The 50th Anniversary of the Prediction of Superfluidity of He^3
FHP Session at the APS 2010 March Meeting
By George Zimmerman
Quick notes on liquid helium and superfluidity: As the lightest noble gas, helium has to be cooled to 4.2K before it liquefies. Cooled further to 2.17K, liquid He4 becomes a “superfluid,” a liquid Bose-Einstein condensation. This results in unusual macroscopic behaviors such as flow with no viscosity and persistent vortex formation with quantized circulations. Above about 2.6 milliKelvins (mK), He3 does not exhibit superfluidity because He3 atoms are fermions. However, below 2.6 mK, He3 atoms can form Cooper pairs, i.e., integer-spin and l = 1 (orbital angular momentum) composites, and exhibit superfluidity. This superfluid is more complicated than the He4 superfluid because of the spin-orbit coupling within the pairs. At high pressure, near the solidification boundary, the superfluid forms a spin-up or spin-down projection phase, the A-phase. At lower pressures and temperature it exists in a spin-up, spin-down, and spin-zero projection phase, the B-phase. This leads to textures akin to those of liquid crystals.Also see Figure 6.Session X8 of the March 2010 meeting celebrated two publications which, only three years after the publication of the BCS theory of superconductors, predicted the occurrence of superfluidity in He3. Those papers were:
- “Level Structure of Nuclear Matter and Liquid He3” by K. A. Brueckner and Toshio Soda (University of California- La Jolla), Philip W. Anderson (Bell Telephone Laboratories-Murray Hill, NJ), and Pierre Morel (French Embassy in New York City), submitted to The Physical Review on 15 January 1960;
- “Possible Phase Transition in Liquid He3” by V. J. Emery (UC-Berkeley) and A. M. Sessler (Lawrence Radiation Laboratory, UC-Berkeley), submitted on 8 February of the same year to the same journal.
Although the initial estimates of the liquid He3 superfluid transition temperature were somewhat high, they were just within the reach of contemporary experimental techniques. These publications inspired a large number of experiments. The experimental discovery of the liquid He3 superfluid phases came twelve years later in 1972 by David Lee, Bob Richardson and Douglas Osheroff, for which they received the 1996 Nobel Prize in Physics.
The session included five talks. Two were presented by a co- author of each of the 1960 papers, Phil Anderson and Andy Sessler. Another speaker was David Lee, one of the experimental discoverers of liquid He3 superfluidity. The two other speakers were Joe Serene, who was a theory graduate student at the time of the experimental discovery, and Tony Leggett, who contributed greatly to the understanding of the experimental properties of the superfluid. Despite the fact that the session was scheduled for the afternoon of the second-to-last day of the meeting, the 400-seat hall was packed to capacity (Fig. 1), with many in the audience obliged to stand or sit in the aisles.
Fig. 1. Capacity audience at Session X8, March 2010 meeting, “The 50th Anniversary of the Prediction of Superfluidity of He3.”
Fig. 2. Phil Anderson about to present “Superconductivity with Very Repulsive Interactions: He3, Pierre Morel, and Me.”
The first speaker was Phil Anderson (Fig. 2), whose talk was entitled “Superconductivity with Very Repulsive Interactions: He3, Pierre Morel, and Me.” He described some of the early ideas about He3, and stated that 1960 was the right time for the prediction to emerge because He3 was becoming available and physicists were starting to think about it. As is evident from the title of the 1960 paper he co-authored, because liquid helium is composed of Fermi particles it was thought to be a model substance for nuclear matter. Brueckner and Soda were nuclear theorists who apparently got the idea of working on He3 by visiting the Bell Laboratories where Anderson and his first graduate student, Morel, were located. Anderson mentioned previous ideas about the superfluidity of liquid He3 that were held by Lev Pitaevski in Russia, who may have ascribed their origin to Lev Landau. Because their ideas were published in Russian journals which were not generally read by American physicists, Pitaevski and Landau had little influence on the two 1960 Physical Review papers. Anderson also mentioned John Fisher, of GE labs, whom he visited in January 1959. At that time Fisher suggested the idea of working on liquid He3. The Brueckner et. al. paper predicted a superfluid phase with l = 2 and a transition temperature of 0.1K. After considering spin fluctuations, Anderson and Morel reduced the prediction of the transition temperature in subsequent papers to 0.02K. The rest of Anderson’s talk was devoted to the technicalities and predictions of the nature of the superfluid phase of He3, as worked out in subsequent papers with Morel and other authors.
Fig. 3. Andy Sessler presenting “Early Thoughts on the Superfluidity of He3.”
