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Superconductivity: From Electron Interaction to Nuclear Superﬂuidity 91

focused more and more on his unsuccessful hidden variables theory and,

apart from a brilliant paper with Aharonov, gradually became lost to the

world of physics as he made the transition from physics to philosophy of

physics to philosophical observations about the brain and the universe, etc.

Moreover, at the time Dave left the US, he arguably understood plasmas

better than any other scientist then alive, and his advice and scientiﬁc input

on work at Princeton and elsewhere on attempts at fusion energy would

have been invaluable. In retrospect, had he been able to actively participate

in the program, through his deep understanding of plasma instabilities and

plasma turbulence he would arguably have saved the US at least ﬁve years

and countless millions of dollars.

As a result of Bohm’s problems with Princeton and his move to Sao Paulo,

it took some time to publish the major ﬁndings in my thesis. After receiving

my Ph.D. I had gone, in September 1950 to the University of Pennsylvania

as an Instructor in Physics. Since soon thereafter Bohm was indicted and

forbidden to work on the Princeton campus, he would come to our apartment

in Philadelphia so that we could begin writing up our work for publication.

Before he left for Brazil we managed to complete the ﬁrst two in our planned

series of papers describing and expanding on my thesis.

In the ﬁrst

we described the warm-up problem in my thesis — a collec-

tive Hamiltonian approach to the modiﬁcation of transverse electromagnetic

waves by a quantum plasma and the description of electron interactions in

a quantum plasma that are induced by their coupling to transverse electro-

magnetic ﬁelds.

In the second

we used an equation of motion approach to examine the

interplay between collective and individual particle motion in mainly classi-

cal plasmas. We introduced the term, random phase approximation (RPA),

to describe the principal approximation made in our approach, and argued

that within the RPA for many metals quantized plasma oscillations would

be lightly damped. Importantly, we noted that there was experimental ver-

iﬁcation of our prediction of quantized plasma oscillations in metals, a veri-

ﬁcation that increased my conﬁdence in our ability to develop a satisfactory

microscopic theory of their behavior.

Conyers Herring had brought to our attention the pre-WWII character-

istic energy loss experiments of Ruthemann and Lang who had studied the

behavior of fast (keV) electrons passing through thin metallic ﬁlms. For

some metals, instead of ﬁnding the expected featureless distribution of en-

ergy losses, they found a series of discrete peaks. For Be and Al these were

at 19 eV and 14.7 eV, amazing close to the energy, [hω

/2π], contained in a

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92 D. Pines

single quantum of plasma oscillation for these materials, [18.8 eV and

15.9 eV, respectively], computed by assuming that all the valence electrons

outside the closed shells of the atoms in these metals were free, while the

mean free path for producing such losses was also quite close to that calcu-

lated under this assumption.

It was while at Penn that I also realized that the RPA might represent a

quite general way of identifying potential collective modes in any many-body

system, and suggested to my ﬁrst and only student there, Mel Ferentz, that

it be applied to the nuclear many-body problem, with particular attention

to explaining the nuclear giant dipole resonance as a collisionless collective

mode brought about in nuclear matter by hadron-hadron interaction. In

work that was published in collaboration with Murray Gell-Mann, who sug-

gested how to deal with its behavior in a ﬁnite nucleus, we showed that the

resulting energy was in good accord with the experimental ﬁndings.

However, completion of the third paper with Bohm, in which we planned

to provide the microscopic justiﬁcation for the central results on electron

interaction in metals obtained in my Ph.D. thesis, was delayed substantially

by his departure for Brazil and mine to Urbana in July 1952. In the interest

of full disclosure, my move from Penn to Urbana was triggered by the quite

unexpected and initially dismaying news that I was not going to be recom-

mended for promotion in the Penn Physics Department. As I look back on

that decision, made just after I had ﬁnished the above papers and received

my ﬁrst national recognition (an invitation to give an invited paper at the

APS meeting in March 1952), I cannot decide whether it was simply because

I was too impatient with my departmental elders or whether my connection

to Bohm played a role. Either way, it was for me a most fortunate turn of

events, as when I sought the advice of Fred Seitz on what to do next, he

responded that he would talk with John Bardeen, whom he had recently

attracted to the Illinois faculty. John responded by inviting me to come to

Urbana as his ﬁrst post-doctoral research associate.

