4 John Bardeen and the Development of BCS Theory11

In the 1930's superconductivity was a natural subject of research for John Bardeen, then a Princeton graduate student in the quantum theory of solids: superconductivity was regarded as the ``only solid state problem that still resisted treatment by quantum theory.''12 The London brothers published their phenomenological theory in 1935, and Bardeen was drawn to theory's description of superconductivity as one macroscopic quantum state. After receiving his first academic post at the University of Minnesota, Bardeen began focusing primarily on superconductivity. Bardeen approached physics from the ground up; he wanted to derive theories from first principles, and his first goal was to do that for a derivation for the Londons' theory of superconductivity. His unsuccessful attempt was quickly interrupted by a call from the Navy during World War II. After the war, Bardeen began working at Bell Labs and in two years Bardeen, along with Walter Brattain, invented the transistor. Politics and jealousy on the part of Bardeen's and Brattain's director, William Shockley, impeded Bardeen's research on transistors, and after two years of fighting with Shockley, Bardeen decided to pursue research that was not in competition with Shockley.

Returning to work on superconductivity, Bardeen soon received confirmation that electron-lattice interactions played in an important role in superconductivity: in 1950 the isotope effect had been discovered, which proved that superconductivity depended on the atomic mass of the superconductor and thus probably on electron interactions with the metal lattice. In a race with Herbert Fröhlich, who had predicted the isotope effect, Bardeen attempted to find the superconducting wavefunction. Leaving the stifling atmosphere at Bell Labs, Bardeen moved to the University of Illinois, where Seitz - one of discoverers of the isotope effect - was building a solid-state physics group. Bardeen's attempts to explain the interactions between the electrons and the lattice quickly returned him to his previous problem with superconductivity: the many-body problem. Bardeen hired David Pines, a graduate student of David Bohm who had recently developed a new many-body formalism, to help Bardeen with the many-body problem. Bardeen and Pines were able to adapt the Bohm-Pines many-body theory to the problem of electron interactions in a metal lattice. They showed that for electrons with an energy near the Fermi surface, the net force between the electrons is attractive.

Bardeen realized that ``some radically new ideas [were] required''13 to tackle superconductivity and hired Leon Cooper, a field theorist, as a post-doctoral student. John Schrieffer, the ``S'' in BCS, joined Bardeen as a graduate student because he thought superconductivity ``looked like the most exciting thing.''14 The three physicists took a family-style approach to their collaboration: Bardeen and Cooper shared an office and all three were closely involved in each other's work. Bardeen's philosophy of breaking down problems into small components and ``using the smallest weapon in your arsenal to kill a monster''15 permeated the group.

The next breakthrough came in 1955 by Cooper: he was able to show that if there is an attractive force between two electrons near the Fermi surface, the two electrons can form a bound state (now called a Cooper pair) with energy below the Fermi surface. The two correlated electrons would act as a single boson and would not be governed by the Pauli exclusion principle that normally keeps electrons out of the filled Fermi sea. Expanding the theory from the formation of one Cooper pair to many pairs proved difficult, and while the team was at a standstill, good news threatened their collaboration. Bardeen won the Nobel prize along with Brattain and Shockley for the invention of the transistor, and Schrieffer won a NSF fellowship for study in Europe. Schrieffer's fellowship was contingent upon him receiving his doctorate and, with his current research at an impasse and Bardeen about to go to Sweden, Schrieffer went to Bardeen to ask about switching his doctorate thesis to a topic more likely to yield results. After working on superconductivity for two decades, Bardeen sensed that they were very close to a breakthrough so, despite his desire not to hold back Schrieffer's progress, Bardeen insisted that Schrieffer stay at least a few more months. Bardeen was right: two months later, Schrieffer had a breakthrough and guessed a possible form of the superconducting ground state and a few hours later, Schrieffer had calculated the energy gap. Over the next few days Bardeen calculated numerous properties that fit experimental data surprisingly well:

``We were continually amazed at the excellent agreement obtained [between our model and experimental results]. If there was a serious discrepancy, it was usually found on rechecking [and] an error was found in the calculations.'' - John Bardeen (Vidali: 1993, p.91)
Two weeks later, the three published their seminal letter in Physical Review (Bardeen et al.: 1957). Their theory fit the data so well that in the paper Bardeen, Cooper and Schrieffer claimed that ``the quantitative agreement, as well as the fact that we can account for the main features of superconductivity, is convincing evidence that our model is essentially correct'' (Bardeen et al.: 1957, p.1198) - a bold assertion considering Felix Bloch's quip that ``the only theorem about superconductivity which can be proved is that any theory of superconductivity is refutable.'' (Vidali: 1993, p.63) But their conclusions were not premature: BCS theory unified the electrodynamic and thermodynamic approaches to explaining superconductivity and provided a microscopic theory for explaining the behavior inside the superconductor. The theory fit not only current data very well, but made numerous predictions that were later proved correct. Despite a policy of not giving the same person two Nobel prizes in the same field, in 1972 the Swedish Academy of Sciences broke tradition and awarded John Bardeen, Leon Cooper and John Schrieffer the Nobel prize in physics for their theory of superconductivity.



Footnotes

... Theory11
The history presented here is based almost entirely on the historical article by Hoddeson (2001). Additional information came from Vidali (1993, p.84-99).
...12
Sommerfeld and Bethe (1933, p.555) as cited in Hoddeson (2001, p.626).
...13
Bardeen (1956) as cited in Hoddeson (2001, p.632).
...14
Schrieffer () as cited in Hoddeson (2001, p.632)
...15
Schrieffer () as cited in Hoddeson (2001, p.633)
Ben Luey