Cooper L.N., Feldman D. (Eds.) BCS: 50 Years
Подождите немного. Документ загружается.
September 17, 2010 9:51 World Scientific Review Volume - 9.75in x 6.5in ch5
Nuclear Magnetic Resonance and the BCS Theory 81
Fig. 18. The combined data taken from Cooper’s Nobel Prize Lecture. Al NMR
data of Hebel and Slichter (blue circles) and Redfield (orange stars) for R
s
/R
n
versus T /T
c
, showing the peak just below the superconducting transition arising
from the coherence of the electron spin pairing, and the low temperature fall-off
resulting from the presence of the energy gap.
Leon’s talk in Stockholm. Later, Redfield made substantial further studies
with his students Anderson and Masuda.
28
Reflections
Al Redfield, Chuck Hebel, and I look back on our experiments with very
special pleasure. It was a time of great excitement. Explanation of super-
conductivity had eluded scientists for many years. To feel that one might be
close to a solution was a great impetus for our experiments. Even before the
breakthrough by John, Leon, and Bob, there was an air of excitement since so
many new results were arising. When John, Leon, and Bob announced their
theory everyone was transfixed! Experimenters rapidly accepted it since it
explained so much experimental data. Some theorists were more cautious in
accepting the theory.
For Chuck and me, the most remarkable thing was to be instructed in the
theory at the very time that its authors were developing their calculations.
What remarkable openness! What remarkable kindness to take the time to
help us when they were racing to explore the consequences of their discovery!
September 17, 2010 9:51 World Scientific Review Volume - 9.75in x 6.5in ch5
82 C. P. Slichter
This experience has put John, Leon, and Bob in a very special place in our
affection and our admiration. It is a great joy to reflect on those days.
Looking back, I am especially impressed at how quickly John in collabo-
ration with his three young colleagues got the solution after leaving Bell Labs
and his work on transistors. His recognition of the consequences of an energy
gap, based on a very simple modification of the free electron theory of metals
in his paper of 1955 illustrates how closely he followed experiment. It also
shows what an intuitive feel he had for the nature of the superconducting
state.
Another special lesson derives from the fact that our work was launched
by John’s thinking before BCS had solved the problem. In his talk that
inspired me to try to measure the nuclear relaxation in a superconductor,
he was presenting a theoretical approach he later abandoned. But he had
already such a depth of understanding that his thinking had tremendous
validity. That is why our experiment turned out to have an interesting re-
sult. It has made me realize how important it is to listen with respect to
the thinking of other scientists, even when there is great scientific contro-
versy, because even an incorrect or an incomplete theory may contain crucial
elements of truth.
John was remarkable in his ability either to work by himself or to work
cooperatively with others. The BCS theory is a triumph of both of these
strengths. He identified and attracted the wonderful postdocs David Pines
and Leon Cooper. And he was the magnet who drew Bob Schrieffer, who
could have gone anywhere he wanted for graduate work, to Illinois. John’s
kindness, his openness, and his friendliness were ever manifest. This spirit
attracted those brilliant colleagues who shared these same qualities. Chuck
and I will forever be grateful for our time with John, Leon, Bob, and David.
Acknowledgments
For me, a key part of this paper is the collection of images of the partici-
pants. They bring back vivid memories of these marvelous people and my
association with them. I am indebted to the Harvard University Gazette
and the Harvard University Archives for their gracious help in providing
the image of Professor Van Vleck, and to Alfred Redfield for the image of
him with his rig in his lab at Harvard. Sid Drell provided my picture dated
1950. Above all, I thank Celia Elliott for her invaluable help and warm sup-
port. She devoted many hours to finding, scanning, and, when necessary,
“photoshopping” all the other images dating to the 1950s of the people who
are important to me. Her work gives life to the story.
September 17, 2010 9:51 World Scientific Review Volume - 9.75in x 6.5in ch5
Nuclear Magnetic Resonance and the BCS Theory 83
References
1. L. C. Hebel and C. P. Slichter, Phys. Rev. 107, 901 (1957); L. C. Hebel and C.
P. Slichter, Phys. Rev. 113, 1504 (1959).
2. C. P. Slichter and E. M. Purcell, Phys. Rev. 76, 466 (1949).
3. R. E. Norberg and C. P. Slichter, Phys. Rev. 83, 1074 (1951); D. F. Holcomb
and R. E. Norberg, Phys. Rev. 98, 1074 (1955).
