormous fun it was for the family to work together.” Jane Bardeen, “one of the most affable, lovable, outgoing people,” played the role of the nurturing mother. “From the very beginning I was invited as part of their family,” said Schrieffer. He recalled telling Betsy stories “about snakes and alligators in Florida.” Typically Bardeen and Cooper would work independently in their shared office, Room 307 in the Physics Lab on Green Street. Schrieffer worked in a larger room upstairs, between the third and fourth floors, shared with other graduate students. A sign on its door read “Institute for Retarded Study.” For a graduate student in that period, “if somehow you were able to move to the Institute for Retarded Study, you had made it.” Whenever a desk opened up, “everyone would sort of scramble around to see who could get in there.” Schrieffer found that he learned as much as he did in his courses from talking with other students in that room. When Schrieffer came to Bardeen’s office, to speak with either Cooper or Bardeen, both would “wheel around their chairs” and join the discussion. “It was a sort of round robin, where I think John and Leon probably didn’t talk too much more than that,” said Schrieffer. Schrieffer also recalled the collaboration as “a very happy relationship, which largely came about because there weren’t enough offices for everyone.” “He was very stubborn,” Cooper said, recalling the work with Bardeen, but “I was very stubborn too!” Cooper was constantly amazed at how quickly the older physicist could calculate and learn. “For example, if I would suddenly understand something he didn’t understand, then I’d show him, you know, one morning— BAM!—he had it instantly. He was using it in the afternoon. He was very fast.” Schrieffer claims that he and Cooper both gained an apprecia- 

Cracking the Riddle of Superconductivity 201 tion for Bardeen’s style of doing physics—his taste in choosing problems, his experiment-based methodology, the way he broke problems down, and his approach of using as little theoretical machinery as possible, “the smallest weapon available in your arsenal to kill a monster.” Schrieffer also found useful the advice that Bardeen passed down from Wigner: “to divide up the problem into small pieces, and attack each one.” In the version that Schrieffer later recalled, there was an added maxim “to focus your shots so that each one counts, and then reassemble.” Bardeen “was always very leery of someone who started out with a grand formalism and deduced proof.” He felt that it was more effective to work on the “little problems along the way.” By synthesizing the smaller components into the larger picture, “the big problem will get solved by nature if you just keep at it.” Of utmost importance was “carefully deciding which is the essential piece.” It seemed to Schrieffer that this was “how [Bardeen] went about everything—thinking about it carefully and isolating those pieces which were relevant. And then coming back.” Bardeen took very seriously the suggestions laid out in the last chapter of London’s book on how to proceed toward a microscopic theory. He felt that “those suggestions were exactly the direction one should go,” although how to “transcribe that into mathemati- cal reality and detailed theory was far from clear.” Schrieffer re- membered that Bardeen “kept saying in effect, ‘This system has to be rigid. There has to be a gap.’” In agreement with London, Bardeen stressed that the condensation of electrons had to occur in momen- tum space, not ordinary space. Bardeen adopted other guiding ideas of London as well. One was that “in an isolated simply connected superconductor and for a given applied field, there is only one stable current distribution” (as a consequence of the Meissner effect). Another posited that in thermal equilibrium there is no “permanent current in an isolated superconductor (in agreement with Bloch’s theorem) except in the presence of an applied magnetic field.” Another was that “there is no conservation of these currents; they differ for every variation of the strength or direction of the applied field.” Bardeen pressed his team to clarify the notion of long-range order using a “phase coherence” parameter that determines the size of a Cooper pair over whatever distance their motions are corre- 

202 TRUE GENIUS lated. Pippard had proposed that this distance was of the order of a micron. Schieffer remarked that Bardeen “had a feeling” the con- densation involved only the electrons close to the Fermi surface. Out of roughly 1023 electrons in every cubic centimeter, only 1019 will be close to the Fermi surface, but this is still an enormous number of condensed electrons! In the 1920s Niels Bohr had helped younger physicists of his generation seek the as-yet-unknown quantum mechanics by formulating a theoretical bridge known as the “correspondence principle.” The principle created a link between wave mechanics and Newtonian mechanics as one approaches macroscopic systems, the limit of high quantum numbers. Similarly Bardeen helped his team strike out into the unknown by offering a principle that would bridge the poorly understood theory of interacting electrons in the normal state with the properties of states of noninteracting elec- trons. Anticipating Lev Landau’s theory of Fermi liquids, Bardeen realized that, although in the normal state electrons are not free, one could assume a one-to-one correspondence between interacting states and free electron states. One can arrive at the interacting gas by turning on the interaction slowly and deforming the free- electron gas continuously into the interacting system. He expected a one-to-one correspondence between the states of real super- conductors with simplified states in which one included only the weak interactions responsible for superconductivity. What they needed to do, Bardeen said, was “to think of the normal state as like a free electron gas, with the excitations being in one-to-one correspondence with those of a free electron gas—the interactions between the actual electrons are enormous, but we have to think in terms of effective excitations which include these strong interactions insofar as they enter the normal state.” In other words, Bardeen assumed that the bulk of the interaction effects would shape the normal state and that small residual interactions which occur in the normal state, but are not fully taken into account theoretically, would lead to superconductivity. He felt that one should start by simply studying the effects of these residual interactions on free electrons. Bardeen was, Schrieffer explained, introducing a basic tenet of the Fermi liquid theory, to be developed by Landau, the idea of “quasi-particles,” “effective electrons” existing in a one-to-one correspondence with the electrons of a free electron gas. Bardeen 