4. John Bardeen and Superconductivity: The Early Years

Let me set the stage for my time in Urbana by sharing with the reader parts

of a recent memoir about John Bardeen and his early eﬀorts to understand

superconductivity.

“John Bardeen, whose 100th birthday we celebrated on

May 23, 2008, was arguably the most inﬂuential scientist/inventor of the

latter part of the twentieth century. Through his scientiﬁc discoveries, his

instinct for invention, and his impact on his colleagues, he made possible

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Superconductivity: From Electron Interaction to Nuclear Superﬂuidity 93

the electronics revolution and the information explosion that have changed

dramatically our every day lives.

Bardeen was an authentic American genius. Scientiﬁc genius is no easier

to pinpoint than artistic genius. It derives from a combination of factors,

including — but not limited to — intuition, imagination, far-reaching vision

and exceptional native gifts that blossom into signiﬁcant technical skills, and

the willingness and ability to challenge conventional wisdom. Perhaps even

more importantly, scientiﬁc genius depends on an instinct for invention, an

ability to focus on the problem at hand, to juggle multiple approaches, and

a ﬁerce determination to pursue that problem to a successful conclusion.

The inventor of the transistor and leader of the team that developed

the microscopic theory of superconductivity, John Bardeen possessed all of

these qualities. But what made him diﬀerent from so many fellow scientiﬁc

geniuses in physics of the 20th century — Einstein, Bohr, Dirac, Feynman,

Landau, Pauli, and Oppenheimer? The answer lies not only in his two Nobel

Prizes for Physics (in 1956 and 1972), but also his remarkable modesty,

his deep interest in the application of science, and his genuine ability to

collaborate easily with experimentalist and theorist alike.”

Early on in his scientiﬁc career, Bardeen had become deeply interested

in superconductivity. “In an abstract of a talk he gave at the Spring (Wash-

ington) meeting of the American Physical Society in May 1941, Bardeen

summarized what might be described as his ﬁrst “wrong” explanation for

superconductivity — suggesting that superconductivity might originate in

a small periodic distortion of the lattice that produced a ﬁne grained zone

structure in momentum space such that the energy gain from the result-

ing discontinuities would outweigh the cost of producing the distortion. He

argued that one could achieve perfect diamagnetism (the ability of a super-

conductor to screen out external magnetic ﬁelds) in this way with only a

fraction of the electrons near their ground state being involved and used his

earlier calculations of the resistivity of simple metals to estimate the strength

of the electron-lattice required to bring this about. He concluded that a high

density of valence electrons and a strong electron-phonon interaction were

favorable to superconductivity, a remarkably prescient argument of which it

could be said that he was right for the wrong reasons.”

Bardeen returned to superconductivity in early 1950, “when he learned

in a phone call from Bernard Serin of the discovery of the isotope eﬀect

(the dependence of the superconducting transition temperature on the in-

verse square root of the isotopic mass) on the superconducting transition

temperature of lead, he essentially dropped everything else to return to his

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94 D. Pines

work of a decade earlier on a connection between lattice vibrations and su-

perconductivity. . . . Bardeen, and independently (and in advance of the

Serin–Maxwell result) the British theorist, Herbert Frohlich, decided that

the key physical eﬀect must be a phonon-induced change in the self energy

of a fraction of the electrons near their ground state conﬁguration, and both

published their ideas in the early part of 1950. However, neither was able to

demonstrate how this could lead to the formation of a coherent state of mat-

ter that could ﬂow without resistance and screen out external magnetic ﬁelds

(“perfect” diamagnetism), the key physical idea introduced by Fritz London

to explain, at a phenomenological level, superconductivity. So this approach

turned out to be Bardeen’s second “failed” eﬀort to develop a microscopic

theory.