4. R. T. Schumacher, T. R. Carver and C. P. Slichter, Phys. Rev. 95, 1089 (1954);
R. T. Schumacher and C. P. Slichter, Phys. Rev. 101, 58 (1956).
5. A. W. Overhauser, Phys. Rev. 92, 411 (1953).
6. T. R. Carver and C. P. Slichter, Phys. Rev. 92, 212 (1953); T. R. Carver and
C. P. Slichter, Phys. Rev. 102, 975 (1956).
7. W. S. Corak, B. B. Goodman, C. B. Satterthwaite and A. Wexler, Phys. Rev.
96, 1442 (1954).
8. J. Bardeen, Phys. Rev. 97, 1724 (1955).
9. W. Heitler and E. Teller, Proc. Roy. Soc. A155, 629 (1936).
10. J. Korringa, Physica 16, 601 (1960).
11. C. P. Slichter, PhD thesis, Harvard University (1949).
12. For detailed background on topics in this article, such as derivation of Curie’s
law, see C. P. Slichter, Principles of Magnetic Resonance, 3rd edition (1996),
Springer, New York. Referred to the present article as “Principles”.
13. H. G. B. Casimir and F. K. du Pr´e, Physica 5, 507 (1938).
14. C. J. Gorter, Paramagnetic Relaxation (Elsevier Publishing Company, Inc.,
New York, 1947).
15. J. H. Van Vleck, Phys. Rev. 57, 426 (1940).
16. See Principles, Chapter 1.
17. R. E. Norberg, Phys. Rev. 93, 638 (1952).
18. G. D. Watkins and R. V. Pound, Phys. Rev. 82, 343 (1951).
19. We later extended the method to obtain phase sensitive detection for signal
averaging spin echoes. J. J. Spokas and C. P. Slichter, Phys. Rev. 113, 1462
(1959).
20. J. Bardeen and D. Pines, Phys. Rev. 99, 1140 (1955).
21. L. N. Cooper, Phys. Rev. 104, 1189 (1956).
22. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 106, 162 (1957).
23. L. C. Hebel, PhD thesis, University of Illinois, 1957.
24. F. Reif, Phys. Rev. 102, 1417 (1956); Phys. Rev. 106, 208 (1957).
25. R. W. Morse and H. V. Bohm, Phys. Rev. 108, 1094 (1957).
26. L. N. Cooper, Nobel Lectures: Physics 1971–1980, ed. Stig Lundqvist (World
Scientific Publishing Co., Singapore, 1992).
27. G. Seidel and P. H. Keesom, Rev. Sci. Instr. 29, 606 (1958).
28. A. G. Redfield and A. G. Anderson, Physica 24, S150 (1958); A. G. Redfield,
Phys. Rev. Lett. 3, 85 (1959); A. G. Anderson and A. G. Redfield, Phys. Rev.
116, 583 (1959).
This page is intentionally left blank
September 13, 2010 17:10 World Scientific Review Volume - 9.75in x 6.5in ch6
SUPERCONDUCTIVITY: FROM ELECTRON
INTERACTION TO NUCLEAR SUPERFLUIDITY
David Pines
Physics Department and ICAM, UC Davis, Davis, CA 94103, USA
I present an expanded version of a talk given at the Urbana symposium
that celebrated the fiftieth anniversary of the publication of the microscopic
theory of superconductivity by Bardeen, Cooper, and Schrieffer — BCS. I
recall at some length, the work with my Ph.D. mentor, David Bohm, and
my postdoctoral mentor, John Bardeen, on electron interaction in metals
during the period 1948–55 that helped pave the way for BCS, describe the
immediate impact of BCS on a small segment of the Princeton physics
community in the early spring of 1957, and discuss the extent to which
the Bardeen–Pines–Frohlich effective electron-electron interaction provided
a criterion for superconductivity in the periodic system. I describe my
lectures on BCS at Niels Bohr’s Institute of Theoretical Physics in June
1957 that led to the proposal of nuclear superfluidity, discuss nuclear and
cosmic superfluids briefly, and close with a tribute to John Bardeen, whose
birth centennial we celebrated in 2008, and who was my mentor, close
colleague, and dear friend.