Cracking the Riddle of Superconductivity 203 introduced this formulation independently of Landau, at a time when the notion of quasi particles was not yet firmly grasped in the Western world. Cooper continued to feel that Bardeen was ignoring the break- through he had made several months after his arrival in Urbana. He spent almost a “year in the wilderness” trying to convince Bardeen that pairing held the key to the solution. He recognized the psychology of his position: “Here I am, totally unknown, this wild-eyed kid. . . . And I say, well that’s the solution.” Bardeen insisted that Cooper’s solution was not complete. They did not yet know how to go from a single “Cooper pair” to a full- blown many-electron theory. “We tried many techniques,” Schrieffer recalled but “things just didn’t jell.” A major hurdle was coping with many pairs at the same time, most of which over- lapped. Even conceptualizing the situation was very difficult. More than a year later Schrieffer found a way to portray the problem using the analogy of a crowded dance floor on which many couples are doing the Frug. In this popular late-1950s dance, the members of couples dance separately but remain bound to one an- other, even when they are far apart and other dancers come be- tween them. The problem was how to represent this situation mathematically. “It was very perplexing to us.” Schrieffer remem- bers Bardeen saying, “Well, it’s in momentum space. You shouldn’t think about the coordinate space so much. It may not be confusing if you view it in the right language.” In seeking wave functions, they worried about the validity of their approximations. If they worked only with the part of the system responsible for pairing, might they be ignoring something else that was even more important? Schrieffer recalled, “We were feeling a little bit downtrodden because things weren’t breaking so quickly after Leon’s contribution.” On November 1, 1956 Schrieffer ran into Bardeen on the street. Bardeen smiled, “Oh, I just wanted to mention—I won the Nobel Prize. ” He was still adjusting to the news, which had taken him by surprise at 7 a.m. while he was in the kitchen frying eggs for the family. He had assumed this duty temporarily because Jane was still under doctor’s orders to rest after her bout with typhoid fever the previous summer. Suddenly Betsy and Bill rushed into the 

204 TRUE GENIUS kitchen shouting that he won the Nobel Prize. It had been announced on the CBS World News Roundup. John dropped the frying pan. “Well, I guess I better go shave,” John drawled during break- fast, when the whole family heard the announcement repeated. Jane scribbled down some notes about that day. “The children were ju- bilant, John a bit pale with a dreamy abstracted look.” After she sent them all off to school, “receiving congratulations was my pleasant chore all day.” Brattain was among the many who phoned. Wheeler Loomis had asked Jane to keep John home. That evening she served a steak dinner in an attempt at “a normal Thurs- day evening.” When the doorbell rang, Bardeen opened the door. He saw Loomis followed by a parade of “about 60 physicists and wives marching down the road carrying flashlight ‘torches’ and singing ‘For He’s a Jolly Good Fellow.’” They brought “champagne, cups and cakes” for an “instant and gala party.” “It was really thrill- ing,” Jane recalled, to see “all those people in the dark, coming down the hill, singing and waving their lights.” Paul Handler reported, “Everybody was elated, everybody was on a high.” Reporters clustered outside Bardeen’s home and office in the days following the announcement. The Washington Observer, the local paper in Washington, Pennsylvania, announced, “Husband of Former Local Girl Nobel Prize Winner.” Congratulatory notes and telegrams poured in from colleagues and friends. Wigner wrote, “I can’t tell you how proud I am of our past association and how much pleasure I derive from this honor that came your way.” The prize was “a matter of great personal pleasure and satisfaction to me,” wrote John Van Vleck. “I like to recall that both you and Brattain studied Quantum Mechanics with me, although I would not for a moment claim that this had anything to do with your careers.” He added, “Also, it is fine to have a recipient who is a Madisonian, a Wisconsin graduate, and a member of the Harvard Society of Fellows. Furthermore, one should not overlook the Minnesota angle, since you and I both taught there, Abigail [Van Vleck’s wife] graduated there, and this is where Brattain took his Ph.D. All told, the award is most satisfying.” Dutch Osterhoudt, Bardeen’s college friend and Gulf Labs colleague, wrote, “Gretchen and I got a thrill when we heard the first announcement over the radio.” Bardeen was deeply gratified by the prestigious award, but a part of him could not fully engage in the celebrations and congratu- 

