Philip W. Anderson - Session II

Kojevnikov:

This is the second section of an interview with Philip Anderson at Princeton University.

Anderson:

I just wanted to talk about the period between when I got back from Japan and when I began the localization paper. This was certainly the period when we were busy forming the new group, and inviting a surprising number of theoretical physicists from several fields to visit us during the summer, and organizing the group, and doing various political things, which I talked about last time, but I was actually also doing science. Although, in a sense, I had a feeling of rather marking time for a couple of years after I got back from Japan. But I was at this point pretty much the house theorist, in a general way for coherent spectroscopy, which includes paramagnetic resonance and nuclear magnetic resonance, all the various resonance spectroscopies which followed on from the equipment people had developed during the war. And so you'll find a collection of papers about paramagnetic resonance, for instance about exchange coupling of nuclear moments. I was working with a number of experimentalists, Bob Shulman and George Feher, as I mentioned last time, and with some theorists, such as Harry Suhl. I played a role in his very early excursion into non-linear effects with Walker, explaining data of Bloembergen and Wang.

One experimentalist I was working with was John Galt, who later became a member of management and then Pat Sandia! But at this time, he was trying to do cyclotron resonance of electrons in metals. He had some wonderful samples of bismuth. And he was seeing very strange phenomena with what turned out later to be the wrong geometry. He was using what seemed to be the obvious experimental technique. But the geometry of the sample and of the field and so on, it turned out actually not to be right. And he and I spent quite a bit of time arguing back and forth. I was doing the theory of the same thing, and I said, "I see nothing but a featureless blob in my theory," and he said, "But I see all these complicated blips here and there. All this complicated structure." And I said, "I don't know what it is." Well, I knew better than to say, "I think it is an experimental artifact." But I had no idea what it was. This led to several things. I bring it up partly because I don't want to give the impression in these interviews that I have any feeling that I am infallible. This was when I learned I was fallible, as a matter of fact. In that just a year later, Charlie Kittel came back from, or rather, one of Kittel's colleagues in California came back from Russia with the news that the Russian theorists Azbel and Kaner had explained some of the complicated effects that were occurring in these very pure metallic samples in terms of some very interesting resonance effects of electrons, following very large extended orbits within the metal. And I didn't have the faintest idea that that was what was going on, and I felt rather badly about it. Especially because essentially I found it was very difficult to work with Galt. We would in the end just get into screaming matches at each other, and so I stopped working with him. So it was generally not a particularly pleasant experience, although he and I remained good friends for quite a number of years thereafter. It also led to a quarrel, whose motivations I still have no idea of, with Charlie Kittel. Galt was doing these experiments. I published some kind of interpretation of at least part of his data—

Kojevnikov:

In what year was this?

Anderson:

This would be in the 1950s. The paper was Electromagnetic Theory of Cyclotron Resonance in Metals, 1955. I didn't publish the full work that I did (there was a technical memo with quite elegant math) because I was so turned off by this terrible telephone call I had from Kittel. He was almost incoherent and angry. I think he had some sense that he had staked out some kind of proprietary right in this field, which there was no way that that made any sense. Besides, it was not my business; it was Galt's business to see that he was not impinging on what someone else thought was his own property. I was just trying to interpret what Galt was seeing. But I had this very unpleasant call from Kittel, and I thought oh dear, that is terrible. I thought we were friends.

Kojevnikov:

Was this also in 1955?

Anderson:

That was in 1955, too.

Kojevnikov:

The Azbel and Kaner resonance came, I think, in 1956?

Anderson:

Yeah, it was 1956. You may know about that. Well, I wanted to say that, because it perhaps explains some of the politics and some of my relations later on. And the other thing I wanted to say is that I know perfectly well that I'm not infallible. I'm a gambler, really. am not the kind of physicist who won't publish if he isn't absolutely sure. What I published was right, more or less. But I certainly missed this whole phenomenon, which eventually led to part of the line of research that led to the whole subject of fermiology (The study of Fermi surface geometry in metals). It was a very important line and I just missed it.

Kojevnikov:

Was Kittel working on this resonance?

Anderson:

Kittel was working with Kip. Kip was the person that came back from the Soviet Union with the understanding. I don't remember who worked with Galt thereafter (probably Peter Wolff, among others) and he started Grimes out doing these experiments when he worked with other theorists and he continued to do work in this field.

Kojevnikov:

Was it necessary to go to the Soviet Union to bring back knowledge what was going on there? Or, were published papers sufficient to track what kind of research was being done there?

Anderson:

Well, there are kind of three answers. Yes there were published papers. It was a little bit later that we began publishing translations of the Soviet journals. And I think that didn't happen until—

Kojevnikov:

I think it started in 1956.

Anderson:

As early as 1956 or 1957. On the other hand, that expedition, that group was the very first people who went to Russia after the thaw.

Kojevnikov:

And who was there in the group?

Anderson:

I don't remember who the people were, Kip was one. I think one was Bozorth from Bell Labs. But he was not exactly then a great choice because he wasn't intellectually in with the younger group. And a couple of others; I don't remember who they were. They would seem to be arbitrarily chosen. I'll tell you about my own Russian trip later on.

Well, then we were going to start talking a little more about the localization paper. There were several lines of thinking that were going on more or less simultaneously. One was this concept of impurity bands. And Wannier, in particular was, I guess he invented the phrase, or at least was concerned about it, and he thought about and we discussed it a little bit. The question is, really, does any set of energy levels in an impure solid that have more or less the same energy form itself into a band? But actually what really focused my attention on it was this period of spending a lot of time looking over George Feher's experimental data. He was following along from I guess what had just started while I was in Japan, the first electron paramagnetic resonance studies of impurity levels in semiconductors. But the sample preparation and the control of impurity concentrations and control of the purities of the samples was enormously improved during this period for obvious technological reasons. And George, as I said, had enormously improved the experimental technology, just the data taking. He was much closer to the modern automated type of laboratory than his predecessors had been. And we very soon began to realize (I think Alan Holden and I made the first suggestion) in the first place that there was a hyperfine, structure of these donor energy levels. They were split by interaction with the nucleus of the phosphorus or indium or gallium, or whatever the impurity was. These were all odd nuclei therefore they have nuclear moments, and so there was a nuclear moment — electron moment interaction. In the case of phosphorus, we saw I think four lines. No, two lines. I think that is a spin one half nucleus. Then these lines had a breadth. And George gradually began to sort them out and realized that the breadth of the line also was a hyperfine interaction. It was a hyperfine interaction with some fraction of the silicon atoms in the background material. And it gave you a certain amount of information about the wave function of the electron, how it is spread out among the silicon 29s, which are only 5% of the Si atoms. Well, so we began investigating with what we called hole burning techniques. He would set his oscillator at a definite frequency. And he would saturate just those spins that had the right atmosphere of silicon 29s around them and the right phosphorus nuclear moment. Then he would watch as the silicons flipped, and so he could measure the silicon relaxation in the presence of the magnetic moment.

He also studied what happened when you increased the concentration of donor phosphorus, so that the phosphorus atoms interacted. The first thing that happened was that you would realize that sometimes one electron was interacting with two phosphorus nuclei. Two of them were close together and the electron was shared equally between the two phosphorus nuclei. The result would be that instead of two lines you had three lines, because you can have also the case when the two nuclei were opposite. Then he would see groups where there were four lines, which was an electron shared among three phosphorus nuclei. So we did it, and this gave us a very accurate calibration of the interactions between the phosphorus nuclei. That told us exactly what the overlap energy was between two phosphorus donors. Then finally, as he increased the density of the donors, quite sharply, (as he was measuring his concentrations in those days, he had about 20% accuracy) suddenly, it would all become a single narrow line. And there obviously the electrons were forming a band and moving among all the donors. And so for the first time we were seeing this explicit process of the formation of the impurity band. First, interactions, but with the electrons still interacting with specific two, or three, or four donor atoms. And then suddenly, the electron interacts with all the donor atoms, averages over the entire sample until we got no net, hyperfine interaction at all. And I was fascinated by this. Well, all the theorists were. Various people made various contributions.

This was the period when Mott came and visited, and we understood that this could well be a Mott type of transition, where the electrons at low enough density, were forced to stay on their own atoms by the interactions, and then at higher density the kinetic energy allowed them to move. So we kind of guessed that it was a Mott transition, or at least it could have been. But then I was puzzled by the whole burning phenomenon. Because of that, and this hopping of the electrons back and forth among the donors, where there are 3 or 4 lines instead of 2. Because that was not caused by hopping and the electron didn't actually move. All that moved was its spin. That was an exchange hopping. That you can not explain with Mott's mechanism. And I puzzled about that, and that was where the ideas came from that were expressed in my localization paper. I actually had seen the phenomenon in the experimental data. I had also talked to Conyers Herring who said, "Oh, there is something like that in a paper by a mathematician named Hammersley ." Hammersley had written papers about the percolation phenomenon and critical thresholds for percolation. But this was a quantum mechanical process, not a classical percolation process. And it was much harder to understand because there is nothing that absolutely blocks one electron, one donor from another as is assumed in percolation theory.