1. Introduction
In 1948, when I was beginning my Ph.D. thesis research with David Bohm at
Princeton, nearly 40 years had passed since the discovery of superconductiv-
ity, yet the prospects for developing a microscopic theory that explained it
continued to be grim. While it could be argued that developing a theory of
superconductivity was the outstanding challenge in all of physics, the failed
attempts to solve it by the giants in the field, from Einstein, Bohr, Heisen-
berg, Born, Bloch, Landau and Fritz London to the young John Bardeen
(see J. Schmalian, this volume), had led most theorists to look elsewhere
for promising problems on which to work, despite the fact that considerable
progress had been achieved experimentally and phenomenologically on the
properties of the superconducting state.
85
September 13, 2010 17:10 World Scientific Review Volume - 9.75in x 6.5in ch6
86 D. Pines
Superconductivity was obviously an amazing emergent electronic phe-
nomenon, in which the transition to the superconducting state must involve
a fundamental change in the ground and excited states of electron matter,
but efforts to understand how an electron interaction could bring this about
had come to a standstill. A key reason was that one had so little fundamen-
tal understanding of the influence of electron interaction on normal state
metallic properties, much less how it could bring about superconductivity.
In other words, the success of a nearly free electron model for most metallic
properties offered no clues for how some metals could be turned into super-
conductors by an electron interaction that seemed barely able to affect their
normal state behavior.
Landau famously said “You cannot repeal Coulomb’s law,” but as far as
the normal metals were concerned, it appeared that the best way to deal
with it was to ignore it. For example, when John Bardeen sought in 1936
to go beyond the free electron model in a calculation of corrections to the
electronic specific heat coming from electron interaction, he ran into seri-
ous trouble. Because of the long range of the Coulomb interaction, which
varies as 1/r, the lowest-order correction term to the electron self-energy
(coming from the Hartree–Fock exchange energy) is such that the specific
heat develops a term that varies as T/ ln T , a variation that was not seen
experimentally. Similar difficulties awaited those who attempted to carry
out first-principles calculations that went beyond the Hartree–Fock approx-
imation in calculating the influence of electron interaction on the cohesive
energy, the bandwidth, etc. Assuming that the interaction between electrons
was screened, as a simple static calculation by Fermi and Thomas had sug-
gested, provided a way out for calculations of the perturbative corrections
of the specific heat, but one then could no longer obtain a qualitative, much
less quantitative account, of the ground state and cohesive energy of simple
metals.
In 1948, Bohm was in his second year of an assistant professorship at
Princeton. He was widely regarded as one of the very best of Robert
Oppenheimer’s students to have come out of Berkeley and as perhaps one of
the three best of the post-WW2 generation of theoretical physicists (the
others being Richard Feynman and Julian Schwinger). He had become
deeply involved in the issue of the transition from a quantum to a classical
description of measurement theory in the course of working on what became
his superb text on quantum mechanics. He was also interested in ways to
deal with the divergences in quantum electrodynamics and in extending his
work with Eugene Gross on the interplay of collective and single particle
September 13, 2010 17:10 World Scientific Review Volume - 9.75in x 6.5in ch6
Superconductivity: From Electron Interaction to Nuclear Superfluidity 87
behavior in classical plasmas to the quantum domain in the hope that by
so doing one might get an improved understanding of electron interaction
in metals and thereby make a start on developing a microscopic theory of
superconductivity.
I had met Bohm much earlier in 1943, when, as an undergraduate in
BerkeIey, I had heard him give a guest lecture on plasmas in 1943 in Joe
Weinberg’s course in electrodynamics, and I came to know him reasonably
well before going off to the Navy in July, 1944. But it was through Robert
Oppenheimer that I came to be Bohm’s graduate student. When I returned
to Berkeley in 1946 as a graduate student, it was my hope and expectation
to do a Ph.D. thesis with Oppenheimer, who was as inspiring as a teacher of
physics as he had been as the leader of the Manhattan Project. When Opje
(his Dutch nickname that we all used) decided to leave Berkeley to become
Director of the Institute for Advanced Study in Princeton the following year,
I very much wanted to follow him to Princeton so I could do a thesis with him
there. Opje liked the idea and arranged for me to receive late admission to
the Physics Department at the university. I then wrote to Bohm to inquire
about housing, and he wrote back that his then roommate, S. Kusaka, had
tragically died in a boating accident, and that I was welcome to share his
room in a house on Nassau St.