It was during this period, in the spring of 1950, that I ﬁrst met Bardeen,

who had come to Princeton to teach a seminar on the physics of semiconduc-

tors. Bardeen was already a legend among those of us who were Princeton

graduate students — as an exceptionally gifted young theorist who had been

Wigner’s best student and gone on to invent the transistor. Bardeen’s lec-

tures on semiconductors were not memorable, but were typical of his lectur-

ing style — clear, informative, low key, softly spoken, with little in the way

of emphasis. A highlight of those weekly visits were his discussions about

superconductivity with my oﬃce-mate, David Bohm, and the excitement he

conveyed that a solution might be on the way . . .

Although it became increasingly clear to Bardeen that a change in the

electron self-energy would not in itself lead to superconductivity, he contin-

ued at Bell Labs to work on ways the coupling of electrons to lattice vibra-

tions could play a signiﬁcant role. He was, however, working in a highly

unsatisfactory atmosphere (he was still a member of Shockley’s group, and

Shockley gave him no latitude to work with experimentalists) and began to

explore opportunities elsewhere. When he told his old friend, Fred Seitz, who

had moved in 1949 to lead a group in solid-state physics at the University of

Illinois in Urbana-Champaign, that he was ready to leave Bell Laboratories,

Seitz quickly put together an oﬀer for Bardeen to join him there, with a joint

appointment in the Department of Electrical Engineering and the Depart-

ment of Physics, which Bardeen accepted, and moved to Urbana in the fall

of 1951.”

5. With Bardeen in Urbana: 1952

1955

When I arrived in Urbana in July 1952, to work with Bardeen as the Physics

Department’s ﬁrst Research Assistant Professor, I was given a desk in a

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Superconductivity: From Electron Interaction to Nuclear Superﬂuidity 95

corner of John’s oﬃce. This gave me a unique opportunity to work with

John on a variety of problems and to learn from him a way of doing physics

that proved invaluable in my subsequent scientiﬁc career.

I arrived with the unﬁnished business of continuing at long distance the

collaboration with David Bohm on extending our collective description to

the quantum domain, but was eager to take advantage of the opportunity

that working with Bardeen provided to move in some new directions. I asked

John what I might work on, and he suggested I look at the polaron problem

— the motion of slow electrons that are strongly coupled to the optical modes

found in polar crystals — beginning with papers by Frohlich and Pekar. John

suggested I do this in the hope that an improved understanding of strong

coupling might provide insight into the role that electron-phonon coupling

played in bringing about superconductivity.

It was part of what I subsequently realized was John’s multi-pronged ap-

proach to solving the problem. These ranged from immersing himself in the

experimental data and developing a phenomenological theory that explained

many of the key experimental facts to exploring the use of matrix methods to

study the behavior of a small number of electrons outside the Fermi surface.

His approach included, of course, developing a better understanding of the

role of phonons in bringing out an eﬀective electron interaction that might

be responsible for superconductivity, a problem on which we subsequently

collaborated.

The polaron problem involved extending to realistic coupling constants

(that were of order 3 to 6), the perturbation-theoretic calculations of the

Frohlich group that were only valid for coupling constants less than 1. Soon

after I started work on it, I encountered T. D. Lee in a hallway of the Physics

Building. We started comparing notes on what we were working on that sum-

mer and realized, in the course of the next ten minutes, that our research

could be connected, T. D., who was spending the summer in Urbana, was

interested in applications in particle physics of the intermediate coupling ap-

proximation that Tomonaga had developed for meson-nucleon interactions,

and we realized that it might be possible to adapt the Tomonaga approach

to the strong electron-phonon interactions governing polaron motion. In the

next few days we carried out the adaptation and used Tomonaga’s approach

to calculate the changes in the electron ground state energy and eﬀective

mass brought about by that coupling.