So it was really accurate thinking about the physical processes that were going on in a real sample. That was one of the summers Elihu Abrahams and David Pines were there. We worked out how big the interactions between these wave functions were. And they just definitely were too big. They certainly were big enough so that any naive theory would have sent those electrons easily hopping back and forth at a very rapid rate. And the rate was just too slow, much too slow.

So, this was in a way that I didn't— I think I went over this much too quickly before. Because it's been my intention in much of what I have done that the most fruitful way to do theoretical physics is to look at the experiments, and then try to conceptualize and understand what concepts are being expressed in the experimental phenomenon. Of course, the other thing was it was really staggering that those electrons didn't move. I don't think there is to this day as good an example, as clear an example of this phenomenon of localization as was expressed by those experimental data. As I said, my first ideas about this I talked about in 1956, and no one understood what I was talking about at that Seattle meeting. And then I developed, over the year of 1957 or so, a really rather formal theory, and it got published in 1958. But by then I was working on an entirely different subject.

Kojevnikov:

I had a couple of questions about this localization paper, too. You mentioned that the notion of impurity band comes to you from Wannier, right?

Anderson:

Wannier? Yes.

Kojevnikov:

This notion appears in your paper without any reference to any other paper—

Anderson:

The concept was in the air. Perhaps the paper where it was first mentioned as a concept is almost certainly the big paper by J. Bardeen and Ralph Pearson. They had a paper on all the physics of semiconductors (about 1948 or 1949). I forget whether it was silicon or germanium. But since they are in semiconductor physics, they went through all the regimes of temperature and concentration, and said here is what is happening here and here is so and so. And they mentioned that in this low concentration, they thought there (for Bardeen and Pearson and Hoddeson's history of semiconductor - also Herring) was probably a banding phenomenon in this low concentration regime, namely the impurity band, but that is about what they did about it.

Kojevnikov:

What happened then to this concept? Did it survive, or?

Anderson:

Well, we just talked about it. I am not sure that it was explicitly out in the literature that much. Wannier wrote this one paper about how really impure diamonds were, and yet they were very good insulators. He called it his Wiggly Band paper. Aside from that, I don't think anyone really was thinking about it. Mott was thinking to some extent, but he was much more interested in his magnetic oxides and things like that. Although I think he may mention impurity bands in his 1956 paper, I am not sure. I remember he came around and we talked it over a little bit. There were discussions with Mel Lax and other people.

Kojevnikov:

You mentioned at one point that these papers— so once you created this new theory division at Bell Labs, that three of you, Walker, Suhl and yourself, chose as a topic magnetic relaxation. And that this somehow led to this paper. What determined the choice of topics? Or was it your decision, or was it somehow connected with other Bell Lab interests? (Walker and Suhl were not in the theory group which was formed by Herring, Wolff, Wannier, Lewis and myself, and added M. Lax and subtracted Wannier and Lewis soon after).

Anderson:

Well, as I said, I had been the house theorist for this whole coherent spectroscopy, magnetic resonance spectroscopy phenomenon.

Kojevnikov:

But the other two as well? Herring?

Anderson:

No. Herring? I guess if I seemed to say that the group as a whole did it, the answer is no, no. They were doing other things. Wolff at the time was particularly interested in the electron gas as a plasma, in the metallic/electron gas as a plasma. And he took over as kind of the house theorist for that general area. Grimes did experiments on pure metal crystals, and his work got quite well know as the so-called helicon, which is a plasma wave propagation phenomenon. That was the correct answer to this physics that I had been discussing with Galt. And Herring was kind of the overall general theorist. We had Kohn and Luttinger who were busy with electrons and semiconductors. Kohn was interested in calculating the wave function, the actual wave functions of these donors. Luttinger was interested in the dynamics of how the electrons behaved in these rather complicated band minima and maxima near the semiconductor gap. So, they were all doing various things. Very useful things, of course.

Kojevnikov:

When did the attitude towards this theory started to change? You said that in the beginning the response was virtually zero. I think in your Nobel lecture you even said that even the author himself didn't fully realize the importance of the paper.

Anderson:

Well that's true.

Kojevnikov:

At that point. So, when can you recall the change of attitude?

Anderson:

Mott did that to some extent working with Helmut Fritsche and the group at Chicago who were interested. Fritsche developed the technique of doping with irradiation. So he could get a very much more continuous range of dopings for his impurity bands. He studied the transport processes of semiconductors as a function of doping. And Mott managed to get a certain amount of that work started in England as well.

Kojevnikov:

How quickly was this after the publication?

Anderson:

Oh, this was — Well, Mott basically invited me to Cambridge in 1961-62 in order to talk about this. I did a lot of other stuff in Cambridge, of course. But we did talk about it. But he and this poor graduate student of his, were certainly the only people in Cambridge who were at all interested in it. By the time I went back in 1967, Mott had quite an appreciable little group of people not just at Cambridge but around England and around the world who were interested in these questions of impurity bands and metal insulator transitions and so on. Well, I would say when I was there in 1961-62, Mott was strictly the only person who had any interest in it whatsoever. And by the time I was back there in 1967, there was a community that was interested in this whole question about metal insulator transitions in various guises. And actually from the bibliography you can date the time when I became interested again myself. Where was it? Here, 1970. Comments on the Fermi Glass, Theory and Experiment, 1970. And actually David Thouless became interested in it and did some important stuff. There is a paper three of us wrote together, Thouless, Abou-Chacra (a Lebanese student) and I. But in 1970, I came back. And the reason I came back, actually, was one theoretical realization which Mott had forced on me. See, I had always been worried that the model I did was strictly non-interacting electrons, hence, strictly linear equations. There was this question of what would the interactions do? And of course, in the presence of interactions the quantum states aren't exact; they fluctuate. So I was worried about interactions, what would they do? And then, all of a sudden, one day I realized that what Mott was telling me was that interactions would make things more local, rather than less local. And so I realized that my theorem had a much better chance of really being meaningful and exact. And at that point, I woke up and rejoined the subject.

Kojevnikov:

So, should we now go back to the '58 and to the next papers?

Anderson:

Yes. Well, what happened was I wrote this paper. George Feher was still working in this field of impurity resonances. He actually got a little embittered, I believe, though he didn't show it at the time. But he was quite annoyed. Then in the course of these summer programs that we had in 1956 and 1957, we invited a lot of people and we invited Leon Cooper. This was the summer of 1956. And he gave a talk about binding of pairs of electrons, that it might have something to do with superconductivity. And we all listened and wondered if it was true. But we didn't do anything about it. We had Hal Lewis in the group at this time. He was part of the group that had formed the department. Hal Lewis was supposed to be our house theorist of superconductivity. So it would have been quite improper for me to worry too much about superconductivity, anyhow. But I certainly registered the Cooper paper and the Cooper ideas. And then the next spring, in early 1957, the first letter about the BCS Theory of Superconductivity was published. And Pines, who had been in Princeton and had gone to Illinois to work with Bardeen he went to Illinois because he wasn't offered tenure in the Physics department at Princeton), came back to Princeton and gave a talk about BCS Theory, and a group of us went down to Princeton to listen to him. I remember going with Suhl and Walker in the same car. I think several other people from the group were there, but I don't remember who. And I came back absolutely convinced that this was the right theory.

Kojevnikov:

What was Pines's attitude towards it? Because he contributed too, right?

Anderson:

Oh, Pines was of course a strong advocate.

Kojevnikov:

What was his own contribution to it?

Anderson:

I'd say less than he would like to think. Well, it is true that a paper was written by Bardeen and Pines, in which they quite properly said that the second order effects of phonons do lead to an effective attraction between electrons in metals. They derived it with an old-fashioned rendering of perturbation theory, nothing very fancy. And I guess this was the first paper in which this kind of interaction had been derived (or one of the first). And Bardeen and Pines was one of the bases for Cooper's paper. He said there is this attraction and it will then make the electrons bind together in pairs. And we have the singular phenomenon that says that there always will be bound pairs if there is an attraction. This was his contribution. Anyhow, BCS had this particular formal way of writing this out. And they had certainly, even already in the spring of 1957, they had worked out enough of the mathematics so that they could demonstrate that it was in agreement with lots of things. There was the Hebel-Slichter relocation peak in nuclear magnetic resonance. We were sufficiently impressed that we hired Charlie Hebel that summer as a new experimentalist in the labs. And so, in the early days of superconductivity, we just went down the hall and asked Charlie Hebel what's—

Kojevnikov:

You were also doing experiments with superconductivity by then?