During those immediate post-war years, it was not unusual for graduate
students to know junior faculty members well, because the world of physics
was still quite small, and many graduate students were in their mid-twenties,
having spent some three to five years in the armed services or government
laboratories before returning to academic life. I shared a room with Dave
Bohm for some nine months, during which I learned a very great deal of
physics through our many informal conversations over shared meals. More-
over, since Opje had become far too busy with directing the Institute for
Advanced Study and providing advice to the government on atomic weapons
to take on any more students, I decided that if I passed my qualifying exami-
nation in the spring of 1948, I would very much like to do my Ph.D. research
with Bohm. I passed the prelim, and Dave took me on as his student. He in-
vited me to share his office, which I did for the next two years while I carried
out the research for my 1950 Ph.D. thesis, “The Role of Plasma Oscillations
in Electron Interactions.”
2. My Ph.D. Thesis
Bohm’s ideas for my research were based on his knowledge of classical plas-
mas, ionized gases made up of freely moving electrons and positive ions, in
September 13, 2010 17:10 World Scientific Review Volume - 9.75in x 6.5in ch6
88 D. Pines
which one found high frequency collective longitudinal modes, plasma oscil-
lations. These are collisionless modes (like the zero sound mode subsequently
proposed by Landau) whose origin is not in the frequent collisions between
electrons that bring about hydrodynamic sound at long wavelengths, but
rather in the influence of the mean electric fields produced by their mutual
Coulomb interaction. Because of the long-range of that interaction, the fre-
quency of a plasma oscillation in the limit of long wavelengths is finite, being
ω
p
= (4πNe
2
/m)
1/2
, where N is the electron density and m its mass.
A second aspect of the emergent behavior Bohm had studied in classical
plasmas was the screening of low energy electronic motion; as a given elec-
tron moves it polarizes the plasma in such a way that its interaction with
another electron is screened, with the screening length being that first cal-
culated by Debye, [hvi/ω
p
], where hvi is an average electron velocity. With
Eugene Gross, my predecessor as his student, Bohm had studied in detail the
interplay between the resulting collective and individual particle behavior in
classical plasmas. The task Bohm set me was to extend his work with Gross
to the quantum domain, where it might be applicable to a simple model of a
metal, electrons moving in a uniform background of positive charge, a state
of matter that Conyers Herring subsequenty dubbed “jellium”.
Bohm suggested that I attempt to develop a Hamiltonian approach in
which plasma oscillations appeared explicitly, and use this to explore the ex-
tent to which that this would take into account the major consequence of the
long range part of the Coulomb interaction. As a warm-up exercise, I studied
the “transverse” analogue of the Coulomb interaction, the magnetic interac-
tion between electrons produced by their coupling to electromagnetic waves.
I developed a classical and quantum Hamiltonian approach in which I used a
series of canonical transformations to calculate both the modification in the
electromagnetic wave dispersion relation coming from their coupling to the
electron plasma and the modifications in the Biot–Savart law that described
the magnetic interaction between electrons arising from that coupling.
I then developed a corresponding classical Hamiltonian approach to the
Coulomb interaction by working in a longitudinal gauge in which subsidiary
conditions linked the vector potential to the charge density fluctuations. By
carrying out a series of canonical transformations on the starting Hamilto-
nian, I could obtain a new Hamiltonian in which plasma oscillations appeared
explicitly, while their coupling to each other and to the electrons could be
calculated. I found that within what is now known as the random phase ap-
proximation (RPA) this coupling produced only small corrections to Debye’s
effective electron interaction while the subsidiary conditions could easily be
September 13, 2010 17:10 World Scientific Review Volume - 9.75in x 6.5in ch6
Superconductivity: From Electron Interaction to Nuclear Superfluidity 89
satisfied. The long-range part of the Coulomb interaction was completely
redescribed in terms of the fields describing plasma oscillation, leaving in its
wake, a short-ranged screened interaction between electrons with a screening
radius, [hvi/ω
p
]. I was thus able to provide a microscopic justification for
the physical approach taken by Bohm and Gross for the classical plasma.