Cracking the Riddle of Superconductivity 205 lations. Deep within, “he felt he didn’t deserve a Nobel for the transistor,” reflected David Lazarus. In late November Bardeen wrote to E. J. W. Vewey at Philips Laboratory, “I suspect that the worry of many of those on the committee was whether the science itself was worthy of the award. I have my doubts of that myself.” The celebrations were a huge distraction from his work on superconductivity. Schrieffer and Cooper may have felt stuck, but Bardeen sensed that they were in fact nearing breakthrough. He was keenly aware of the competition—especially from Feynman, who in September had spoken on superfluidity and superconduc- tivity at the International Congress on Theoretical Physics in Seattle. Feynman ended the talk with a statement about the problem of superconductivity: “When one works on it—I warn you before you start—one comes up finally to a terrible shock: one dis- covers that he is too stupid to solve the problem.” It appeared to Jane that John worked on his research all the time in the days before going to Stockholm. She wrote in her Nobel diary that he “really worked, day and night, until we left Champaign November 29.” When one reporter who had discovered Bardeen’s passion for golf, remarked, “Oh! Just like President Eisenhower!” Bardeen grumped, “Yes, only I don’t have as much time for it as he does.” Schrieffer, now a fourth-year student, also had “mixed feelings” about Bardeen’s prize. He was enormously pleased for Bardeen and the excitement “sort of boosted us up.” But he had a personal matter to resolve. He wanted to accept an attractive National Science Foundation fellowship he had won for study in Europe dur- ing the following year. But a condition was that he be done with his thesis. That seemed to be going nowhere. He went to see Bardeen shortly before the latter’s trip to Stockholm. Cautiously, Schrieffer asked whether it might make sense for him to switch to another problem—perhaps ferromagnetism, which he had started “to quietly work on.” Bardeen mumbled, “Give it another month, or a month and a half. Wait ’til I get back and keep working. Maybe something’ll happen.” The preparations for Stockholm absorbed much energy. A “three- way phone call with Walter and Bill settled the division of labor on the Nobel speeches, which had to be written.” Appropriate clothes 

206 TRUE GENIUS had to be found for all the events. For the formal ceremony, Jane wanted something “significant.” Seitz recalled, “The girls all piled in to help her.” Then John started to worry that Jane would “spend all the money before we get it.” On one rainy day, after much fruit- less searching for a dress in town, Jane took a Greyhound bus to Indianapolis and found a long royal blue silk faille gown and several other formal dresses and accessories. The celebrations began even before the Bardeens reached Stockholm. On November 30, William Baker, then vice-president in charge of research at Bell Labs, hosted a pre-Stockholm dinner in honor of the Nobel laureates in New York City. Jim took a break from his studies at Harvard for his father’s occasion. Many friends and colleagues from Bell attended. A series of talks were part of the celebration. Ralph Bown spoke on “the origin of the transistor discovery,” Conyers Herring on “the contribution of the transistor discovery to basic scientific knowl- edge,” Jack Morton on “measures of the transistor’s impact,” and Karl K. Darrow on “history of the Nobel Prizes, particularly in physics.” John and Jane stayed in New Jersey, at the home of Philip and Joyce Anderson. The Andersons could sense Bardeen’s impa- tience with all the fanfare. At one moment, when John thought he was alone, Joyce heard him swear ferociously at a shoe. Bill and Betsy, then 15 and 12, stayed home in Champaign with friends. “We didn’t expect that it would be proper” to bring them along, said Jane, who also felt that, as the two younger children had been in Europe the previous summer, they “had had their share of knocking around over there.” Jane later regretted not bringing them when the King of Sweden, Gustav VI Adolf, asked, “Mrs. Bardeen, do you have children?” “Yes, we do. We have three.” “And why didn’t you bring them?” John and Jane coordinated their travels with Walter and Keren Brattain, who brought along their young son, Billy. The five prefaced the celebrations in Stockholm with vacation time in New York City and Copenhagen. In New York, after a leisurely break- fast, John went off on an “expedition to buy a vest for his full dress outfit.” On the plane to Copenhagen, after their airplane dinner and a little nap, they all awoke thirsty. “Did the steward have cham- pagne?” Brattain wrote: “He not only did but it was a vintage year.” They learned it was only $4 a bottle, 