Later that summer, as I was describing what T. D. and I had done

to Francis Low (who like me had arrived in Urbana that summer) Francis

argued that there had to be a simpler way to obtain our result, and he soon

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96 D. Pines

proved right. Thanks to Francis we found a simple and elegant expression

for the polaron wave function and described it in our subsequent paper

(LLP) which showed that our intermediate coupling solution was equivalent

to arriving at a coherent state in which the phonons in the cloud of strongly

coupled phonons around the electron were emitted successively into the same

momentum state.

At ﬁrst sight, this work seemed to oﬀer little insight into how one might

develop a microscopic theory of superconductivity, but matters proved oth-

erwise. Thus Bob Schrieﬀer has cited that LLP coherent state as the inspi-

ration for his January 1957, invention of the “Schrieﬀer” wave function for

the ground state of a superconductor that was the start of BCS. To see the

connection, note that the LLP wave function took the form:

LLP

∼ Π

exp[Σ

f(k)(a

∗

+ a

)]Ψ

where Ψ

was the ground state wavefunction and f(k) a form factor for the

phonon. Schrieﬀer’s brilliant insight was to try a ground state wavefunction

for the superconductor in which the LLP phonon ﬁeld was replaced by the

coherent pair ﬁeld of the condensate, b

∗

= c

∗

k↑

∗

−k↓

; his wavefunction thus

took the form:

Ψ ∼ Π

exp[Σ

∗

f(k)]Ψ

which is easily shown to reduce to the BCS wavefunction,

BCS

∼ Π

[1 + b

∗

f(k)]Ψ

In the fall of 1952, I returned to my (by now long-distance) collabora-

tion with David Bohm on developing a collective description of the quan-

tum plasma. There appeared to be two stumbling blocks to developing a

Hamiltonian approach that was isomorphic to that introduced for the mag-

netic interactions in a quantum plasma: clarifying the role of the subsidiary

conditions that accompanied our introduction of supplementary ﬁelds to de-

scribe the quantized plasma oscillations, and justifying our use of the RPA

in dealing with the long range part of the Coulomb interaction. We grad-

ually overcame both of these in the course of a correspondence that lasted

some seven months, ending in mid-April 1953. It involved the exchange of

well over forty handwritten letters that came to a total of several hundred

onion-skin pages, and not a little frustration as each of us began to worry

that the collaboration was taking too much time away from other projects

we had undertaken. Thus I found in my copies of our correspondence the

following words from David Bohm to me: “I am beginning to wonder if we

will ever ﬁnish the paper. It had better be soon, as I won’t have time to

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Superconductivity: From Electron Interaction to Nuclear Superﬂuidity 97

work on it any more, as I have many other duties. Now for a few general

remarks”. I wrote to Bohm at about this time — April, 1953 — “I’ve put

in about as much time as I possibly can on the writing of this paper —

so while I welcome any further suggestions you might make, you can rest

assured that they will probably be followed in toto. Thus I don’t envisage

any further tightening of this Mss on my part, and I’d be willing to send it

to the Phys. Rev. as it is!!”

In the course of our work and correspondence we decided to divide the

planned paper into two parts; Part III of the series would be written jointly

and describe the collective Hamiltonian approach to the quantum plasma

and overall physical picture, while I would write Part IV which dealt with

the application of our results to electrons in metals.

Both papers were ﬁnally typed up in Urbana and sent oﬀ to the Phys-

ical Review in mid-May. In Paper III

we introduced the supplementary

longitudinal ﬁelds that were coupled to the electrons and would, following

a series of canonical transformations, describe the quantized plasma oscilla-

tions that were the major consequence of the long range part of the Coulomb

interaction. We showed in an explicit calculation that if we did this only for

wavevectors smaller than k

∼ ω

where v

is the Fermi velocity, the

corrections to the RPA description of the long-range part of the Coulomb

interactions were small. We also presented arguments that the accompany-

ing subsidiary conditions would have no inﬂuence on the ground state energy

or wave function, and gave estimates of their role in general that suggested

these would play a negligible role. We thus arrived at the following basic

model Hamiltonian for jellium,

H = Σ

/2m

∗

+ H

where m

∗

(∼m) was an eﬀective mass that took into account the change in

electronic mass produced by their coupling to plasmons, H

described the

plasma waves brought about by the Coulomb interaction and H

described

the residual short-range interaction between the electrons.

