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Explaining superconductivity and superfluidity

The path breaking work by the trio of Nobel awardees leads us to a better understanding of the bizarre behaviour of condensates at very low temperatures.

Alexei A. Abrikosov

THE QUANTUM physics that controls the micro-world has a wide range of spectacular effects that do not normally occur in our ordinary macro-world. There are, however, certain situations in which quantum phenomena are visible. This year's Nobel Prize in Physics is awarded for work concerning two of these situations: superconductivity and superfluidity. Alexei Abrikosov and Vitaly Ginzburg have developed theories for superconductivity and Anthony Leggett has explained one type of superfluidity. Both superconductivity and superfluidity occur at very low temperatures.

An unexpected cold effect

When investigations were first carried out into the nature of electricity, it was evident that metals and certain alloys conduct electricity by allowing electrons to move between the atoms. In addition it was found that an electric current through a conductor creates a magnetic field, which in turn generates current in the opposite direction. In 1911 the Dutch physicist Heike Kammerlingh Onnes made a remarkable discovery. He was particularly interested in the properties of substances at low temperatures and had succeeded in producing liquid helium, which has an extremely low temperature. When Onnes investigated the electric conductivity of mercury, he found that when the metal was cooled by means of liquid helium to a few degrees above absolute zero, its electric resistance vanished. He named this phenomenon superconductivity. Almost 50 years passed before the physicists John Bardeen, Leon Cooper and Robert Schrieffer (Nobel Prize in Physics, 1972) were able to present a theory (the BCS theory) that explained the phenomenon. This theory shows that some of the negatively-charged electrons in a superconductor form pairs, called Cooper pairsThese pairs of electrons flow along attracting channels formed by the regular structure of the positively charged metal atoms in the material. As a result of this combination and interaction the current can flow evenly and superconductivity occurs. These superconductors are called type-I. They are metals and are characterised by the Meissner effect.

But it is known that there are superconductors that lack or show only a partial Meissner effect. These are in general alloys of various metals or compounds consisting of non-metals and copper. These retain their superconductive property even in a strong magnetic field and are called type-II superconductors.

Alexei Abrikosov, working at the Kapitsa Institute for Physical Problems in Moscow, succeeded in formulating a new theory to describe the phenomenon. His starting point was a description of superconductivity in which the density of the superconductive condensate is taken into account with the aid of an order parameter (a wave function). Abrikosov was able to show mathematically how the order parameter can describe vortices and how the external magnetic field can penetrate the material along the channels in these vortices.

Abrikosov was also able to predict in detail how the number of vortices can grow as the magnetic field increases in strength and how the superconductive property in the material is lost if the cores of the vortices overlap.

Abrikosov's argument was based on what was formulated in the early 1950s by Vitaly Ginzburg and Lev Landau. This theory was intended to describe superconductivity and critical magnetic field strengths in the superconductors that were known at that time. Ginzburg and Landau realised that an order parameter (wave function) describing the density of the superconductive condensate in the material had to be introduced if the interaction between the superconductor and magnetism was to be explained. When this parameter was introduced, it was evident that there was a breakpoint when a characteristic value, approximately 0.71 was reached and that in principle there were two types of superconductor. For mercury the value is approximately 0.16 and other superconductors known at the time have values close to this. There was therefore, at that time, no reason to consider values above the breakpoint. Abrikosov was able to tie up the theory by showing that type-II superconductors had precisely these values.

Two fascinating superfluids

The lightest rare gas, helium, exists in nature in two forms, two isotopes — 4He and 3He. If helium gas is cooled to low temperatures, approximately 4 degrees above absolute zero (-273.15C), the gas passes into liquid form, it condenses.

Anthony J. Leggett

If liquid helium is cooled to even lower temperatures, dramatic differences arise between the liquids of the two isotopes; quantum physical effects appear that cause the liquids to lose all their resistance to internal movement, they become superfluid. This occurs at quite different temperatures for the two superfluids and they exhibit a wide range of fascinating properties, such as flowing freely from openings in the vessel they are kept in.

Historic discoveries

The fact that 4He becomes superfluid was discovered by Pyotr Kapitsa, among others, already in the late 1930s. The transformation from normal to superconducting liquid occurs at approximately 2 degrees above absolute zero for 4He.

For the 3He isotope the transformation into the superfluid state was not discovered until the early 1970s by David Lee, Douglas Osheroff and Robert Richardson (Nobel Laureates in Physics in 1996). Even though 3He differs in quantum physical respects from 4He and cannot directly undergo Bose-Einstein condensation, this discovery was not unexpected. Thanks to the microscopic theory of superconductivity presented in the 1950s by Bardeen, Cooper and Schrieffer, there was a mechanism, the formation of Cooper pairs, that ought to have been paralleled in 3He.

Vitaly L. Ginzburg

The theoretician who first succeeded in explaining the properties of the new superfluid in a decisive way was Anthony Leggett, who in the 1970s was working at the University of Sussex in England. His theory helped experimentalists to interpret their results and provided a framework for a systematic explanation. Leggett's theory, which was first formulated for superfluidity in 3He, has also proved useful in other fields of physics, e.g. particle physics and cosmology.

As superfluid, 3He consists of pairs of atoms, its properties are much more complicated than those of the 4He superfluid. In particular the pairs of atoms of the superfluid have magnetic properties, which means that the liquid is anisotropic, it has different properties in different directions. This fact was used in experiments in which studies were made of the liquid immediately after its discovery. By means of magnetic measurements it was revealed that the superfluid has very complex properties, exhibiting a mixture of three different phases. These three phases have different properties and the proportions in the mixture are dependent on temperature, pressure and external magnetic fields.

Superfluid 3He is a tool that researchers can use in the laboratory to study other phenomena as well. In particular the formation of turbulence in the superfluid has recently been used to study how order can turn into chaos.

This research may lead to a better understanding of the ways in which turbulence arises — one of the last unsolved problems of classical physics.

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