The second speaker was Andy Sessler (Fig. 3) whose talk was entitled “Early Thoughts on the Superfluidity of He3.” He started by pointing to a paper written by L. N. Cooper, R. L. Mills, and A. M. Sessler a year before the publication of the Emery-Sessler paper. The paper was written at a time when Sessler, Cooper, and Mills were at Ohio State University, where low-temperature experiments were being conducted by J.G. Daunt, D.F. Brewer and D.O. Edwards. Their joint 1959 paper did not find superfluidity. Sessler attributed this to the omission of the consideration of the nonzero angular momentum states, and to the concentration on the beautiful mathematical formulation by Mills. Sessler had previously met Cooper and Mills at Columbia University, where Sessler was between 1949 and 1953. (Parenthetically, Sessler mentioned a conversation he had with I.I. Rabi at Columbia, who allegedly remarked that the physics research carried on there was, in his opinion, not first rate! As it turned out, about ten of the researchers who were there at the time subsequently received the Nobel Prize and many others went on to distinguished careers.) Sessler and Emery met during a sabbatical at the Lawrence Berkeley Laboratory. Sessler noted that the two 1960 papers, in whose honor the session was held, did not mention each other as a reference; they were quite independent. He concluded his talk by showing some pictures of his associates, and mentioned a subsequent paper in which the dynamics of anisotropic superfluid He3 were worked out prior to its experimental discovery.
Fig. 4. Joe Serene presenting “Historically Related Puzzles in He3: Spin Fluctuations, the Specific Heat, and the Superfluid Phase Diagram.”
The third speaker was Joe Serene(Fig. 4) who presented “Historically Related Puzzles in He3: Spin Fluctuations, the Specific Heat, and the Superfluid Phase Diagram”. At the time of the experimental discovery of the superfluidity in He3 in 1972, Serene was a graduate student of Vinay Ambegaokar at Cornell University. In the talk Serene concentrated on the time of intense competition between the theoretical groups at Cornell University and Bell Laboratories. He discussed the consequences of odd versus even angular momentum pairing and the influence of spin fluctuations on the magnetic susceptibility and specific heat of He3. He described the superfluid phases of He3, the A-1 and A-2 phases which are best described by the Anderson-Brinkman-Morel model, and the B or Balian-Werthamer phase. [8,9] Serene had gone to a conference where he met W. Brinkman. They discovered that they were working on similar ideas using similar methods. That discovery resulted in Serene’s being invited to Bell Laboratories, and collaboration ensued between him and the Bell Labs theory group.
Fig. 5. David Lee presenting “Early Days of Superfluid He3.”
The fourth speaker was David Lee (Fig. 5) whose talk “Early Days of Superfluid He3: An Experimenter’s View” began with a description of how He3 was obtained. He then reviewed some of the experimental results of measurements made on liquid He3, including parameters in the Landau theory of Fermi liquids. In the theoretical predictions the transition temperature to superfluid phases depended on the Landau parameters which were obtained from the calculated and measured interaction of He3 atoms in the liquid. The initial 1960 prediction put the transition temperature at or just below the experimentally achievable temperatures of the time. The techniques of adiabatic demagnetization, and the subsequent addition of a first stage of a He3 refrigerator, could cool He3 down to several tens of milliKelvins. When some experimental groups started looking for the transition without finding it, they measured the Landau parameters by looking at the specific heat, spin diffusion, viscosity, magnetic susceptibility, and thermal conductivity. Those groups were at Cornell University (David M. Lee et. al.), Ohio State University (John G. Daunt et. al.) , Yale University (Henry A. Fairbank et. al.), as well as the University of Illinois and later University of California at San Diego (John C. Wheatley et. al.). There was intense competition among these groups, and all their measurements pointed to the behavior of He3 as a Landau-Fermi liquid, including the measurement of “Zero Sound” by the Wheatley group. Lee specifically mentioned the magnetic susceptibility measurements by William M. Fairbank and G.K. Walters as the early evidence of Landau-Fermi liquid behavior.
Lee then went on to describe the breakthroughs for achieving temperatures sufficiently low to make possible the discovery of the various superfluid phases. These were the discovery of the separation of He3-He4 mixtures into a He3-rich phase, and a phase having a mixture of He3 and He4 at zero temperature. That enabled the development the dilution refrigerator at the Leiden Laboratory in the Netherlands and by Henry Hall in the U.K. The design was perfected by Wheatley at UCSD. The dilution refrigerator could reach temperatures of five to ten mK which was used as a first stage in the cooling procedure. The other development was the measurement of the He3 liquid-solid coexistence curve which showed a minimum at about 0.3K on the pressure-temperature diagram with a negative slope below that temperature. According to the Clausius-Clapeyron equation, this indicated that the substance could be cooled by compression, which led to the adiabatic cooling technique first suggested by Isaak Pomaranchuk and demonstrated by Yu D. Anufriev in the USSR. Thus the transition was initially discovered.
