Nobel Lecture : Superfluid 3 He : the early days as seen by a theorist *

It is needless to say that I feel it a great honor and privilege to have been selected for the 2003 Nobel Prize in Physics for my theoretical work on superfluid He; I am particularly pleased to be sharing the award with Professors Ginzburg and Abrikosov, whom I have always looked up to as giants of the closely related field of superconductivity. The story of how, in roughly the twelve-month period July 1972–July 1973, we came to a theoretical understanding of the experimental data on what we now know as superfluid He is a sort of complex detective tale, involving many actors besides me; for reasons of time I will concentrate in this lecture on my own involvement and will have to omit several important developments in which I had no direct role. The element helium comes in two sstabled forms, He and He; at low temperatures and pressures both form liquids rather than solids. The liquid phase of the common isotope, He, was realized nearly a century ago, and since 1938 has been known to show, at temperatures below about 2 K, the property of superfluidity—the ability to flow through the narrowest capillaries without apparent friction. By contrast, the liquid form of the rare isotope, He, has been available only since about 1950, when enough of it was produced by the decay of the tritium manufactured in nuclear reactors. However, it was soon recognized that liquid He is in many ways similar to a system that has been known for much longer, namely, the electrons in metals. Although there is one obvious difference sthe electrons in metals are electrically charged whereas the He atom is electrically neutrald, both systems are dense systems of particles that have spin 1 2 and are therefore expected to obey FermiDirac statistics. sBy contrast, the atoms of He have spin zero and should therefore obey Bose-Einstein statistics.d If we consider a noninteracting gas of such particles in thermal equilibrium at a temperature T!TF=eF /kB swhere eF is the “Fermi energy,” determined by the mass and densityd, then all states lying well below eF in energy are occupied by a single particle, and all those well above eF are empty; rearrangement of the particles can take place only in an energy “shell” of width ,kBT around eF, and all the thermal, transport, and response properties are thus determined by the properties of the states in this shell. In a famous 1956 paper, L. D. Landau s1956d showed that under appropriate conditions this picture remains qualitatively valid even in the presence of strong interparticle interactions; the system is then known as a “degenerate Fermi liquid.” Experiments on liquid He in the 1950s and early 1960s showed that this system indeed appeared to be behaving as a degenerate Fermi liquid below ,100 mK, down to the lowest temperatures then attainable saround 3 mKd. Now, it has been known for nearly a century that the electrons in metals, which have a Fermi temperature of ,104−105 K, may sometimes, at temperatures &20 K, enter the so-called superconducting state, in which they can flow without apparent resistance; this is just the analog, for a charged system, of the superfluidity of liquid He. Since, for liquid He, the Fermi temperature is only a few kelvins, it would have been reasonable to speculate that the atoms might undergo a similar transition at temperatures of the order of millikelvins; since the atoms are electronically neutral, the result would be not superconductivity but rather superfluidity, as in He. However, in the absence of a microscopic theory of superconductivity, no quantitative approach to this question suggested itself. Remarkable progress in the phenomenological description of superconductivity was made in the early 1950s sas recognized in the awards to my co-laureatesd, in particular, by introducing the concept of a “macroscopic wave function” or order parameter. The microscopic underpinning sBardeen et al., 1957d of this concept was provided by my late colleague John Bardeen and his collaborators Leon Cooper and Bob Schrieffer in 1957, in what is now universally recognized as the correct microscopic theory of superconductivity sat least, as it was known at that timed, the “BCS” theory. They postulated that in the superconducting state the electrons within a “shell” of width ,kBTc around the Fermi energy swhere Tc is the temperature of the superconducting transitiond tend to form Cooper pairs, a sort of giant “dielectronic molecule,” whose radius is huge compared to the average distance between electrons sso that, between any two electrons forming a Cooper pair, there are billions of other electrons, each forming their own pairsd. An essential feature of the BCS theory of superconductivity is that the Cooper pairs, once formed, must all behave in exactly the same way, that is, they must have exactly the same wave function, as regards both the center of mass and the relative coordinate. In fact, the macroscopic wave function of Ginzburg and Landau turns out to be nothing but the common center-of-mass wave function of all the pairs. This wave function can *The 2003 Nobel Prize in Physics was shared by A. A. Abrikosov, Vitaly L. Ginzburg, and Anthony J. Leggett. This lecture is the text of Professor Leggett’s address on the occasion of the award. REVIEWS OF MODERN PHYSICS, VOLUME 76, JULY 2004