In IV

I showed that this Hamiltonian provided for the ﬁrst time a mi-

croscopic justiﬁcation of the nearly free electron model of metals. I showed

it was possible to obtain a self-consistent account of the inﬂuence of elec-

tron interaction on metallic properties, and calculate, at the same level of

approximation, both the correlation energy and the speciﬁc heat, with re-

sults in good agreement with those found experimentally for simple metals.

The key physical argument presented there was that electrons in metals are

never seen in isolation, but always as quasi-electrons, a bare electron plus

its accompanying screening cloud (a region in space in which there is an

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98 D. Pines

absence of other electrons). It is these “quasi-electrons” that interact via a

short-range screened Coulomb interaction. For many metals, the behavior of

these quasielectrons is moreover protected by the adiabatic continuity that

enables them to behave like the quasiparticles in the Fermi liquid theory

developed subsequently by Lev Landau.

Once papers III and IV were oﬀ to the Physical Review, I began work on

generalizing Bohm–Pines theory to study the inﬂuence of electron-electron

interactions on electron-phonon interaction in metals, as a step toward de-

veloping a microscopic theory of superconductivity in which phonons could

play the key role the isotope eﬀect experiments had established. Frohlich

had proposed that since the phonon-induced modiﬁcation in the electron

self-energy could not explain superconductivity, perhaps the phonon-induced

interaction between electrons might provide the answer. He found, to lowest

order in the electron-phonon coupling constant, that this interaction would

be attractive for electrons lying within a characteristic phonon energy of the

Fermi surface. But while this seemed an interesting possibility for bringing

about superconductivity, it was diﬃcult to see how such a comparatively

weak interaction could prevail over the much larger Coulomb interaction he

had neglected. What I was after was a Hamiltonian description of the full

problem — electrons interacting with each other and with phonons — that

would tell us about the new features arising from their coupling to phonons

and the role played by electron screening and repulsion in determining the

overall eﬀective electron interaction.

Before he left Princeton, David Bohm had started work there on the same

problem with Tor Staver, a young Norwegian graduate student. They used

the RPA to study collective motion in a coupled electron-ion plasma and were

able to derive a simple expression for the longitudinal phonon dispersion

relation for jellium. They then sought to develop a physical picture for

the phonon-induced interaction along lines similar to those Bohm had used

with Gross for classical plasmas, studying the response of an electron to

the phonon wake produced by another. They were in the midst of doing

this, when Staver tragically died in a ski accident before their work could be

completed and published.

In developing a collective Hamiltonian approach to the full problem, I

was at ﬁrst successful, in that I could easily obtain the Bohm–Staver dis-

persion relation. However, I became stuck on how best to develop a fully

self-consistent treatment of the electron-electron interaction. One morning

in late 1953, in the course of discussing my lack of progress with John, he

suggested that perhaps what was missing was an explicit addition of ionic

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Superconductivity: From Electron Interaction to Nuclear Superﬂuidity 99

motion to the canonical transformation that took one from an arbitrary sup-

plementary ﬁeld to the collective coordinates that described the collective

modes of the coupled electron-electron-phonon system. We tried putting

that in, and everything worked.

In the paper describing our results

we showed how once this was done,

a straightforward generalization of the canonical transformations Bohm and

I had utilized earlier led to a self-consistent account, within the RPA, of

the way electron interactions modiﬁed their coupling to ions and to one

another and how the combined ionic and electronic Coulomb interactions

gave rise to both sound waves and plasma oscillations. We found that for

electrons lying on the Fermi surface, their phonon-induced interaction was

cancelled by their direct screened interaction, but that for electrons lying

within a characteristic phonon energy of the Fermi surface, the phonon-

induced interaction could win out, producing a net attraction. We closed

our paper with the prophetic line, “The equations we have presented here

should provide a good basis for development of an adequate theory.”