Anderson:

Bell Labs was. B. Matthias was already doing experiments. But Matthias' experiments were mostly irrelevant, because Matthias was a materials preparer. He was just interested in whether a metal, a particular alloy, was superconducting or not.

Kojevnikov:

He didn't accept BCS?

Anderson:

No, he didn't accept BCS. It was not chemical enough for him. It was orthogonal to his way of thinking.

Kojevnikov:

How were attitudes at that time, in 1957, with different people? So you said you were obsessed with this from the very beginning.

Anderson:

Well, we had— Wentzel was one of our visitors. He was a close friend of Matthias. Matthias had gotten to know him in Chicago (and he was Swiss). So he was one of the very, very, high-level field theorists, particle theorists who came and visited us. A lot of them came. They were invited in various combinations and for various reasons. So Wentzel was a fairly regular visitor. And he in fact wrote a paper against BCS. He was one of the sources of the arguments that BCS was not gauge invariance.

Kojevnikov:

Was this the main difficulty with the theory?

Anderson:

Yes, that was the main difficulty. Well you could essentially divide people into two groups in a very simple way. Those that had worked on the problem of superconductivity and either developed their own theory or not been able to develop a theory were opposed to the BCS Theory. There were those who came to the subject afresh and looked at the achievements of the BCS Theory, and they were almost universally in favor of the BCS Theory.

Kojevnikov:

Is this also true with theorists or for experimentalists?

Anderson:

Well this was particularly theorists. Experimentalists believed it from the start. Except for Matthias. But Matthias was not a measurement type of experimentalist, he was a materials type of experimentalist. He was interested in could you predict whether metal A was superconductive or not? And so, his interests were just orthogonal to the kind of model building experiments that experimentalists were interested in: did it predict the relation between energy gap and specific heat, or the shape of the specific heat or anything like that? And those were ultimately— all of those that were predicted perfectly. So, experimentalists were very well willing to accept it. It was just that theorists tend to have well, I don't know what it is, professional pride.

Kojevnikov:

Was it after the Pines seminar at Princeton that you decided to start working on this topic?

Anderson:

Yes, I thought about it and we discussed it. Harry Suhl—I forget whether it was Suhl or Walker, they always worked very close together—made some beginning steps towards thinking of a somewhat preferable formalism. Which I later developed into a kind of effective spin formalism. And then during that summer, Wentzel came and talked about this problem of gauge invariance. There was this group from Australia, Blatt, Schafroth and so on, who made their own vaguely equivalent theory and who said that the BCS Theory has these serious problems. There was a paper by Kohn that said the BCS Theory has serious problems. As a result, I don't remember the exact point, I do remember that it was that summer that basically I began to think about it, and to realize in the first place that I think I had a sense of how the formalism should work. Here was this theory that was to any truly unbiased observer, was obviously right. I mean, it was just ridiculous to think it wasn't right. I couldn't understand people like Kohn and Wentzel, because their attitude towards physics was not my attitude towards physics. My attitude towards physics is an experiment is an experiment, and physics is an experimental subject. And if the experiments says something and your theory says something else, then your theory is wrong, it is not the experiment. So the theory had to be right, because it agreed so well with experiment. But I also was willing to accept that in the form that it was expressed, that it had certain difficulties that Wentzel and Kohn (and lots of others) were quite properly objecting to. And so this was my attitude, which it seems should have been everybody's attitude. But things which often are absolutely straightforwardly obvious to me very often turn out not to be straightforwardly obvious to other people. It was straightforwardly obvious to me that what was needed was somebody to reconcile these two incompatible logical propositions. One is here is the theory that is right; two is here is the theory that is not gauging well, it has got to be a gauge invariant. And so I thought, and I put in some ingredients from this little formal approach that was called pseuedospins that came from Larry and Harry. There were a lot of ideas also going around our group. Another pair of people that we had visiting was Elliot Montroll and John Ward, the Ward identities, and so on. They had been inventing a new form of perturbation theory, which was later formalized by the Russian group. So there were ideas about many body theory traveling around in the group at that point. And I was learning, or had learned what Pines and Bohm had done, reading from Bohm-Pines's papers and some of the field theory papers.

Kojevnikov:

Was Pines around?

Anderson:

He spent summers with us. Although I didn't actually— actually I found it not very easy to cooperate with David.

Kojevnikov:

But in this paper, you refer to some contacts with Bardeen. Were they by correspondence or personal?

Anderson:

No. Only by correspondence and meetings and so on. He wasn't around. Schrieffer was there the summer of 1956, but not the summer of 1957. And we never discussed, at that time, never discussed superconductivity with him. I discussed it a lot with Harold Lewis, but I don't think to any great usefulness. My main contacts were kind of the many body theory people, my own reading, Suhl, Walker, and Wentzel. Really, during the course of that summer, I stopped really spending much time with George Feher and I really became focused on this problem of superconductivity. Another thing that I— oddly enough, the Landau-Ginzburg paper or the Ginzburg-Landau paper of course had existed six years prior to this summer. And it was in the library, somewhere I read it—it was in microfilm/microfiche, and a very bad translation. So I had little or no understanding of the Ginzburg-Landau paper at that time. So to me it was a new idea. It was my own new idea that there was an order parameter for superconductivity. And I knew that magnetism, either anti-ferromagnetism or ferromagnetism had an order parameter. I knew the Landau Theory had outlined the idea of order parameters. But the BCS theory didn't have an evident order parameter, and I was trying to invent something which looked much more like an order parameter than the energy gap. So I was kind of sticking all these things, all these concepts together. And I developed these two papers, which essentially solved the gauge invariance problem.

Kojevnikov:

It's just in connection with BCS that you mentioned earlier, that the three of them "had perforce -though they tried very hard not to - to use states emphasizing the field of electron pairs rather than the number." (Science (1964) 144: 375) I have a difficulty understanding this point. What does it really mean, in terms of what they were trying and not trying to do in their theory?

Anderson:

Well, to kind of understand the difference, you have to ask the question how could Bose and Einstein get Bose-Einstein condensation, and yet not understand that the Bose-Einstein condensate was a superfluid? And the theory of Bose-Einstein condensation was expressed by applying the Bose-Einstein statistics in fact. My picture there - [on the wall]? That is Bose. Did you know that?

Kojevnikov:

Where?

Anderson:

You see the Indian gentleman—

Kojevnikov:

Okay.

Anderson:

And the picture above him is of Einstein. So that is a picture of Einstein and Bose. Anyhow, Bose-Einstein expressed the statistics in number form. They said, well, let's take Bose-Einstein statistics, which is an expression for the number of particles in a given state as a function of temperature and energy. So that is a number focused, micro-canonical, if you like, theory. And then they showed that there is some point below which the number of particles in the ground state necessarily becomes macroscopic. And so you had Bose-Einstein condensation. What they didn't realize is that if you have a macroscopic number of particles in the ground state, that means that the field becomes macroscopic, too. You have a state in which there is a coherent field. That is macroscopic value of a field operator at whatever point you have this finite density. And so if they had taken the square root, if you like, of their number and said, the number is 142 , and that the number is finite, implies that the field 4 is finite. The field has a phase, and the phase is that order parameter. BCS tried to build a theory which had a thermodynamic transition, but they didn't recognize that that thermodynamic transition implied existence of a macroscopic quantum field. And this wasn't what BCS did, as they were trying to do. They expressed their theory entirely in terms of numbers of particles, and they kind of averted their eyes from the fact that the numbers of particles implied that there was a quantum field, a finite field. But you couldn't quite really do that. You can't really do BCS without, in fact, effectively reintroducing the finite macroscopic field. So that's why I said, in that article, perforce they were driven to it, even though they tried their dead-level best to avoid it.

Kojevnikov:

So, what had to be added to their theory to make it gauge invariant?

Anderson:

Well, it's basically just exactly this concept, that the theory implied that there was a macroscopic quantum field, and you had to allow that quantum field to vary in space. If you make a gauge transformation, the gauge transformation is, in fact, a change in phase of the wave function. A space dependent change in the phase of the wave function. And so you had to get the right space dependent equations for the field. And this was the reason why— I mean they had made a rigid determination of the phase in this field, just as a basic postulate of the theory. And I said, "That is too rigid, let's use the whole Hamiltonian and allow the field to vary and see what the proper equations of motion are of the space dependent field." Now in doing this, I was basically, although I didn't know it, re-deriving Ginzburg-Landau. And a little later, Gorkov set to work and derived Ginzburg-Landau from BCS theory. And as far as the gauge invariance question is concerned, that is all that is needed. Essentially if you can derive Ginzburg-Landau, which is a gauge invariant phenomenological theory, from BCS, which is a non-gauge invariant microscopic theory, then you'd solve the problem of the gauge invariance of the microscopic Theory. So Gorkov essentially did the same job; he just did it later.