By 1971, before the He3 superfluid transition was discovered, most of the low temperature He3 research had become directed towards the exploration of solid He3 and He3-He4 mixtures. Indeed, when graduate student Willy Gully fixed a helium leak on a Cornell apparatus, which enabled adiabatic compression, and Doug Osheroff observed a kink in the pressure versus time curve during a continuous adiabatic compression, the superfluid liquid He3 phases were observed. Since the compression cell contained both liquid and solid He3, the kink anomaly was initially thought to be due to the solid which was expected to undergo a transition to an ordered state (the solid magnetic ordering was discovered several years later, at pressures above 30 atm). The confirmation that the kinks were due to the He3 liquid came within a few months with the measurement of the nuclear magnetic resonance at Cornell, after several suggestions by John Goodkind of UCSD and Viktor Vvdenskii of the Kapitza Institute in Moscow. The capacitive pressure gauge in the experimental cell was developed by G.C. Straty and E.D. Adams of the University of Florida. By applying a magnetic field gradient at the cell while observing the NMR signal, one could tell where the solid and liquid portions were, perhaps one of the first applications of the MRI technique now used in medicine.
Fig. 6. Phase diagram of liquid He3. The polycritical point (PCP) occurs at about 22 bars. From D.N. Paulson, J.C. Wheatley, and D.M. Lee, Phys. Rev. Lett. 32 (1974), 1098; repeated in J.C. Wheatley, Reviews of Modern Physics 47 (1975), 417 and D. Lee, Reviews of Modern Physics 69 (1996), 657.
Subsequent measurements were made in short order by the Cornell group and the UCSD group that mapped out the phase diagram. Two phases of superfluid He3 liquid were determined (Fig. 6). The initially-seen A-phase occurs at high pressure and corresponds to the parallel spin phase described by the Anderson-Brinkman- Morel model with Sz = 1, -1. The B-phase is identified with the Balian- Werthamer model where Sz = 1, 0 , 1. Two other phenomena were discovered during the NMR measurements. One was a frequency shift in the superfluid which corresponded to an internal magnetic field of about 30G, and the other was the 104 degree angle which confirmed that the B-phase conformed to the Balian-Werthamer model.
Lee’s talk ended with the mention of measurements made by the many low-temperature groups in the US, Great Britain, Finland, the Netherlands, Denmark and elsewhere, which followed up on the experimental discovery and the rich physical patterns discovered in superfluid He3. Many members of those groups mentioned, or their collaborators, were in the audience.
The fifth speaker, Tony Leggett (Fig. 7), concluded the session with his talk entitled “Superfluid He3: Understanding the Experiments.” He reviewed the couple of years following the experimental discovery of the He3 superfluid transition. There were many questions to be resolved and experimental phenomena to be explained. One of the questions concerned the orbital pairing of the transition, which was determined to be the l = 1 state, although initially the l = 2 state was predicted. Other questions were about the nature of the A-phase which existed at high pressures and relatively high temperatures and the B-phase which existed at lower temperatures and pressures down to saturated vapor where the transition occurs at about one mK. It was determined that both have an orbital state of l = 1, that the A-phase corresponds to the Anderson-Brinkman-Morel model with the spin pairing of Sz = 1 and Sz = -1, while the B-phase corresponds to the Balian-Werthamer model with Sz = 1,0,-1. The Balian-Werthamer phase was supposed to be more stable and thus why the A-phase existed at all was puzzling. This was explained by Anderson and Brinkman as being caused by fluctuations when the substance became a superfluid. Another puzzle was the NMR frequency shift in the A-phase which amounted to a 30 Gauss magnetic field. That field was much greater than the field due to the individual He3 spins. That puzzle was explained by Leggett as being due to the spin-orbit coupling in that phase.
Since there was no question time during the talks, audience members met individually with the speakers after the talks were over (Fig. 8).
Fig. 7. Tony Leggett presenting “Superfluid He3: Understanding the Experiments.”
Fig. 8. Tony Leggett presenting “Superfluid He3: Understanding the Experiments.”
 J. Bardeen, L.N Cooper, J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). The electron pairing of the BCS theory that explained superconductivity also applies to He3. When the Cooper pairs form in with helium-3 below ~0.002K, the fluid has zero viscosity and zero thermal resistivity, analogous to the zero resistance of a superconductor.
For further references please consult these review articles: From Rev. Mod. Phys. 69 (1997) see Robert C. Richardson, “The Pomeranchuk effect,” 683–690; David. M. Lee, “The extraordinary phases of liquid He3,” 645–666; Douglas D. Osheroff, “Superfluidity in He3: Discovery and understanding,” 667–682. From Rev. Mod. Phys. 47 (1975) see Anthony J. Leggett, “A theoretical description of the new phases of liquid He3,” 331–414; John C. Wheatley, “Experimental properties of superfluid He3,” 415–470.
Note Added: This article represents the views of the author, which are not necessarily those of the FHP or APS.