Cracking the Riddle of Superconductivity 207 . . . just the thing. After one bottle, John pointed out that we were losing $4 for every bottle we did not drink, as it would certainly cost $8 in the U.S.A., so we had another. After this John was still worried about saving another $4 but the rest of us said he would have to do his saving alone, so we quit and went to sleep, waking up at about 12 midnight New York time for breakfast and then our landing in Copenhagen. In Copenhagen, Keren and Jane enjoyed “a shopper’s paradise,” while Walter and John visited Niels Bohr at his institute. On a side trip to the town of Göteborg in Sweden, Brattain delivered a lecture at Chalmers Technical University. They met with Professor Wallman, who had been a graduate student at Princeton with Bardeen, Seitz, and Robert Brattain. Worried that Walter was get- ting more publicity than John, Jane wrote home, “I hope John gets a square deal when we get to Stockholm.” Their December 6 arrival in Stockholm, where they traveled next by train, left them a few more days to sightsee and acclimate as they settled into Stockholm’s Grand Hotel. Brattain noted that Sweden was a “low hilly country with many lakes—evergreen forests of pine and fir—not a dense forest as one would find in the Pacific Northwest.” The big ceremony was to be held, according to tradition, on December 10, the anniversary of Alfred Nobel’s death. The Swedish Foreign Office assigned each Nobelist a guide to help them through their busy days filled with press conferences, photo sessions, cere- monies, luncheons, and dinner celebrations. “Flash bulbs were popping at random as we moved out of the station and waited for our cars,” Brattain wrote. When Bardeen and Brattain visited Hafo, the Institute for Semi- conductor Research, they were each presented with a “stickpin with a single crystal of silicon cut on definite planes as the jewel.” Shockley missed this party because of a flight delay. He and Emmy had flown to Paris on Air France, but as the Paris airport was fogged in, they had to spend the night in Bordeaux, in a cheap hotel with no hot water. When they arrived in Stockholm on Saturday, they barely had enough time to wash up and begin celebrating. More like brothers than collaborators, Bardeen and Brattain were enjoying more time together than they had in years. On Monday, the day of the ceremony, they both suffered queasy stomachs. Brattain “hit on the idea of a bottle of quinine water to 

208 TRUE GENIUS settle my stomach and Bardeen had some too, then a light lunch and up to our rooms to climb into our monkey suits.” The phone rang in the Brattains’ suite while Keren, Billy, and Walter were get- ting dressed. It was “a last minute call from John for a spare tie because of some accident to his.” Brattain was used to such crises, for “Bardeen had already borrowed one of his vests.” The one John had just bought in New York “had laundered green.” The award ceremony took place in the concert hall. The stage had been decorated lavishly with yellow chrysanthemums. All the laureates had been instructed in the proper procedure for bowing to King Gustav VI Adolf, who presented the awards, and to the Queen. Brattain fretted over getting it all right. It was the only occasion at which “the King stands to receive, so the honor is very great,” Jane wrote. Brattain watched as Shockley “went first and made all his bows properly.” Then he cringed for Bardeen as the King acciden- tally stepped in between Bardeen and the Queen, making John’s bow to the Queen awkward. Brattain followed Bardeen unevent- fully, and the most nerve-wracking part of the ceremony was over. It had been rumored that the King’s dinner that evening, usually an affair of a thousand people at the town hall, would be cancelled because of the current political upheavals in Hungary, whose abor- tive revolution had been brutally suppressed by the Soviet Union. The dinner was not cancelled, but it was reduced to 175 guests and relocated to the Stock Exchange Building. After the formal dinner the party moved to the dining room of the Grand Hotel. The Brattains sent Billy to bed and joined the Bardeens as well as other laureates and their attendants. They cel- ebrated into the wee hours, plying one another with champagne. “It was a grand time; we were certainly in a hilarious frame of mind,” Brattain later reported. He woke up “very bubbly” the next morning. The next evening the King entertained the Nobelists in his pri- vate apartments. Jane wrote home that “conversation was not difficult,” as the royal family consists of “very genuine people.” She admired the King’s art collection and his orchids and noted that “their living room is much like ours, in a sense, books piled on all the tables.” The group wound down a bit over the next few days. John and Jane took some time to write postcards to a few friends and family, alluding to the “fabulous life” they had been leading during the 