Kojevnikov:

So, this was the first of the three of your papers on superconductivity, right?

Anderson:

Actually the first was the one about gauge invariance.

Kojevnikov:

Yes, that is the first paper.

Anderson:

Yes, that one. This is the second one ("Equations of Motion"). That was the basic principle of gauge invariance. This was the equations of motion of the fields that I was led to from those considerations. This is, in many ways, roughly equivalent to Ginzburg-Landau in the sense that it is one way of getting a general set of equations which the operators, which bi-linear combinations of operators, of fermion operators, obey. So this is a way of deriving any collective modes, and the behavior of any response functions that you need to do. One of the important things is that... or the important thing about it is that I derived it in parallel with the methods that Bohm, Pines, and later on Sawada, and Brout and others had used for doing the plasma oscillations. And so I can show that the superconductivity did not disturb the theory of plasma oscillations. See, if it hadn't been a gauge invariant theory, (and of course it had to be), but if it hadn't been, then, all this high energy structure of the electron gas, the whole theory of plasmons would have fallen apart. The whole energy of the electron gas would have gone crazy.

And so you have to have some way of doing plasma effects and superconducting effects in the same formalism. It was that part of the subject which in fact Gorkov and Ginzburg-Landau doesn't have. Doesn't have the screening and so on. That is all inserted by hand. And this method in principle would allow you to, and in fact it did allow you to study how the phonons are affected by superconductivity as well. So this is a kind of generalized, well, I called it the generalized random phase approximation. And it was, I think really the first generalized many body way of expressing the theory of superconductivity. It's not better than what was later developed, in fact it is not as good as what was later developed by others. But it certainly was very early, and it solves a lot of problems.

Kojevnikov:

You allude in this paper to yet unpublished papers by Bogolubov. How did you know about these unpublished papers?

Anderson:

Bogolyubov sent a stack of papers over to, I think, to Bardeen and various other people. I don't remember. Bogolyubov actually came to that 1956 meeting in Seattle. Bogolyubov was one of the first Russian physicists to be allowed the freedom to travel. I suspect because he was not Jewish. But he actually appeared in Seattle in 1956. He thought, in fact, when he saw the Wards and Cooper letter and the early BCS letter, he thought they weren't as far along as they were, and so he very quickly published a whole bunch of papers. Which essentially came a little after the BCS papers, but they did the same job. And also, I don't know, he got that stuff out terribly fast. I think he actually had a book out by the end of 1957. He had a book out more or less when the actual BCS paper was published. And yet, everyone knew that it had come second, because we had been hearing the full results of BCS for a number of months when Bogolyubov's papers began to appear.

People kept referring to it as the BCS/Bogolyubov theory. That was something that John Blatt in particular took great delight in doing. But I think it was demonstrable that essentially all the components were in place by certainly what Pines talked about was the full theory, and that was in early spring of 1957. Well, one of the interesting bits of timing, for instance, is that if you look in BCS, in the actual final BCS paper, you find a note added in proof that I proved gauge invariance. So, even though my paper— When did my paper appear? 1958, early 1958. They were aware of it. I am pretty sure I had given a talk in Illinois already by then, at that point.

Kojevnikov:

How close was the exchange of information between Bardeen's group and Bell Labs?

Anderson:

Oh, very close. And various other places. Not Princeton particularly. Chicago, of course. Schrieffer went to Chicago for a couple of years before he was hired back at the University of Illinois. Nambu from Chicago was one of our summer visitors in 1957 and '58.

Kojevnikov:

And was he visiting from Illinois?

Anderson:

From Chicago. He was a field theorist. And so Nambu came and gave talks. And of course, Wentzel was in Chicago. And Hebel was going back and forth. Slichter was going back and forth. It seems as though we were all in very close contact during that period. I don't remember the exact occasions. There was a Geneva meeting in 1958. In 1957 we had that summer program. I don't remember. I should have a better idea of when and where all the informal contacts took place. But I think that all I can say is that a good description of it would be that they were very fast and furious. Everyone was talking to everyone, and was quite open with everyone.

Kojevnikov:

This third paper, random phase paper, there was a note that it was done in Berkeley.

Anderson:

It was written in Berkeley.

Kojevnikov:

Was this before there was a fallout between you and Kittel?

Anderson:

No, after. That was why I told you the Galt story.

Kojevnikov:

Why did you go to Berkeley? How did this happen?

Anderson:

So I had the idea of the new, the new method paper. Do you have a copy of the "New Method in the Theory of Superconductivity"? Where did I— you showed me one.

Kojevnikov:

Just a second.

Anderson:

This is the new method paper, and that was submitted February 1958. So, I must have worked all of that winter and you notice that I acknowledge Harry Suhl. Suhl was the one who— I guess Suhl rather than Walker who helped me invent this formalism of the pseudo spins. In the first paper I got the general idea of the gauge invariance and distinguished longitudinal from transverse and so on. Then I needed a formalism, and I borrowed this formalism that Harry Suhl had thought of I think almost immediately after hearing Pines talk about the BCS theory that spring. I know that it was the late summer or late fall of 1957 when I was working on the gauge invariance paper, because I can remember staying home—it was a beautiful late summer and fall, and I can remember staying home and walking up the hill near where I lived in [Maudham?] and lay in the grass and got most of the thinking clear. And coming down kind of like Moses from the Mount, feeling that I should be carrying these golden tablets or something. Then working with Harry, particularly with Harry and various other people, about putting it together in formalism. Then, there was a long period of just calculating commutators. I mean, these were very, very complicated equations of motion that I wrote out. And I calculated commutators until I was blue in the face, and got the basic results here. Which was that I could get the plasma modes— that there were not collective modes of the sort that Bogolyubov had in his paper of the same sort. In other words, that the true q = 0 mode, which ensures gauge invariances, was isolated — not a conventional Goldstein mode. Sometime that spring, I talked about this stuff in the spring meetings. I gave a talk at Berkeley. I gave a talk at the Monterey Meeting of the American Physical Society, believe it or not, we fit the solid state meeting of the American Physical Society into the Naval College at Monterey. It was wonderful. It was a wonderful spring meeting. Beautiful weather in Monterey, of course, in March. And rather to my surprise, in view of the fact that the last telephone call I had had from Charlie had been this very incoherently angry call, he called me up and said, "Well Freeman Dyson has been here the last two summers. I got this money, this big grant," from I think from, who were the graphite people?

Kojevnikov:

Yes, National Carbon Corporation.

Anderson:

National Carbon Corporation. "I got this big grant, and Freeman Dyson has been using it the last two summers but he can't this summer. He is going off to design reactors. So will you come and spend the summer here on Freeman Dyson's grant?" and stay in the same house and so on. A very palatial house in Berkeley Hills, very close to the cyclotron lab, 800 feet high in the Berkeley Hills, on Berkeley Hill with a fantastic view. Anyway, I was rather surprised and I— but it didn't take me very long to say, "Sure. Of course." And so Joyce and I flew halfway across the country and drove from Denver to Berkeley and spent the summer in this beautiful house in the Berkeley Hills.

And things were happening. Let's see. What else was happening in Berkeley? Number one, Jim Phillips was there doing a post doc. So we saw a fair amount of him. Ted Geballe, who had been at the labs, and was still at the labs at that point was visiting Stanford. He was a very close, very good friend. And he was the head of the department in which Matthias was. He is also the husband of Francis Geballe, born Koshland, who was one of four heirs and heiresses of the Levi Straus Company. And so her family kind of owned San Francisco though I didn't know it at the time. And so they were there for the summer and so they hosted us on a number of occasions. Which was very pleasant and luxurious. Tom Lehrer was there, singing at the Hungry Eye. And he was, of course, an old friend. So it was a very pleasant summer. Except for the fact that the house had a beautiful view for exactly three days, and the entire rest of the summer, it was in the fog. So we never saw the view again. But we did have a pleasant time. Tom, in fact, invited us to the Hungry Eye, and he said, "When you come, be sure and catch the act before me." You probably, being Russian, don't know these names, but the warm up act for him was a trio called the Kingston Trio, which later became nationally very popular. Had several platinum records and so on. Now, what I did was to finish up that paper, and that is why I gave that acknowledgment. But really, the work had been done during the spring.

And I was thinking at the same time— well, some time during this four years between returning from Japan and this summer of 1958, Fred Seitz had gotten in touch with me for two things. One was that he wanted me to write a review article on anti-ferromagnetism and exchange interactions.

Kojevnikov:

That was for his series?

