In the early twentieth century, scientists discovered the non-intuitive phenomena of superconductivity and superfluidity, in which electrons and atoms, respectively, flow without resistance over great distances. Superfluidity was beautifully demonstrated 80 years ago in two papers published in Nature by Allen and Misener1 and Kapitza2. The authors observed the flow of liquid helium-4 through extremely narrow channels and showed that the substance becomes a superfluid at very low temperatures. The studies presaged the firm understanding of the relationship between superfluidity and superconductivity that now exists, and which provides the foundation for investigating unconventional superconductors and superfluid phases.
Allen and Misener observed the flow of liquid helium-4 through long, thin tubes, and found that the fluid’s viscosity became immeasurably low at temperatures below 2.17 kelvin. Kapitza obtained similar results by measuring the flow through a small gap between two glass disks (Fig. 1). With foresight, Kapitza noted a possible connection to superconductivity, for which a complete theory was eventually realized3 in 1957 by Bardeen, Cooper and Schrieffer (BCS). Shortly after the two Nature papers were published, an explanation for the superfluidity of liquid helium-4 was offered: Bose–Einstein condensation4, the process whereby many particles known as bosons ‘condense’ into a single quantum state.
In the quantum world, particles of the same type are indistinguishable, and there are only two classes of particle: fermions and bosons. However, an even number of interacting fermions can make a composite boson — for example, an atom of helium-4 is a composite boson that comprises six fermions (two protons, two neutrons and two electrons). At sufficiently low temperatures, helium-4 atoms undergo Bose–Einstein condensation and become a superfluid. Similarly, in the BCS theory of superconductivity, electrons that have a suitably attractive interaction can combine into charged composite bosons called Cooper pairs, which condense to form a superconductor.
In the wake of the Second World War, substantial quantities of the light isotope of helium, helium-3, became available through production of the heavy isotope of hydrogen (hydrogen-3 or tritium) for use in the hydrogen bomb. Because helium-3 contains an odd number of fermions (two protons, one neutron and two electrons), it is not a composite boson. It might therefore be considered that Bose–Einstein condensation could not take place and that helium-3 could never be a superfluid. However, the success of the BCS theory suggested another possibility: composite bosons comprising Cooper pairs of helium-3 atoms might condense into a superfluid, much like the electrons of a BCS superconductor.
The properties of this hypothetical superfluid were studied theoretically5,6,7 in the 1960s. Research on the subject then exploded following the unexpected discovery8 in 1972 of this superfluid at temperatures below 0.003 K. At first, the observations were interpreted as spontaneous nuclear magnetic ordering in solid helium-3, but shortly afterwards, they were correctly identified as the transition to a superfluid9. Nuclear magnetic ordering in solid helium-3 was discovered10 two years later at a temperature of 0.001 K.
Cooper pairs have two types of angular momentum, characterized by the orbital quantum number (L) and the spin quantum number (S). Conventional BCS superconductors have L = 0 and S = 0, whereas superfluid helium-3 has L = 1 and S = 1. Nevertheless, the superfluid’s properties can be understood using a modified version of the BCS theory11. The discovery of superfluid helium-3 therefore marked the birth of unconventional superconductivity — and, more precisely, of superfluids that break certain fundamental symmetries of the normal (non-superfluid) state. The non-zero values of L and S in superfluid helium-3 correspond to broken rotational and time-reversal symmetries, which cause the substance to have a non-trivial topology.
In the absence of a magnetic field, superfluid helium-3 has two phases: A and B, with the B phase dominating the pressure–temperature phase diagram (a graph that plots the physical state of a material at various pressures and temperatures). The B phase can exist in many excited states, as a consequence of broken rotational symmetry associated with the total angular momentum of Cooper pairs7,12,13. The states of the B phase are classified by total angular momentum quantum numbers (J) of 0, 1 and 2. The J = 2 state comprises bosons that are analogous to the famous Higgs boson14. A remarkable finding is that the broken symmetry of the B phase, and its J = 2 state, enable the propagation of transverse sound waves15,16 — a feature that was unheard of in liquids and was often assumed to be a property only of rigid solids.
Since the discovery of superfluid helium-3, many unconventional superconductors have been found. The best known are copper oxide compounds known as cuprates, which have the quantum numbers L = 2 and S = 0, and certain heavy fermion compounds17. However, only one superconducting compound, the uranium–platinum system UPt3, has been discovered that has more than one superfluid phase, like helium-3. UPt3 has L = 3 and S = 1, as predicted18, and one of its phases breaks time-reversal symmetry in a similar way19 to the A phase of helium-3.
In the past few years, helium-3 has been shown to exhibit new superfluid phases when confined to low-density materials called aerogels, small pores and narrow slabs20. Such phases are being investigated further. Eighty years after the discovery of superfluidity in liquid helium-4, the search is on for other scientifically interesting superfluids and superconducting materials.
Nature 553, 413-414 (2018)