Cracking the Riddle of Superconductivity 209 celebrations. “We have only time enough to sleep, eat, and go to parties.” Stockholm was “wonderful but strenuous,” John wrote in a postcard to Nick Holonyak. The Nobel whirl, he wrote, had “been like living in a different world.” He also said that they “had a din- ner in the King’s apartment in the Palace shown in the picture. Returning soon to a more normal existance [sic].” Holonyak was then a member of a small unit of the Army Sig- nal Corps in Yokohama. A stodgy lieutenant he was working for in a special operation “would go out just before noon and get our mail, and then he would come back with the mail and throw it at us.” During the winter of 1956–1957, the lieutenant came back one day and shouted, “Holonyak! Who in the hell do you know by the name of John in Sweden?” In later years Holonyak would smile fondly when he recalled Bardeen’s misspelling of the word “existence” on the postcard. He told his friends that John said his inability to spell was a legacy of his having been skipped in elementary school. When John and Jane returned to Champaign-Urbana, it took Bardeen a few days to adjust to his normal routine. He brought his Nobel medal into the office to show his colleagues. As he told them about the heady experience they had had in Stockholm, Charles Slichter thought Bardeen was “sharing in the nicest pos- sible way.” Bardeen finally bought a television as a sort of consolation gift to the children who had missed the festivities in Sweden. For some years John had resisted the family’s entreaties for a television set, saying he was waiting for the cost of transistorized color TVs to drop to a reasonable price. Afterwards the family noted with amuse- ment that John watched TV more than anyone else. Although he rarely cooked, he especially enjoyed watching Julia Childs’s cook- ing show. He spent many happy hours watching sports, but never home games, for those he attended in person, always rooting with enthusiasm. Not long after that, Bardeen achieved one of his lifelong goals, a hole in one. It happened on the university golf course near the Champaign airport. According to Bob Schrieffer, “He thought that was almost as good as the Nobel.” Years later Bardeen was asked which he considered the greater accomplishment, a Nobel Prize or a hole in one. He replied, “Well, perhaps two Nobels are worth more than one hole-in-one.” 

210 TRUE GENIUS By Christmas Bardeen was again deeply immersed in superconduc- tivity. The children could tell the problem “was desperately impor- tant to him.” Jim, home from Harvard for the holidays, could see a big difference from the way his father had worked on the transistor nine years earlier. “I remember him being much more uptight” and trying “to push harder to get things done.” Betsy remembered that her father was off in another world that Christmas. But the problem did not yield during the holidays. Then in the last days of January the turn came. Schrieffer and Cooper were on the East Coast attending physics conferences—one on the many-body problem was held in Hoboken, New Jersey, on January 28 and 29 and hosted by the Stevens Institute of Technol- ogy; the other was the annual American Physical Society meeting in New York City, from January 30 through February 2. Schrieffer often took public transportation while commuting between the two meetings and from them to Summit where he was staying with a friend. One day, while riding on the Hudson Tubes, Schrieffer wrote down the wave function for the superconducting ground state. He recalled the process of developing the wave function as a sort of intellectual tinkering. Talks he had just listened to on the nuclear interaction between pi-mesons, protons, and neutrons, as well as other ideas tumbled around in his head. Among them were the Cooper pairs and the variational approach that Tomonaga had used in the pion-nucleon problem. He was thinking constantly about superconductivity. Calculating on a pad while on the subway, “I realized that the algebra was very simple.” He called on Bardeen’s bridging principle and formed “the wave function as a coherent super-position of normal state-like configurations.” Then, following Tomonaga, he tuned the expression up. Trying a product, he noticed that his con- struction did not conserve the number of electrons. He fixed this problem by adding in a “chemical potential term,” as in the grand canonical ensemble of statistical mechanics. Schrieffer worked more on the expression that night at his friend’s house. In the morning he did a variational calculation to determine the gap equation. “I solved the gap equation for the cut- off potential. It was just a few hours work.” Expanding the expres- sion, he found he had written down a product of mathematical operators on the vacuum that expressed adding electrons to the 

Cracking the Riddle of Superconductivity 211 vacuum. In his sum of a series of terms, each one corresponded to a different total number of pairs. He could hardly believe it. The ex- pression “was really ordered in momentum space” and the ground- state energy “was exponentially lower in energy,” as required for the state to be stable. By chance Schrieffer and Cooper flew into Champaign at the same time. Schrieffer had to show his wave function to Cooper right there in the terminal. Cooper was enthusiastic. “I knew immediately we could calculate that,” he recalled. “It was this marvelous, elegant, subtle solution that you could calculate. And essentially what it said is don’t drive yourself crazy, just take the pairs, put them together so they satisfy the Pauli principle.” Cooper said, “Let’s go and talk to John in the morning.” The next morning Bardeen looked at the wave function and said “he thought that there was something really there. So we chatted around about that for a few hours.” Schrieffer remembered that Bardeen “was quite convinced that there would be an energy gap in the excitation spectrum.” Then using the wave function to compute the gap, “John showed that the gap was exactly the same parameter, delta—we called it epsilon zero at that time—that I’d found entering in the ground state energy!” Not long after that Cooper walked into the office he shared with Bardeen. “How would you like to write a paper together on superconductivity?” asked Bardeen. Cooper replied, “I would like that just fine. And then we began to calculate and we calculated for just about six months, day and night.” The most exciting moment in the work occurred several days later when Bardeen calculated the condensation energy in terms of both the energy gap and the critical field, obtaining a relationship between these two experimental quantities. “We had the experi- mental number from the Tinkham group for the gap. We knew the critical field, and the whole problem was converting units.” At first Bardeen “was very upset that he couldn’t get the numbers to work out.” When they finally did, “something like 9 compared to 11 in the appropriate units, we were really overjoyed, and sort of hit the roof. Things looked like pay dirt.” All the pieces of the puzzle were fitting together. Once Bardeen “felt that this was the right direction, then it was clear that the mode of operation changed.” Bardeen knew just what to do, recalled Schrieffer, having had “almost all the pieces” 