Anderson:

For his series. The other was that he wanted me to come take a job in Illinois. And that was a little agonizing, but in fact wasn't in the cards, because both my wife and I love our parents, but do not believe in close proximity to our parents. We were very independent people, and were quite happy not being tied to the parental apron strings. Particularly true of my wife, but also true of me. And mine were at the University of Illinois, and her parents were in Chicago. Anyhow, I felt guilty because for several years I had not written this review article. And I kept thinking about super exchange, and thinking and thinking, and it didn't seem to me that it was really putting itself together. But I had this review article project that I was going to do, and so I kept thinking about it. And sometime during this summer, I think it was in the early part of the summer, I don't know why. This is one that really did come out of the blue. I put together the idea of the Mott state with the Mott transition (which had been something I had been thinking about for many years, ever since the localization paper) and the idea of super exchange, and I realized they were the same idea. And so in the first month of that summer, I actually was, while I was writing this random phase approximation paper, I was also thinking about super exchange. And sometime during that summer— then at Berkeley everything was happening at once. Leslie Orgel came and visited the physics department at Berkeley. And he explained the way, which hadn't really been clear to me, how crystal fields, how magnetic ions interact with their surroundings in such a way as to create preferential orientation for the orbits of the magnetic electrons. So he explained crystal field theory. This explanation of crystal field theory was actually due to my old professor, Van Vleck, but I have to confess I never read it. So Leslie Orgel explained to me Van Vleck's theory of crystal fields. And that gave me a way of quantifying these ideas about super exchange. So there is the Mott transition, or the Mott phenomenon, and the idea of putting in the parameters from crystal field theory. They all came together, and so I invented the superexchange theory. That is that paper. Interesting too— I don't know whom I acknowledged or where I was. Discussions with Carl Ballhausen, Leslie Orgel, Toro Moriya [?]. Yes, he was visiting. He visited me in the following winter. Oh, Charlie Kittel, Frank Morin, we were worrying about metal insulator transitions. And Bob Shulman was working at the same time on transferred hyperfine structure, which is part of the crystal field story.

Kojevnikov:

Is there any connection between this paper and your work on superconductivity?

Anderson:

No. This was totally— this was just something that I was doing at the same time. Work was begun during the stay at the University of California made possible by a US grant from US Carbon, again. So, I was finishing superconductivity. But these ideas of the Mott insulator and this connection with crystal field theory, which gelled while I was in California. But I actually worked on it, this was February 4, 1959, and the ideas really were that winter of 1959. Also, that same summer, I was talking with Jim Phillips one day about superconductivity and he was saying, "Why, why, why is it that superconductivity is so independent of impurities?"

Kojevnikov:

Chemical impurities.

Anderson:

Chemical impurities. And without knowing what I was saying, I just said, "Well, it has be to time reversal—time reversal invariance." And I think if you can find the paper about the theory of dirty superconductors, you may find one of those—

Kojevnikov:

There is one here, and the other one is in the book.

Anderson:

The one in the book, probably. You may find the...no, there's not the famous carbon acknowledgment; there should have been. 1959, so it has to have been written during that same winter. The original idea was conceived in California just in this conversation with Jim Phillips. For some reason I didn't acknowledge him. But I can remember being back in my office at Bell in the fall before I actually put it together formally. So, it's appropriate that it not have the US Carbon acknowledgment.

Kojevnikov:

How is this related to controversies about the Knight shift? Is this another difficulty of the BCS?

Anderson:

It is a difficulty of the BCS, but I never felt that—

Kojevnikov:

There were a lot of papers about that.

Anderson:

Yes, there were a lot of papers about that.

Kojevnikov:

What were the papers that you know of?

Anderson:

This is the correct explanation. I mean, my paper is the correct explanation, and this is not. They didn't realize the difference between the two different relaxation times, and so on. I think you showed me a paper by R.A. Ferrell.

Kojevnikov:

What was the difficulty there?

Anderson:

Reif was going around. Ferrell I guess thought he had explained it. The difficulty was that if you calculate the Knight shift, the uniform magnetic susceptibility of a pure superconductor, it's zero and has to be zero, because the electrons are all in singlet states, and the uniform susceptibility of a singlet— There is a well known selection rule, J = 0, goes to J = 0. It's a well known electromagnetic selection rule, perfectly satisfied. So there is no way that you could possibly have any spin susceptibility. Yet, spin susceptibility was observed. And a lot of people made a great fuss about this. I never felt that it was important. But Reif had himself a good time traveling around, giving talks about how BCS was wrong. Because when he divided superconductors up into five particles and measured the Knight shift, it was quite large. That is, the Knight shift is supposed to measure the uniform susceptibility. And the answer is spin orbit scattering. And it is easy to quantify, because, you know, there have been measurements of the rate of spin orbit scattering in a magnetic resonance, and the phenomenon of the spin orbit scattering is well understood. One can, by measuring the width of the resonance line, show that some of this is killed by superconductivity, and the rest of the resonance line is above the gap. It is not killed by the energy. So that was kind of trivial. That was a conventional medium kind of paper. The dirty superconductor paper was a little more than knitting, because it was the first appearance of something I called the n-representation. The scattered state representation with time reversal invariant pairs in scattered wave functions rather than in free plane wave functions. And that technique was used by deGeirnes and his group very, very effectively in explaining all kinds of things about superconductors. It would have been picked up by Tsure too, and then deGeirnes and his group picked it up and ran with it. So it was a useful formalism, but also an interesting idea. On the other hand, it isn't of the quality of this superexchange paper, nor is it the quality of the random phase paper.

So, I was very busy during that roughly six-month period. But I did one other thing. Charlie Kittel apparently— Far as I can tell, his problem was that he really felt ashamed of himself for having screamed at me over the phone about cyclotron resonance. Because he was certainly quite pleasant and warm during that whole summer. And about halfway through the summer he came to me and he said, "Look, I am forming a group to go to the Soviet Union. Would you like to join me?" And, I said, "Sure! Of course."

Kojevnikov:

Was that a second time for him? Or he didn't go the first time?

Anderson:

No, he didn't go that first time. So, he, I, Matthias, Cole, of the Cole-Cole graph, and Walter Metz formed a delegation and went to the all-Soviet Conference on Dielectrics in December of 1958.

Kojevnikov:

That was 1959, or 1958?

Anderson:

1958. These were theorists and experimentalists—

Kojevnikov:

Yes, all in condensed matter?

Anderson:

All in condensed matter. Three experimentalists, two theorists. I hadn't done anything about dielectrics since 1951. Charlie Kittel had one paper about dielectrics, but I think that basically the invitations to this were controlled by some committee, and certainly Landau wanted Kittel and me, and maybe Bogolyubov, although we had no contact with him. Anyhow, so we went in December. As you can imagine—

Kojevnikov:

Could Bardeen be included in such a delegation?

Anderson:

I don't know. Well, Bogolyubov would have had veto power. And I don't know. There were obviously internal politics involved in Landau versus Bogolyubov. The Landau group couldn't abide Bogolyubov. I suspect the feeling was mutual. But this was apparently more under the control of the Landau group. Anyhow, we went. My main reason for going was to get in touch with both Bogolyubov and Shirkov, because they were the only other people who had thought about collective modes in superconductors, and I wanted to talk to Shirkov about collective modes in superconductors. Matthias went, because Matthias likes to go places. Kittel went because he was running it. I put together a talk explaining the ideas that I had back in 1951 about ferroelectrics.

Kojevnikov:

Where was the conference?

Anderson:

Moscow at the—

Kojevnikov:

At Landau's Institute?

Anderson:

No, it was not at Landau's, it was at the Lebedev [?], which is across the street, isn't it?

Kojevnikov:

Not very far.

Anderson:

Not very far. I remember just basically going across the street to the Landau Institute. Charlie knew Landau and knew members of the Landau group. And so we were invited to the Landau Institute and spent a day, day and a half, visiting. Lifshitz actually translated my talk at the dielectric conference. But of course, we mostly went to the dielectrics conference, which was very boring because it was full of rather bad physicists arguing kind of very bitterly about rather inconsequential points. This was an internal meeting. This was not an international congress. This was the all-Soviet meeting. So we were the only foreign visitors. We were the second—

Kojevnikov:

Was there translation? Or, how did you follow the talks?

Anderson:

We had simultaneous translation. There was a remarkable man whose first name was Yuri. Matthias called him Harold, because his name was Yuri. Mattias by now was at San Diego and he knew Harold Urey very well. He was, well, I didn't really register it at the time, he was the most obvious KGB man you could possibly imagine. He spoke impeccable English with a slight Australian Cockney accent. He claimed he had never been in the West. Where he learned English at that level— there is no way, unless he had been trained like in the KGB.

Kojevnikov:

Did he know any physics at the translations?

