The Extraordinary Phases of Liquid 3He*

The extraordinary phases of liquid 3He* David M. Lee Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853 [S0034-6861(97)00403-0] INTRODUCTION peratures where the thermal de Broglie wavelength becomes greater than the mean interparticle distance. Modern low-temperature physics began with the liq- A remarkable phase transition was discovered in liq- uefaction of helium by Kamerlingh Onnes (1908) and uid 4He under saturated vapor pressure at 2.17 K. As the discovery of superconductivity (Kamerlingh Onnes, the liquid cooled through this temperature, all boiling 1911) at the University of Leiden in the early part of the ceased and the liquid became perfectly quiescent (At- 20th century. There were really two surprises that came kins, 1959). We now know that this effect occurs because out of this early work. One was that essentially all of the the liquid helium becomes an enormously good heat electrical resistance of metals like mercury, lead, and tin conductor so that thermal inhomogeneities which can abruptly vanished at definite transition temperatures. give rise to bubble nucleation are absent. The specific This was the first evidence for superconductivity. The 4 other surprise was that, in contrast to other known liq- heat vs temperature curve of liquid He was shaped like uids, liquid helium never solidified under its own vapor the Greek letter lambda, characteristic of a second- pressure. Helium is an inert gas, so that the interactions order phase transition at 2.17 K. This temperature is between the helium atoms are very weak; thus the liquid called the lambda point (Atkins, 1959; Keesom and Clu- phase itself is very weakly bound and the normal boiling sius, 1932; Keesom and Keesom, 1932). Below this tem- 4 point (4.2 K) is very low. The small atomic masses and perature, liquid He was found to possess remarkable the weak interaction lead to large-amplitude quantum flow properties as well as the ‘‘super’’ heat transport mechanical zero-point vibrations which do not permit mentioned above. If a small test tube containing the liq- the liquid to freeze into the crystalline state. Only if a uid was raised above the surrounding helium bath, a mo- pressure of at least 25 atmospheres is applied will liquid bile film would form, allowing the liquid to be trans- 4He solidify (Simon, 1934). It is thus possible, in prin- ported up the inner walls, over the top and down the ciple, to study liquid 4He all the way down to the neigh- outer walls, eventually dripping back into the bath and borhood of absolute zero. thereby emptying the test tube. (Daunt and Men- 4 Quantum mechanics is of great importance in deter- delssohn, 1939). Furthermore, liquid He could flow mining the macroscopic properties of liquid 4He. In- freely through the tiniest pores and cracks as shown by deed, liquid helium belongs to a class of fluids known as Kapitza (1938, 1941), who performed a number of inge- quantum fluids, as distinct from classical fluids. In a nious experiments involving flow properties of superfluid helium. Perhaps the most dramatic manifestation quantum fluid the thermal de Broglie wavelength lT 5 h(2pmkT)21/2 is comparable to, or greater than, the of anomalous flow behavior was the so-called fountain mean interparticle distance. There is then a strong over- effect discovered by Allen and Jones (1938a, 1938b). If a lap between the wave functions of adjacent atoms, so glass tube packed tightly with a powder such as jeweler’s 4 quantum statistics will have important consequences. rouge was partially immersed in a He bath and then 4He atoms contain even numbers of elementary par- heated, a fountain of helium rising high above the level ticles and thus obey Bose-Einstein statistics, which of the surrounding helium bath was produced. A model means that any number of atoms can aggregate in a called the Two-Fluid Model to describe these phenom- single quantum state in the non-interacting particle ap- ena was developed by Landau (1941) and Tisza (1940). 4 proximation. In fact macroscopic numbers of atoms in a According to this model, liquid He below Tl can be quantum fluid can fall into the lowest-energy state even thought of as two interpenetrating fluids, the normal and at finite temperatures. This phenomenon is called Bose- the superfluid components. The latter component is in- Einstein condensation. On the other hand 3He atoms, volved in superflow through pores and cracks and does each of which contains an odd number of elementary not carry entropy. Furthermore, it does not interact with particles, must obey Fermi-Dirac statistics: only one the walls of a vessel containing the fluid in a dissipative atom can occupy a given quantum state. Therefore one fashion. Superimposed on this background superfluid should expect a very large difference between the be- component is the normal component which transports havior of liquid 4He and that of liquid 3He for low