Anthony J. Leggett - Nobel Lecture

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 3He; 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 fleld 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 3He 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 (stable) forms, 4He and 3He; at low temperatures and pressures both form liquids rather than solids. The liquid phase of the common isotope, 4He, was realized nearly a century ago, and since 1938 has been known to show, at temperatures below about 2K, the property of superfluidity – the ability to flow through the narrowest capillaries without apparent friction. By contrast, the liquid form of the rare isotope, 3He, 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 3He is in many ways similar to a system which has been known for much longer, namely the electrons in metals. Although there is one obvious difference (the electrons in metals are electrically charged whereas the 3He atom is electrically neutral), both systems are dense systems of particles which have spin 1/2 and are therefore expected to obey Fermi-Dirac statistics. (By contrast, the atoms of 4He have spin zero and should therefore obey Bose-Einstein statistics). If we consider a noninteracting gas of such particles in thermal equilibrium at a temperature T TF = F /kB (where F is the “Fermi energy”, determined by the mass and density), then all states lying well below F in energy are occupied by a single particle and all those well above F are empty; rearrangement of the particles can take place only in an energy “shell” of width ~ kBT around F , 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 [1]