Anderson:

He seemed to know physics, too. And he claimed that he had had no training as a physicist. But he would— someone would get up or stand up in the audience and give a long question, technical question. And Yuri would look down at us and smile and say, "He's asking are you really right?" And then an equally long answer would come from the speaker, and Yuri would look down at us and say, "He says no." And he was, you know, he was right. He actually had a good enough understanding of the technical matter at the level of most of that conference. So there is no way he was just an Intourist guide. There was no way— we had three of them. Victor, Yuri, and a girl, I forget what her name was. And the three of them were of a quality that was not Intourist guides. They were obviously our three KGB minders. But they were very pleasant, very easy to get along with. When the conference was over, I stayed a couple of days, just to look around. And Yuri spent a whole lunchtime trying to persuade me on the superiority of the communist system. And again, I didn't realize at the time, but I am sure that he was— had in mind recruiting me, but decided better. I didn't recruit, anyhow.

Kojevnikov:

What did you talk about at the Institute, at Landau's?

Anderson:

At Landau's Institute, I talked about the Random Phase Approximation paper. Landau let me talk for an hour, and then he said, "Well, if you need any more time to complete what you are saying, you're welcome." And so I talked another 15 or 20 minutes. I gather this is pretty unique, being allowed to talk for an hour and 20 minutes by Landau. Abrikosov was my host, more or less. Well, at first, as you know, he was more of, kind of a direct assistant to Landau. And I hung around there quite a bit and talked a lot with Abrikosov. I tried very hard to see Shirkov or Bogolyubov, and Yuri and the Intourist organization tried to make all kinds of contacts and telephoned all the time, and we were basically blocked from seeing this group. Whether it was done by the political establishment or by the KGB or by Bogolyubov himself, I don't know. We did eventually get a sight seeing tour to Dubna.

Kojevnikov:

That basically, was where he was, right?

Anderson:

Yes, he was at Dubna. And Dubna, one way or another, and I am not sure exactly how it happened, Shirkov came up to me as we were being escorted around on a tourist tour. I had gone to Dubna assuming I would be brought in and we would talk physics. We were given the absolute tourist treatment. But Shirkov appeared at one point, and he and I ran off to an empty room with a blackboard and we talked for about 15 minutes about collective modes, and in a very friendly way. It was clear that he wanted to see me and it was clear that I wanted to see him, but there were— we had minders. And eventually the minders came into the room and escorted us, and said, "Professor Anderson has to go elsewhere." And then I had to go elsewhere. So I was clearly directly prevented from talking to Shirkov.

Kojevnikov:

Would it be possible somehow to clarify what were the commonalties and differences between the approaches of superconductivity by you, Shirkov and Bogolyubov? And perhaps, how Landau group understood superconductivity at that time?

Anderson:

Well, when we got to see the Landau group, the first thing they said was Gorkov has derived Ginzburg-Landau from BCS. And therefore, there isn't a problem of gauge invariance. I didn't really— I was gradually coming to understand Ginzgburg-Landau, but I really didn't understand it totally clearly as yet. And I said, "Yes. I suppose that is right." But on the other hand, there is this interesting question of how do you have Ginzburg-Landau and gauge invariance, and at the same time have plasma oscillations?

Kojevnikov:

Which are the collective modes?

Anderson:

Which is a collective mode, and in particular, the point is that you have this order parameter. I mean, this is the key factor of superconductivity. You have the order parameter, but you do not have a Goldstone boson. You do not have a low frequency boson that represents the distortion of the order parameter. The distortion of the order parameter is not soft. At least the longitudinal distortion. And that was the key thing that I had understood in these papers. Which is now called the Higgs Phenomenon, that if you couple a superfluid state with a gauge field, that you can break the Goldstone boson. You can have broken symmetry, but no Goldstone boson. And that is the structure that is in that paper that was vaguely expressed. So in that sense, it's not really true that Gorkov had the right gauge invariance, because he had to have an understanding of what the role of the gauge field of the photon— the photon field is. And he didn't. He didn't say how did the phonon field live with this. And the answer is plasmons. So Gorkov did not have, again, the Higgs Phenomenon. On the other hand, it is very important. And that derivation that was by Gorkov is really in many ways one of the three major achievements of Superconductivity Theory. Namely, Ginzburg-Landau, and BCS, and the connection between the two. But the Landau group had been looking at the thing from the Ginzburg-Landau point of view, but they hadn't understood it. They had been looking at the pairs. BCS looked at the thing from the pair point of view, but didn't realize that it was an order parameter. And Gorkov understood how to put the two together and so did I, but not quite in such a useful form. So, Gorkov and I, were in my eyes playing the role of, the kind of a Dyson role or Dirac's role. You had wave mechanics, you had matrix mechanics, somebody had to put them together—that was Dirac. You had diagrams, you had Green's functions, somebody had to put them together, that was Dyson. You had BCS, which was the microscopics of the phenomenon; somebody had to put them together, that was Gorkov.

Kojevnikov:

When did you get your gauge theory or where did you learn gauge theory? What did you know of the particle physics at that time? What papers have you read?

Anderson:

Not much, not much. I absorbed it, kind of by osmosis, which means, not particularly well.

Kojevnikov:

From whom?

Anderson:

I read Dyson over and over again, and gradually understood a little more every time.

Kojevnikov:

You have the original papers?

Anderson:

Yes. The gauge interaction idea, probably that was absorbed from lectures that John G. Taylor, who was one of those many visitors we had. I don't remember...I don't really remember where I learned the gauge principle. I didn't really understand the gauge principle until actually a little bit later when I had kind of learned it in connection with Yang-Mills Theory.

Kojevnikov:

But that is the modern version of the gauge principle anyway.

Anderson:

That is the modern version. But we had a couple of field theorists. We had Wentzel but particularly we had J. G. Taylor.

Kojevnikov:

And Nambu, or was it later?

Anderson:

Nambu, yes. But not, I believe for long.

Kojevnikov:

Why would they come to Bell Labs?

Anderson:

We invited them. For one they came because of superconductivity. He was interested in giving us his version on superconductivity. And then there was Nambu Jona-Lasinio which was the first particle version of broken symmetry. This was a period when there was contact between the two worlds — the world of particle physics and the world of many body physics. We had a number of these people who visited Bell Labs fairly regularly. Klauder was a mathematical physicist interested in coherent states and things like that. John G. Taylor came around. John Ward came in and out of the Bell Labs. At the same time, we saw these people in meetings. People— well, I went to the Utrecht meeting a little bit later, and it was attended not just by many body physicists but by Yang and Lee. Yang and Lee came to Bell Labs, or at least Lee did. And particularly Kerson Huang spent a couple of summers at Bell Labs talking about—

Kojevnikov:

Doing what?

Anderson:

Well, he was interested in— he had this theory for hard core bosons and hard core fermions, and he talked about that. He was doing that. Peter Wolff had been a field theorist, and I talked a lot with Peter about field theory. So, I kind of learned it all by osmosis and gradually, and very incompletely.

Kojevnikov:

But it was the gauge question that sort of brought you in this?

Anderson:

Yes. And this was from Wentzel.

Kojevnikov:

And if we can return to this visit to the Soviet Union, how do you explain the difference between the Bogolyubov group and your approach?

Anderson:

Well, Bogolyubov had been in and out of many body theory. Well, like Landau. He had this theory of the Bose gas, which turns out to be roughly right. Well, not roughly right, but is what the present theories of the Bose-Einstein condensate in gasses are based on.

Kojevnikov:

At that meeting when you talked to Shirkov about the collective modes in superconductivity? Did you have the same understanding?

Anderson:

Well, we were all very much on the same wavelength. I mean, Bogolyubov's theory was all but the same as BCS, except that he had a better formalism for the structure. Instead of square of h and 1-h, he called them U and V, and he had these alpha operators, we called bogolyubons. That is a much better formalism than the BCS formalism, which is very awkward. It was the same formalism as BCS, essentially not similar to Nambu's. Nambu's was the same that Harry Suhl had invented which I took over for any random phase paper. So, we were all on very much the same wavelength. The Landau group, I think, was quite a bit ahead of us in many ways, in that they were already expressing everything in terms of Green functions and correlation functions. So their formalism was way ahead. They had re-invented the Montroll-Ward formalism. Kadanoff-Baym, or actually Schwinger-Martin, Montroll-Ward, and Abrikosov-Gorkov-Dzyaloshinsky, all three groups invented the same formal way of expressing many body theory. There is no priority, because none of them knew that the other one was doing it. And they all did it about the same time. And the Landau group was basically on that level, but they didn't have the understanding of the microscopic level, that to some extent, Bogolyubov and certainly Bardeen and company and then we had. And they hadn't been thinking about phonons and how phonons fit into the general structure of this many body theory and so on. It was a wonderful period in that this was a period when everyone was talking to everyone else. And there was tremendous cross-fertilization between Nambu, me, Bogolyubov, Landau, later on Weinberg, Ward, John Taylor, and Pines, the Bohr Institute group, Jerry Brown. And everyone was doing things in more or less the same game asking the same kinds of questions.

