True Genius The Life and Science of John Bardeen: The Only Winner of Two Nobel Prizes in Physics (2002) / Chapter Skim
Currently Skimming:
11 Cracking the Riddle of Superconductivity
11 Cracking the Riddle of Superconductivity
Pages 190-218
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 190... ...
"I believe that the explanation of the superconducting properties is to be found along the lines suggested by Fritz London." The hint that bolstered Bardeen's confidence was small but significant: "The wave functions for the electrons are not altered very much by a magnetic field." From this "rigidity" of the superconducting wave function Bardeen derived his sense of certainty about the nature of the solution. The rigidity followed from the energy gap.
|
From page 191... ...
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)
|
From page 192... ...
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 shortrange single-particle excitations.
|
From page 193... ...
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 repulsive one. This exciting result implied that for pairs of electrons near the Fermi surface the net interaction is attractive!
|
From page 194... ...
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 generalization 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 machinery for computing the interactions between electrons or between electrons and phonons (lattice waves)
|
From page 195... ...
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 frequently." He never felt "any problem of coming and chatting with him.
|
From page 196... ...
He explained that Cooper "had a field theory background and that this might be useful." Cooper had studied nuclear theory under lames 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.
|
From page 197... ...
or a hole are equivalent 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.
|
From page 198... ...
" 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?
|
From page 199... ...
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 atmosphere of the Bell Labs semiconductor team before the invention of the transistor.
|
From page 200... ...
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.
|
From page 201... ...
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
|
From page 202... ...
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 freeelectron gas continuously into the interacting system.
|
From page 203... ...
" 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?
|
From page 204... ...
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 VIeck.
|
From page 205... ...
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!
|
From page 206... ...
Darrow on "history of the Nobel Prizes, particularly in physics. " lohn and lane stayed in New Jersey, at the home of Philip and Joyce Anderson.
|
From page 207... ...
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. 207 In Copenhagen, Keren and lane enjoyed "a shopper's paradise, " while Walter and John visited Niels Bohr at his institute.
|
From page 208... ...
lane 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 lane took some time to write postcards to a few friends and family, alluding to the "fabulous life" they had been leading during the
|
From page 209... ...
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.
|
From page 210... ...
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.
|
From page 211... ...
" 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.
|
From page 212... ...
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.
|
From page 213... ...
And what he was thinking about was how to get the second order phase transition, and exactly how to write the wave function down. The next morning Bardeen phoned Schrieffer.
|
From page 214... ...
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 solidstate physics. It was held that year in Philadelphia from March 21 to 23.
|
From page 215... ...
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.
|
From page 216... ...
Their paper also showed how the BCS theory offers quantitative agreement for many experimentally determined quantities, including the specific heat and the penetration depth of the magnetic field near the surface. Most of the experimentalists who had worked on superconductivity were enthusiastic about the BCS theory.
|
From page 217... ...
Bardeen wrote to Anderson in October 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 theoretical framework of particle physics.
|
From page 218... ...
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
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.