tem- heat efficiently and exhibits viscosity, allowing transfer of energy between the liquid and the walls. This latter effect was the basis for the ingenious experiment by An- *The 1996 Nobel Prize in Physics was shared by David M. dronikashvili (1946), who actually measured the normal Lee, Douglas D. Osheroff, and Robert C. Richardson. This fluid density as a function of temperature by studying lecture is the text of Professor Lee’s address on the occasion of the damping of a torsional pendulum, which interacted the award. only with the normal fluid. It was found that the normal Reviews of Modern Physics, Vol. 69, No. 3, July 1997 0034-6861/97/69(3)/645(21)/$13.15 © 1997 The Nobel Foundation 645 646 David M. Lee: The extraordinary phases of liquid 3He fluid density decreased with decreasing temperature and The major breakthrough in our understanding of su- consequently the superfluid density increased, becoming perconductivity occurred in the late 1950s when dominant at the lowest temperatures. The normal fluid Bardeen, Cooper and Schrieffer (BCS; 1957) proposed carries heat away from the heat source and is replaced their theory of superconductivity. This theory resulted in by the superfluid component, so we have a countercur- a vast revolution in the field of superconductivity. As rent heat flow. The flow of the superfluid component mentioned earlier, BE particles (bosons) can congregate toward a source of heat is spectacularly manifested in in their ground state at finite temperatures as a result of the fountain effect, mentioned above. BE condensation. This provides the basis for the estab- According to Landau the normal fluid consists of a gas lishment of a superfluid order parameter. (The situation of quantized thermal excitations which include the ordi- is really more complicated and requires that interactions nary longitudinal sound waves (phonons) and short- be taken into account.) For a simple model involving wavelength compact excitations which he named the ro- non-interacting electrons, the conduction electrons in a tons. On the basis of the two-fluid model, it was metal form a sea of FD particles (fermions). At T 5 0 all predicted that heat transport would obey a wave equa- the lowest states are occupied up to the Fermi energy. tion which describes the compressions and rarefactions Because of the Pauli exclusion principle, only one elec- in the phonon/roton ‘‘gas.’’ Such a wave phenomenon tron is allowed in each quantum state, so that macro- was indeed discovered experimentally (Peshkov, 1944) scopic congregation in the ground state is not permis- and was named second sound. sible. The BCS theory overcame this difficulty by The nature of the superfluid background still needed showing that, when a metal became superconducting, to be characterized. Fritz London’s (1954) great contri- the electrons in the metal formed pairs (now known as bution was to note that superfluidity could be viewed as Cooper pairs (Cooper, 1956)), which had some of the quantum behavior on a macroscopic scale associated properties of bosons. These pairs could thus congregate with the Bose-Einstein (BE) condensation. As the tem- into a single ground state (in a loose analogy to BE perature is reduced through the transition temperature, condensation) described by an order parameter which the occupancy of the one-particle ground state becomes does not violate the Pauli principle but which leads to a macroscopic and can be thought of as the BE conden- conducting superfluid of electrons. The wave function sate. The superfluid component in the two-fluid picture describing this ground state was devised by Robert could be roughly identified with this condensate, al- Schrieffer (Bardeen, Cooper, and Schrieffer, 1957). The though strong interactions between the atoms in the liq- partners in a Cooper pair consist of two electrons whose uid modify this picture. In this scheme, the superfluid motion is correlated even though they may be separated atoms are governed by a wave-function-like entity called by distances much larger than the interparticle spacing. the order parameter, as introduced by Ginzburg and In other words, the pairs do not behave like Bose con- Landau (1950) for the case of superconductivity. The densed discrete diatomic molecules. The difference may order parameter c for superfluid 4He is characterized by be understood in terms of modern rock and roll dancing a phase f and an amplitude c0 and is given by c vs ballroom dancing, according to a marvelous analogy if 5c0e where c0 can be roughly thought of as the invented by Schrieffer and discussed by him in a number square root of the density of the superfluid component. of public lectures. In ballroom dancing, the partners The fact that the macroscopic order parameter is also hold tightly to one another in analogy with diatomic described by a definite phase is called broken gauge molecules.

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