Kojevnikov:

How was the discussion of your talk at Landau's seminar? How did people behave and what questions were asked?

Anderson:

Oh, they were fine. I mean Landau's remark was just, "Well, it is interesting there is another way to do it." He didn't say Gorkov's is better, or worse. And he was particularly interested in this business of the collective modes, which Gorkov's theory or the Ginzburg-Landau theory gives you no way to approach. So the collective modes are to this day called the Anderson—Bogolyubov modes, because we were the only people who were thinking about them. And they are found in other cases, not in BCS, but in other cases.

Kojevnikov:

Were you all, at that time, thinking about liquid helium? Or did it start only after the superconductivity phase?

Anderson:

No, no.

Kojevnikov:

So what motivated you to start working on the liquid helium, the liquid helium III? I guess that's...we are going over to the next set of papers.

Anderson:

Yes, we did, we're jumping. We're not jumping anything, just... Well, there is this paper about dielectrics, which was the soft mode paper, and that of course was given just in order to get to the conference. Then there was this sequence of papers about dirty superconductors, Knight shift, and spin alignment in the superconducting state. I was going around to conferences on superconductivity. The way we had formed the group, we certainly were free to travel, and I certainly traveled. First I went to Berkeley, then I went to Russia, then in 1959 went to no less than two conferences in England. We went to a conference at Cambridge on superconductivity where I talked about my stuff.

Kojevnikov:

Is it this one?

Anderson:

No, no. That is much later.

Kojevnikov:

Okay.

Anderson:

In 1959. It was held at Clare College, or we ate and slept at Clare College. I don't really remember where the meeting was. That was my first kind of conventional international conference. Joyce came, and Susan my daughter came, and we had a wonderful trip around England. I went to a sequence of conferences on superconductivity. There was also a Lake Geneva Conference, where this whole group met. Of course, there were ideas going back and forth in all of these meetings. But one of the people that had been particularly visiting Bell Labs and spent quite a bit of time at Bell Labs during these summers, and I think summer of 1959 in particular, was Keith Brueckner, whom I had already met in Japan once. But he seemed to like to come to Bell Labs. And he was very much into, well, we were all very interested in the nuclear many body theory. Well, if we're doing well with electron many body theory, why don't we think about nuclear many body theory? And he introduced us the idea that there was another fermion system namely, Helium III. And of course we were also talking about the Landau work on many body theory, demonstrating the existence of the Fermi surface and Landau's Fermi-Liquid Theory, and so on. Luttinger in particular was interested in that. So, we were absorbing a lot of formalism at the same time. But it was Keith Brueckner who began my interest in Helium III. At the same time, in the course of talking around at these various conferences, I had come across the idea, actually in an obscure, long paper by a guy at GE. John, Fisher. The idea that BCS wasn't only the uniform BCS state. There is the possibility of angles in the BCS states. And so I had acquired this graduate student, a very bright guy named Pierre Morel, who was the scientific attaché at the French Consulate in New York. He had come to New York expecting to be able to work with David Pines. The reason why Pines had good contacts with France was that his long time collaborator was Nozieres, who was Morel's closest friend. But then, unfortunately, Pines left in 1957 for Illinois, so Pierre Morel could not work with him, and Pines said, "Well, why don't you work with Phil Anderson at Bell Labs." I had just come across this idea of an isotropic super-fluids, and so he and I started to work on an isotropic super-fluids and put together a formalism for an isotropic super-fluids. Keith Brueckner came through with the idea that Helium III was a Fermi liquid system. And I said, "Well, maybe it's an isotropic super-fluid." And before I knew it, there was Keith Brueckner with a paper on the theory of the an isotropic super-fluid, Helium III. And I said, "Hey, wait a minute. I've got a graduate student working on this." And he allowed as how he had gotten the idea from me, and that therefore he ought not to publish it independently. So that produced this weird collection of authors, Brueckner, Soda, Anderson, and Morel, on a tentative theory of liquid helium III.

Kojevnikov:

How was it related to Landau's Fermi Liquid Theory?

Anderson:

Well, only that Landau's— I didn't know whether it was Landau or Pomerauchuk or some experimentalist, but it had been gradually appearing that helium III was a Fermi liquid. Actually had a Fermi surface, quasi particles, and so on. From the experimental measurements, mostly by John Wheatley, who developed para-magnetic cooling down to three millidegrees Kelvin. You need to get down to some tenths of degrees Kelvin before you're quite sure it's a Fermi liquid. The reason why Helium III was just being investigated at this point. I didn't appreciate this until later. The point is, that tritium decays into the Helium III with a half-life of 12 years, and tritium is essential for hydrogen bombs. The hydrogen bomb was first built in 1950, so around 1960 you began to have enough Helium III so you can do macroscopic experiments on it. So the timing of experiments on Helium III has to do with when hydrogen bombs were invented. Tritium, of course, was produced in nuclear reactors, but then it decayed into Helium III, which we had no use for except to do experiments. So, we had a pretty good supply of Helium III. Los Alamos had a pretty good supply of Helium III, and John Wheatley was allowed to work on it. So we were beginning to realize it was a Fermi fluid.

Kojevnikov:

Was any of these experiments performed at Bell Labs? Or were you doing this superconductivity and helium III stuff, all the experiments you needed, you just took from other labs?

Anderson:

From the literature. As a matter of fact, at this point there were almost no experiments. So this was a conjecture. And then Morel and I, in the course of his thesis developed a formal theory.

Kojevnikov:

I think we came to the gist of this paper, to the generalized BCS states.

Anderson:

Yes. So, Pierre worked this out for me. This was the first time I guess I had a student who was more than just a summer helper. I have had summer students who more or less worked out my ideas for me. I didn't mention the summer students, but Jim Talman was my summer student a couple of years. He is a fairly well known relativist, as a matter of fact, a student of John Wheeler's. In the second year, I didn't know that I was trying to, but I was trying to invent the scaling theory of phase transitions, and failing terribly, with Jim. But he did what I wanted him to do. I also had Frank Stern one year with whom I originated the concept of "frustration"! But this was a real collaboration, and Pierre produced as much as I did. And I think it has more in it, really, than is acknowledged, rather than less. Basically, what we recognized is what no one else who was thinking in this field came within miles of. That you have a phase transition and it is observed in helium III. It is very much the characteristic of helium III. There was the phase transition, which is controlled by kind of the overall structure of the potential. If you like, the L = 2, or whatever the angular momentum is, scattering matrix. This is the result of a linear equation and its phase transitions are separated off by angular momentum, by the group theory of the system. But then angular momentum 1 or 2 can be realized in many different possible ways. And that turned out to be the case in helium III. There is the A phase and the B phase. It is a very strange structure, and it is not to be anticipated. And we invented it. We said, "Look, there are lots of structures. Lots of L = 2 phases." Not lots, but a number of them, a discrete number. And you'll have different properties but the same transition temperatures for these different phases. And we calculated some typical ones. But it's understanding the nature of the broken symmetry that's important. Well, for once, we were discovering something really important without having any experiments whatever. We predicted that rather than discovered it. Other people predicted that helium III would be super-fluid. Emory and Sesler claimed to have done. They predicted the L-isotropic super-fluid idea after we did. Derivative, probably, from what we did. But no one really looked into this interesting symmetry structure and phase boundary structure that we found. I think that's important, and it has been characteristic of this type of phase transition ever since.

Kojevnikov:

How did you work together? Did he come out?

Anderson:

He came out. He came out to visit.

Kojevnikov:

How frequently? Or how often was it?

Anderson:

Every week or so. That was not the only thing I did with Morel.

Kojevnikov:

Was he like a post-doc, or [inaudible]?

Anderson:

At least in those days, a French Ph.D. candidate was equivalent to a post-doc in that there is a preliminary degree and then there is a final true Ph.D. You may know the structure, I don't know exactly. But Nozieres, for instance, did a degree. I believe he did a starter project with Pines and had a formal academic status. Then his final Ph.D. was much more advanced that a typical Ph.D. And the same thing was true of Morel.

Kojevnikov:

What happened to him then?

Anderson:

Well he ran, maybe still runs, in France, the Space Program. He became very eminent. I met him a couple of years ago, several years ago, three, four years ago. It was when I was in France getting an honorary degree.

Kojevnikov:

There was another period when you worked together, but that was on a separate issue, was it not?

Anderson:

Yes. Entirely separate. This is I think, in many ways, more important. Well, not more important, but this is also an important paper. This I talked about in this article I wrote, called, well, "It Isn't Over Until the Fat Lady Sings." Which, Lillian Hoddeson used as material for her history of superconductivity. Almost intact. It's really my words. I didn't give her permission to make me a co-author. And the point was, I had been thinking, well, ever since 1959, when I put together a set of lecture notes for Stanford when I was there, more or less being looked over for that job, trying to understand the physics of the electron phonon interaction in BCS superconductors, I had gradually gotten together a very clear physical picture of what goes on.

