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The Nobel Prize in Physics 2003
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.
Flow without resistance
An unexpected cold effect
When investigations were first carried out into the nature
of electricity in the 19th century, it was evident that metals
and certain alloys conduct electricity by allowing electrons
to move between the atoms. But the disorganised way in which
the electrons move causes the atoms to vibrate, so heat is
generated. If the current is too strong, the heat can be so
great that the conductor melts. 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.
Electricity and magnetism interact and can thus counteract
each other.
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.
Although no theoretical explanation could be found for this
phenomenon, it was evident that it could have far-reaching
significance in a modern society that was becoming more and
more dependent on electricity. Onnes was awarded the Nobel
Prize in Physics in 1913 for this work.
Superconductors of two types
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, named
after the initials of their surnames) that explained the phenomenon.
This theory shows that some of the negatively-charged electrons
in a superconductor form pairs, called Cooper pairs. These
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.
The paired electrons are usually thought of as a condensate,
similar to the drops of liquid that form in a cooled gas.
Unlike an ordinary liquid this “electronic liquid”
is superconductive.
These superconductors are called type-I. They are metals
and are characterised by the Meissner effect, that is, in
the superconductive state they actively counteract a surrounding
magnetic field as long as its strength does not exceed a certain
limit (fig. 1). If the surrounding magnetic field becomes
too strong, the superconductive property disappears.
Fig. 1. Type-I superconductors repel a magnetic field (the
Meissner effect). If the strength of the magnetic field increases,
they lose their superconductivity. This does not happen with
type-II superconductors, which accomodate strong magnetic
fields by letting the magnetic field in.
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. Experiments show that the properties
of these so-called type-II superconductors cannot be described
by the BCS theory.
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 (fig. 2).
Fig. 2. This image is of an Abrikosov lattice of vortices
in the electron fluid in a type-II superconductor. The magnetic
field passes through 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. This description was
a breakthrough in the study of new superconducting materials
and is still used in the development and analysis of new superconductors
and magnets. His papers from the late 1950s have been quoted
more and more frequently during the past ten years.
The theory Abrikosov's argument was based on was formulated
in the early 1950s by Vitaly Ginzburg and Lev Landau (the
latter was awarded the Nobel Prize in Physics in 1962 for
other work, see below). 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.
Our knowledge of superconductivity has led to revolutionary
applications (fig. 3). New compounds with superconductive
properties are being discovered all the time. In the past
few decades a large number of high-temperature superconductors
have been developed. The first one was produced by Georg Bednorz
and Alex Müller, who were awarded the Nobel Prize in
Physics in 1987. All high-temperature superconductors are
type-II. Cooling is a critical factor for the utilisation
of superconductors. An important limit is 77 K (-196°C),
the boiling point of liquid nitrogen, which is cheaper and
more manageable than liquid helium.
Fig. 3. An MRI image of a human brain. The resolution in the
magnetic resonance camera is dependent partly on the strength
of the magnetic field. Today strong superconducting magnets
are used, all of them type-II.
Two fascinating superfluids
The lightest rare gas, helium, exists in nature in two forms,
two isotopes. The usual form is represented as 4He, where
the figure 4 stands for the number of nucleons in the atomic
nucleus (two protons and two neutrons). In the unusual form,
3He, the atomic nucleus has only one neutron, so it is lighter.
In helium that occurs naturally the heavier isotope is more
frequent than the lighter one by a factor of about 10 million.
That is why it is only in the last 50 years that it has been
possible to produce large amounts of 3He, at nuclear power
stations, for example. At normal temperatures the gases of
the two isotopes differ only in their atomic weights.
If helium gas is cooled to low temperatures, approximately
4 degrees above absolute zero (-273.15°C), the gas passes
into liquid form, it condenses. This happens in the same way
as when steam condenses into water. Provided the temperature
is not too low, the liquids of the two isotopes have similar
properties. Liquid helium is used widely as a coolant, in
superconducting magnets, for example. In this case naturally-occurring
helium is used, of course, that is, the usual and cheaper
form of helium, 4He.
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. These effects can be explained only by means
of quantum physics.
Historic discoveries
The fact that 4He becomes superfluid was discovered by Pyotr
Kapitsa, among others, already in the late 1930s. This phenomenon
was explained almost immediately by the young theoretician
Lev Landau, who was awarded the Nobel Prize in Physics in
1962 for this discovery. (Kapitsa was also awarded the Nobel
Prize in Physics, but not until 1978.) The transformation
from normal to superconducting liquid, which for 4He occurs
at approximately 2 degrees above absolute zero, is an example
of Bose-Einstein condensation, a process that has also been
observed more recently in gases (cf. the Nobel Prize in Physics
awarded in 2001 to Eric Cornell, Wolfgang Ketterle and Carl
Wieman).
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). One reason why this discovery came so much
later is that the transformation occurs at a very much lower
temperature, approximately 1,000 times lower than for 4He.
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 (see above)
by Bardeen, Cooper and Schrieffer, there was a mechanism,
the formation of Cooper pairs, that ought to have been paralleled
in 3He (fig. 4).
Fig. 4. The pair formation that occurs in superfluid 3He differs
from that which occurs between electrons in a superconductor
(Cooper pairs). The magnetic properties of the helium atoms
act together, whereas those of the electrons counteract each
other.
The multifarious superfluid
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 (fig. 5).
Fig. 5. Superfluid 3He can exist in three phases called A,
A1, and B. The type of phase is determined by pressure, temperature
and magnetic field according to the figure's phase diagram.
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 (fig. 6).
This research may lead to a better understanding of the ways
in which turbulence arises – one of the last unsolved
problems of classical physics.
Fig. 6. It has recently been shown that if a vortex is created
in a rotating vessel containing superfluid 3He (a), the result
can critically depend on the temperature. Above a critical
temperature the vortex lines up along the axis of rotation
(b). Below the critical temperature a confusion of vortices
occurs (c).
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