As Nozieres subsequently pointed out, our results for the net eﬀective

frequency-dependent electron interaction at low frequencies, V

eﬀ

, could be

put in especially simple form for jellium,

eﬀ

(q, ω) = [4πe

ε(q, 0)][1 + ω

/(ω

− ω

)]

where ε(q, 0) is the static dielectric constant. The screened Coulomb in-

teraction sets the overall scale for the strength of the interaction, and it is

evident that the net interaction will always be attractive for those electrons

of momentum p and p + q near the Fermi surface whose energy diﬀerence,

ω = ε

p+q

− ε

, is below the natural resonance frequency, ω

, of the phonon

that is being virtually exchanged.

6. The 1954 Solvay Congress

Thanks to Fred Seitz and John, I was invited to describe the above results in

the opening talk of the 1954 Solvay Congress on “Electrons in Metals”. I was

more than a little apprehensive about how my talk would be received, be-

cause there in the front row was Wolfgang Pauli, who had a justly-deserved

reputation for his ferocious put-downs of new theoretical results. (I was far

less worried about the presence in my audience of his fellow Nobel Laureates

Lawrence Bragg and Louis Neel, or that of those distinguished colleagues

there who went on to win the Nobel Prize — Neville Mott, Lars Onsager,

John Van Vleck, Cliﬀord Shull and Ilya Prigogine). I began with a sum-

mary of our work that clearly demonstrated that Heisenberg’s attempts to

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100 D. Pines

ﬁnd a microscopic theory of superconductivity by a careful treatment of the

Coulomb interaction were doomed to failure, and I started to relax a bit

when Pauli started shaking his head vigorously to indicate his agreement

with my ﬁndings. When I ﬁnished my report,

his was the ﬁrst comment,

which I quote: “I always told that fool Heisenberg that his theory of super-

conductivity was wrong.”

7. Deciphering, Teaching, and Applying BCS

In early 1955 I left Urbana to return to Princeton to a promised tenure-

track position that subsequently disappeared, and it was there, some two

years later, that I received a brief letter from John reporting that he thought

superconductivity had been solved. He enclosed a dittoed copy of their not-

yet-published PRL. I shared the news with Elihu Abrahams, who was newly

arrived at Rutgers, and my prize graduate student, Philippe Nozieres, who

had come from Paris to work with me. Filled with excitement, we decided

to see if we could ﬂesh out the details of what BCS had done. After three

intensive days in the living room of our house on Clover Lane we succeeded

suﬃciently well that I was able to teach it to my class later that spring.

In the course of these lectures, I did some simple calculations showing

how the eﬀective interaction that John and I had derived, and that formed

the starting point for BCS, led in a natural way to the famous Matthias

rules for the occurrence of superconductivity. I showed these to John when

he came to Princeton to give what may have been his ﬁrst colloquium on

BCS and he encouraged me to publish them. A footnote: when I sent the

paper

describing these results to Phys. Rev. in late May, its Editors were

uneasy about accepting it, since John, Bob and Leon had not yet completed

their full account of their theory, but John reassured them that I was in

no way trying to scoop BCS, and that what I had done complemented, not

competed with, their work in progress. In fact, it could easily have been

written two years earlier, since it dealt with the extent to which the above

eﬀective interaction enabled one to decide what elements would, or would

not, be superconducting, not the ensuing microscopic theory.

What I did in this paper was ﬁrst to see how well one could do with

a “minimalist” approach to calculating the average eﬀective interaction V ,

which had to be attractive to bring about superconductivity, and the prod-

uct N(0)V that determined the superconducting transition temperature, T

in BCS theory. I took the eﬀective interaction to be that John and I had de-

rived in the RPA, with the repulsive part a screened Coulomb interaction and