Later I realized that what one wants to do is to average, more or less, in the spirit of my dirty superconductor paper. I wanted to average over all momenta, average around the fermi surface. If you average over that many momenta, you might as well average over the whole space of momentum values. Which means you have basically a local theory, a theory which has no space dimension in it. Essentially that means averaging over the unit cell, and kind of an Einstein model. Treating the phonons as though they were Einstein phonons, treating the interaction as though it were actually directly local. Using the linear structure of the interactions entirely in frequency space, or entirely in time space. It's retarded in time, but you're not taking into account anything that has to do with space. You're saying the electron only interacts with other electrons that are in the same unit cell. But, then interaction may take place at a later time. So the time dimension is long, the space dimension disappears. And I talked it over at length with Bob Schrieffer at the Utrecht meeting. Well, let me say some more about the Utrecht meeting later. And Bob at that time told me a little bit about the Eliashberg equations. He had been in communication with the Russians. And he talked at length to Eliashberg, or to Gorkov who told him about Eliashberg. And Eliashberg had this set of equations, which were on the formal working out of Hartree-Fock theory for the case of superconductivity, to essentially rethinking BCS Theory as a mean field theory, and working it out in the correct formal structure.

But again, that structure has both a frequency and a space variable. You use an interaction, which is an arbitrary function of X and T. Well, Eliashberg hadn't really thought about the physics that was going on. He just had written down the right formal theory. So, I told Morel about Eliashberg, and he went and spent a little time at Illinois and talked to Schrieffer and got the Eliashberg equations from Schrieffer. So I had set the problem to Pierre to express the theory essentially in time variables and suppress the space variable and work with an interaction potential which is only a time function. And we realized that— Well, the first thing we did was to give an overall view of what elements are superconducting and what are not. It works pretty well. You can estimate that using the old Bohm-Pines-Tree Theory of phonons, phonons as a plasma phenomenon. And this time dependent theory, you can more or less get an overview of superconductivity in the periodic table and it worked surprisingly well. We also successfully estimated the isotope shift parameter. You have a pretty good correlation between your prediction and the actual transition temperatures, or lack thereof In the course of doing this, I mean, that was the only experimentally relevant result we could think of, but in the course of doing that, we solved some model equations for real metals. And developed various methods for doing this calculation. And that is what this paper is. But then, while I was in Cambridge the next year, I heard that John Rowell at home back in Bell had been studying tunneling between superconductors, and he discovered that there was energy structure in the energy gap by tunneling. Then it turns out that this set of equations is exactly what you need to understand these tunneling singularities or bumps in the tunneling curves. And at the same time, Bob had been busy putting Eliashberg's equations on line with my simplification as to averaging over the space variable. And so, this eventually led to a program of actually making correlations between measured phonon spectra and coupling constants in lead and tunneling curves in lead, which was really the thing that has pinned down the theory of superconductivity, ordinary, normal BCS superconductivity. And that was what I called the point when "the fat lady sang." Or you can really make a quantitative comparison between the transition temperature and the resistivity of lead, the phonon spectrum of lead, and the tunneling curve of lead.

So this was the first stage in that it first became clear that you can really calculate instead of just saying, "Well, there is a phonon interaction and it is approximately so big, and it extends over so and so much," that you couldn't even calculate. That you could do superconductivity, actually, at that time, much more accurately than you could do theory for any other phase transition. So that this was the beginning of the quantitative period of superconductivity theory. And, well, there were some very important things that Pierre contributed to this, too. In particular, since we didn't have computers in those days, there was a lot of analytical mathematics that only a French graduate student would have known. And he contributed that. So that was in 1961. It was quite a bit after the period that we have been talking about.

Kojevnikov:

I think we should move to the localized magnetic states, or should we leave it for the next?

Anderson:

I think we better leave that for the next one. In particular, I don't really— Oh, I do know. That came out of superconductivity, too. That was the superconductivity theorists rather than the magnetic resonance theorists. And so I heard all the stuff that went on in superconductivity. But, well, what we ought to do the last little bit about the Utrecht meeting. A good place— there's the picture. There's the room, and it's full of names. There is Harry Suhl, there is Bill Fairbank, that's DeBoer, that's A. Klein, that's Paul Martin back there, that's Cyrano de Dominici dome, but, oh here, this is T. D. Lee. It had everybody.

Kojevnikov:

What year is that?

Anderson:

That's 1960, June, 1960. This is the period, above all, where we really all met in the same room and we were thinking about the same things. That is David Pines, Jeff Chester somewhere over in here, Jerry Brown, Sawada, Kerson Huang, Claude Bloch. Well, I could—

Kojevnikov:

And was it on superconductivity?

Anderson:

David Thouless. It was many body theory and field theory. It was everything. In the first place, this was only for a meeting, and in the second place I decided, well, this was almost my first big international blast, I was going to gamble and so I gambled. I talked about Morel and Anderson and anisotropic superfluidity. So I gave the first talk about anisotropic superfluid helium III in 1960 at this meeting to this audience. And that was all right. It was fun—it was fun meeting all these people. Montroll was there. That's Van Hove, of course.

Kojevnikov:

I'll just put this up. Just coming through his diverse set of papers, how would it be possible to summarize what was the underlying common approach or style or concept? Or maybe it comes more about the question of philosophy or research philosophy or style?

Anderson:

When you first brought that up, I realized that it went the other way, almost the other way. The philosophy developed from the subject, rather than the other way around, from the material. I was developing a philosophy, and in the end I wrote it down. And the philosophy well, it's several things. One of the themes is best expressed in the More is Different paper. And the other theme is this general theme of broken symmetry. I didn't know yet that I had a philosophy. I suppose I was— but I was developing a sense of unity in this very diverse looking batch of material. But it isn't fair for me to project back to that time the idea that I developed later. There was this idea about broken symmetry, and that implied an order parameter. The order parameter had the freedom to move that was controlled by the missing symmetry elements in the broken symmetry. And that was to come in a lot of different places. It was perhaps clearer when we get to the Josephson's Effect and so on.

The other thing is this idea, which now I call it emergence. It's the idea that there are concepts and structures which are the result of the behavior of these complex large systems. And that aren't automatically obvious from the underlying level of microscopic phenomenon, so that you get this emergence of new concepts and new behaviors of new things. In the old days when I first started, I would call it the one big molecule idea. The fact that the big, the macroscopic has its own rules, and obeys quantum mechanics just as much as the microscopic. But it can do different things. That was the thing I had glimpsed in the mention of, if you like, Goldstone bosons. We invented Goldstone bosons twice. Once as anti-ferromagnetic spin waves, and the second as these Anderson-Bogolyubov modes, and then I wiped them out again. And I realized I was doing something very general there. I mean, that is why I saw that they had to be there in the superconducting case. I saw that there had to be an order parameter which had symmetries, and that it had to be mobile. That somehow it didn't cause any Goldstone bosons. Thus I was looking for the connection between the macroscopic and the microscopic. And that it isn't really fruitful to keep the two levels completely separate from each other. The localization says there is a behavior of a macroscopic object, which is generic to dirty systems, generic to disordered systems. No, it's not that the disordered system is a messy version of the clean system. It's the disordered system is entirely different and it's something on it's own. It's something generic, intrinsic—that there is such a thing as intrinsic dirt effects. Some deep meaning to a system being fundamentally disordered, not fundamentally regular. Behavior that happens in a disordered system that doesn't happen in a regular system. Just as behavior happens in a macroscopic system that doesn't happen in the microscopic system. To some extent, I have been developing these things later. But it was going through examples that I developed these concepts, this new philosophical attitude.

Kojevnikov:

If this was clarified, I guess one of the basic problems with the solid state is how to distinguish between something which is specific for a particular material, or a particular substance, from a more general—

Anderson:

Yes, there is a third element to the style and the third element is, trying to find commonality. And never count on using the unitary [?] system. Never do examples one and one and one and one. Never try to answer the Red Queen's question. Never do things one at a time. ..what's one and one and one and one and one and one?" Try to find the common feature of a lot of different examples. Try to find the model, which will typify, which will tell you the intrinsic nature of the phenomenon without having to go into lots of messy details. The modeling trick is two-fold. This I guess I did understand very early. There are two conflicting goals. One is to simplify and the other is to get a behavior which is really different from the underlying substrate. So if I want a model for localization, it has to be simple enough so I can solve it, but it has to be complicated enough so it shows localization. And other people have demonstrated to me that the possibility of over-simplifying is there. I mean, I have had I proved to me again and again and again that localization doesn't happen, because the guy built his model so that it doesn't happen.