212 TRUE GENIUS assembled for some time in his mind. He had an idea of “how the theory must ultimately work out,” and he knew “what you should work out, what theoretical predictions of which experiments you should go after, and what experimental predictions are such that they will be critical of different parts of the theory.” And, said Cooper, “because he had done all these calculations for normal metals, he knew everything that happened there.” Their job was to “take that normal calculation” and rework it using the super- conducting wave functions. “The point is he just knew everything that had to be done and he was very good and very fast. I mean I was the young hotshot and let me tell you he could calculate paths faster than I could. I was amazed. And sometimes he used very old methods and still got the answer first.” It was only a week after Schrieffer first wrote down the wave function, but they still felt pressed. They knew Feynman was work- ing on the problem “using all sorts of complicated field theory.” Worrying that Feynman “might break the problem from another point of view” and scoop them, the team made an effort to bull- doze through their calculations, working intensively over the next six months. Bardeen laid out a program of tasks. To save time he divided them among the members of the team, assigning Schrieffer thermo- dynamic properties, asking Cooper to work on the Meissner effect and other electrodynamic properties, while he worked out the transport and nonequilibrium properties. Bardeen’s colleagues knew something was up when they asked him a question and were told, apologetically, that he was too busy to think about anything else just then. Schrieffer’s wave function initiated “a period of the most concentrated, intense and incredibly fruitful work” that Cooper had ever experienced. Two weeks after Schrieffer’s breakthrough, the team was still a long way from completing the work. They had not yet succeeded in deriving the second-order phase transition. Bardeen decided to pub- lish an announcement of their breakthrough in the form of a letter to the Physical Review. On February 15, he sent off the letter. He wrote in a cover note to Samuel Goudsmit, the editor of the Physi- cal Review, “I know that you object to letters, but we feel that this work represents a major breakthrough in the theory of super- conductivity and this warrants special handling.” The letter, received by the journal on February 18, explained 

Cracking the Riddle of Superconductivity 213 how superconductivity arises from the coupling between electrons and phonons, an interaction in whose presence the system forms a coherent superconducting ground state in which individual particle states are occupied in pairs, “such that if one of the pair is occu- pied, the other is also.” The letter summarized the advantages of the theory: (1) It leads to an energy-gap model of the sort that may be ex- pected to account for the electromagnetic properties. (2) It gives the isotope effect. (3) An order parameter, which might be taken as the fraction of electrons above the Fermi surface in virtual pair states, comes in a natural way. (4) An exponential factor in the energy may account for the fact that kTc is very much smaller than hω. (5) The theory is simple enough so that it should be possible to make calculations of thermal, transport, and electromagnetic properties of the superconducting state. By the time the letter was received, they understood the second-order phase transition. As Schrieffer later recalled, shortly afterwards, the Bardeens were entertaining a distinguished Swed- ish scientist at their home. John was somehow off on Cloud 7 that night, and there were long gaps in the conversation where John was staring into space and the conversation was going on but in a very strange sort of way. And it was clear that John was thinking hard about something. And what he was thinking about was how to get the second order phase transi- tion, and exactly how to write the wave function down. The next morning Bardeen phoned Schrieffer. “He was really excited.” Schrieffer remembered that the phone call “woke me up early in the morning.” Bardeen had had the Eureka moment. “I think at that point he had felt everything was correct.” Bumping into Slichter in the hall, Bardeen announced the breakthrough in his characteristic way. As usual, he struggled for words. Then he drawled: “Well, I think we’ve figured out super- conductivity.” Slichter and his student Charles Hebel were among the first to confirm the new theory experimentally. Measuring the rate at which nuclear spins relax in aluminum, they found that as they lowered the temperature below the point at which aluminum becomes superconducting, instead of falling, the nuclear magnetic resonance rate increased: it rose to more than twice its value in the 