It seemed straightforward to extend this Hamiltonian approach to the
quantum domain, but at the time Bohm and I did not see an easy way
to sort out the quantum influence of the subsidiary conditions on electron
motion. Therefore in my thesis, I confined myself to a derivation of the
dispersion relation for the quantum plasma in two different ways: a self-
consistent field approach and an equation of motion approach for its density
fluctuations, ρ
k
= Σ
i
exp[ik ·r
i
] = Σ
p
c
p−k
∗c
p
, on using the second quantized
operators that create and destroy individual electrons. In both approaches,
I found that on making the RPA, the plasma dispersion relation could be
written as:
1 = [4πe
2
/m]Σ
i
1/[(ω − k · P
i
/m)
2
− h
2
k
4
/16(mπ)
2
]
where ω is the oscillation frequency for a collective mode of momentum k,
and one is summing over all electron momenta, P
i
, from which it follows that
at long wavelengths, ω = ω
p
. Moreover, ρ
k
and its time derivative could be
taken to be the field coordinates, Q
k
and P
k
, for quantized plasma waves,
in that when suitably renormalized, these obeyed the canonical quantum
commutation relations.
I concluded in my thesis that a proper quantum treatment of a starting
Hamiltonian identical to that considered classically, with due account of
the subsidiary conditions, would lead to a new Hamiltonian in which the
long range part of the Coulomb interaction was replaced by that for the
plasma waves, while the remaining short range part would resemble closely
a screened interaction with the quantum Fermi–Thomas screening length,
and expressed the hope that in this way, one could begin a systematic study
of the influence of electron interaction on metallic properties.
3. Physics, Politics, and Collaboration
My thesis work and its subsequent publication (which I will describe shortly)
became entangled in politics when I was less than half-way through my
research, as Bohm became a target of the House Committee on Un-American
Activities as part of its efforts to taint his mentor, Robert Oppenheimer,
with a Communist brush. Bohm received a notice to appear before that now
infamous group in late April 1949, and in his subsequent appearances (in late
September 13, 2010 17:10 World Scientific Review Volume - 9.75in x 6.5in ch6
90 D. Pines
May and early June) refused to testify about his one-time Berkeley Radiation
Laboratory colleagues or his own involvement with the Communist Party (of
which one subsequently learned he had been a member for some nine months
during 1942–43) on the ground that such testimony would interfere with his
First Amendment right of free speech and his Fifth Amendment right to
avoid self-incrimination.
Dave was by then sharing a house near Roosevelt, NJ with my wife and
myself and another graduate student couple, and needless to say our con-
versations for some months were more about politics than physics. He was,
however, supported by his colleagues and the Princeton administration, so
that despite the distractions occasioned by his trips to Washington, he was
able to continue teaching and directed my thesis research until its completion
in July 1950.
However Bohm’s support by the Princeton administration disappeared in
December 1950, when he was indicted by Congress and arrested for his re-
fusal to testify. Without waiting for the outcome of his trial, Harold Dodds,
the then President of Princeton University, suspended Bohm from his posi-
tion on the Princeton faculty, while proposing to continue his salary as long
as he did not set foot on the campus. Despite his 5/31/51 acquittal in a
federal court, when his initial university contract expired in July 1951, in a
decision made by Dodds without input from the Physics faculty, Bohm was
not rehired by the university. Despite efforts to find him another faculty po-
sition or research appointment in the US by those in the physics community
who knew him well, from Albert Einstein to colleagues at Bell Laboratories
and RCA Labs, and especially by Lyman Spitzer, the leader of Princeton’s
Matterhorn Project that was directed toward harnessing the fusion energy
of the sun, the political atmosphere in the US was at that time so poisonous
that he could not obtain any physics-related position in the US. He became
arguably our most distinguished scientific political exile when, not long af-
ter his seminal text on quantum theory had been published, he accepted a
position at the University of S˜ao Paolo. He went there in October, 1951,
beginning an exile from the US scientific community that continued, apart
from occasional visits, until his death in London 41 years later.
Bohm’s scientific exile from the US was enormously costly to both Dave
and to the United States. Dave, who was described once by Eugene Gross as
a “professional thinker”, typically had some five new ideas a day. He relied
in no small part on daily conversations with his students and colleagues
and his frequent contact with experimentalists to decide which of these to
pursue. Once he was no longer in a major center of physics research, he