214 TRUE GENIUS normal state. But as the temperature was further reduced and passed below the transition temperature, the rate again began to fall. The Bardeen-Cooper-Schrieffer theory, which became known as BCS, explained the effect easily. When one tries to make nuclear spins line up, they try to relax by banging into the electrons. In the process they transfer their spins to the electrons. When this happens in a normal metal, the nucleons exchange spins until half point up and half point down. In the BCS state, however, the number that can be flipped is greatly reduced because the electrons are locked together. In consequence, the relaxation takes much longer. Cooper said that Slichter became so “heavily involved” in the computations that “by April or May he was calculating along with us and pointing out errors.” Within a few months many experimenters at other institutions were validating the BCS theory. Among the first major confirma- tions outside Champaign-Urbana were those of R. W. Morse and H. V. Bohm at Brown University and those by Rolfe Glover and Michael Tinkham at Berkeley. Morse and Bohm studied the acous- tic attenuation as a function of temperature. In accordance with the BCS theory, they found a rapid decrease of the attenuation in pure superconductors as the temperature fell below the transition value. Experiments by Glover and Tinkham, studying far-infrared transmission through thin superconducting films, provided direct evidence for an energy gap corresponding to just twice the fre- quency at which the absorption sets in. These experiments seemed to be saying, “Come on now. The wave function looks right.” The team announced the BCS theory in March 1957 at the annual meeting of the American Physical Society devoted to solid- state physics. It was held that year in Philadelphia from March 21 to 23. Seitz phoned Eli Burstein, the secretary of the society’s Divi- sion of Solid-State Physics to tell him about the breakthrough. The abstracts were sent to Karl K. Darrow, the secretary of the society. Two post deadline papers were arranged, one to be given by Schrieffer, the other by Cooper. Schrieffer, who had gone to New Hampshire to write up his thesis, received word too late to attend the meeting. So Cooper had to deliver both papers. Bardeen chose not to attend the March meeting. “He wanted to make sure that the young people got the credit.” Schrieffer consid- ered it remarkable that “having finally come to the pinnacle of achievement in his professional life,” Bardeen now “steps aside for 

Cracking the Riddle of Superconductivity 215 two young people.” Schrieffer saw Bardeen’s act of saying, “OK, you go out and tell the world, and I will stay here in Urbana” as a “striking example” of giving credit, “even to an extent beyond that which is due and also pushing young people as fast as they can to become professionals, and treating them as professionals, and making them rely on themselves.” During March the team worked on understanding the coher- ence factors, the size of the Cooper pairs. They were concerned that the superconducting wave functions did not appear to con- serve the number of particles and thus were not obeying gauge invariance, a condition referring to the symmetry of Maxwell’s electrodynamics. They wondered whether their formalism was completely valid because it demanded superposing states having different numbers of electrons. Eventually it became clear that the superposing of states was but a trick that simplified the mathematics. It did not really imply that electrons were not being conserved. The intense work that spring continued through all the ups and downs of personal events. Bardeen was saddened when he learned in April that Keren Brattain had died of cancer. After enjoy- ing the trip to Stockholm in December, she suddenly fell ill two months later and “in the space of a few months she was gone.” John dropped everything to visit Walter. During the visit young Billy became fascinated with John’s solar battery-powered transis- tor radio. John spontaneously presented it to the boy. Billy never forgot the gesture. Cooper’s first daughter was born around 4:30 A.M. on May 6, 1957. After making sure that mother and baby were fine, he decided to go in to work. He had always felt awkward when he arrived at the office about 10 A.M. and found that Bardeen had been there since 8:00. Bardeen had assured Cooper, “I could work any way I wanted to—as long as I worked.” Still Cooper felt embarrassed by his pattern. That morning Cooper rushed home to change. He grinned as he showered and shaved. “This time I would be first.” But when he arrived at the office around 7:30, he found “the door was already open; John was sitting at his desk working. He had chosen this morning to come in early.” (Cooper had not realized that Bardeen was now coming in earlier every day.) The feverish pace of the work continued into the summer. By July they were ready to send their full-length article to the Physical 

216 TRUE GENIUS Review. In this masterpiece of modern physics, they showed in more detail how their theory explained (1) the infinite conductivity that Kamerlingh Onnes had discovered in 1911; (2) the diamagnetic (magnetic-field expelling) effect found by Meissner and Ochsenfeld in 1933; (3) the second-order phase transition at the critical tem- perature; (4) the isotope effect first observed by Serin and Maxwell; and (5) the energy gap in the excitation spectrum, first postulated by the London brothers. Their paper also showed how the BCS theory offers quantitative agreement for many experimentally de- termined quantities, including the specific heat and the penetra- tion depth of the magnetic field near the surface. Most of the experimentalists who had worked on superconduc- tivity were enthusiastic about the BCS theory. But many of the theorists, especially those who had invested much time on the problem, met the new theory with skepticism. Pippard (both a theorist and an experimentalist) wrote a series of pointed letters to Bardeen. He apologized for the detail with which he probed BCS. “In case what follows gives you the impression that I am bent solely on destructive criticism, let me say at once that I am sure you have made an important step forward towards a theory of superconduc- tivity; I am not wholly convinced that you have its final answer, but I think it will be found along the lines you suggest.” John wrote Jane from a September conference in Madison that the skeptics were “mostly those who have tried and failed them- selves and do not yet really understand what we have done.” He was confident about dealing with the resistance. “I expect they will come around eventually. Experimental checks have been remark- ably good.” He also wrote to Cooper about the Madison meeting, which he described as “quite interesting and well attended.” Com- menting on the reception of the BCS theory: “There was consider- able interest in the superconductivity theory. While very few had had a chance to study the theory carefully, the reaction was gener- ally favorable. Experimentalists were particularly enthusiastic about the theory. Objections were raised mainly by those with pre- conceived notions of what the theory should look like.” Bardeen, Cooper, and Schrieffer spent more than a year “defending the fort” against the “enormous number of people who had vested interests in themselves solving that problem, and in our having not yet solved it.” The team faced an impossible problem, for their opponents “wanted to be really convinced that this was a 

Cracking the Riddle of Superconductivity 217 correct solution,” and there just was no simple and rigorous way to prove BCS. “It was an intuitive leap.” They could only appeal to a long series of experimental “tiepoints” and “ultimately you hope there is a theoretical deductive way of getting there, but it was certainly far from there.” As Bardeen wrote to Pippard in late Sep- tember 1957: “In formulating our theory, we have attempted to construct the very simplest model which we believe has the essen- tial features of superconductivity as it exists in actual metals. With this approach we would hope to find a qualitative and perhaps even semiquantitative agreement with experiment. The remarkably close agreement we have found for most properties surprised us.” One major objection was the theory’s apparent lack of gauge invariance, the issue concerning conservation of the number of par- ticles, which the team had worried about. Attempts to address the issue eventually bore fruit in several major papers by Philip Ander- son, Pines and Schrieffer, and others, addressing the gauge invari- ance. They showed that deep down in the formalism the gauge invariance is indeed present. Bardeen wrote to Anderson in Octo- ber that his manuscript “certainly gives the answer to gauge invariance.” An important by-product of the BCS theory and its reception concerned “broken symmetry,” which Yoichiro Nambu, one of the original objectors to BCS, subsequently introduced into the theo- retical framework of particle physics. Viktor Weisskopf would lament in 1960: “Particle physicists are so desperate these days that they have to borrow from the new things coming up in many- body physics.” When Schrieffer “came through Copenhagen” between May and August 1958, after spending the previous fall in Birmingham working with Rudolf Peierls and the winter in Italy, “where the weather was a little bit better,” he spoke about the theory with Niels Bohr, whose long-standing interest in superconductivity dated back to the 1920s. “It just can’t be true. I don’t believe it,” Bohr said to Schrieffer. “It’s an interesting idea, but Nature isn’t that simple.” Schrieffer then “wrote about two hours of notes try- ing to recall what Bohr had said.” Based on these notes, Schrieffer composed a long letter to Bardeen explaining, “Unfortunately, it’s wrong. Bohr has told me it’s not right.” Schrieffer got back a prompt reply from Bardeen that said, in essence, “Bohr doesn’t know what he’s talking about.” The 

218 TRUE GENIUS problem was that Bohr’s remark hit a sore spot. Schrieffer admitted that he himself “thought it was too simple and this can’t be the answer.” In the years that followed, all three members of the BCS team continued to clarify their understanding of the meaning and impli- cations of their theory. After returning from his National Science Foundation fellowship year in Europe, Schrieffer went to the Uni- versity of Chicago for a year. After that he returned to the University of Illinois for three years as an assistant professor, before moving on in 1963 to the University of Pennsylvania. Cooper taught at Ohio State for a year after finishing his postdoctoral research at Illinois. He then moved to Brown University, where he eventually changed fields and became prominent in neural net- works research. BCS became recognized as among the “big ideas” of physics, a theory applicable to problems in many fields of physics. In 1958 the superfluidity (superconductivity without charges) of nuclear matter was proposed by Aage Bohr, Ben Mottelson, and David Pines and developed further in 1959 by Arkady B. Migdal as well as Spartak T. Belyaev. Then Migdal and later Vitaly L.Ginzburg and D. A. Kirzhnits applied the idea of superfluid pairing to the matter inside neutron stars, a theory fleshed out subsequently by Baym, Pethick, and Pines in Bardeen’s many-body theory group at Illinois. It seemed natural that the system of 3He, which is neutral, would also become superfluid at low temperatures. The phenomenon was discovered experimentally by Robert Richardson, David Lee, and Douglas Osheroff (below one millikelvin), and the nature of that helium state was explained theoretically by Anthony Leggett. It became clear that all these problems are tied together by the fundamental property of electrons that had allowed Wolfgang Pauli to open the development of the quantum theory of solids in the first place, the fact that the particles involved obey Fermi-Dirac statistics: one cannot put two of them in the same quantum state. If there are attractive interactions in a system, these “fermions,” whether charged or not, will form superconductors or superfluids by forming a system of pairs with one another. BCS became recog- nized, as Lazarus pointed out, as “a tremendous universal.”