Superconductivity
24 February 2009
Paul Wilson
Tutor: Justin Evans
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Intended Audience
This report is intended for anyone wishing to understand the fundamentals of
superconductors and their growing importance in modern science and engineering.
Summary
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Superconductors exhibit negligible resistance at low temperatures
•
There are two types of superconductor: low temperature (type 1) and high
temperature (type 2)
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‘BCS Theory’ explains low temperature superconductors in terms of cooper-pairs of
electrons
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No theory currently exists to adequately explain high temperature superconductors
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A major goal is to find a material that is superconductive at room temperature
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Superconductors have major applications in computer circuitry, medical scanning and
magnetic levitation transport
What is superconductivity?
Numerous cryogenic experiments in the late 19th and early 20th centuries showed that if a
substance was cooled its capacity to conduct electricity increases in proportion to the
reduction in temperature, something already known to be a consequence of reducing the
resistance according to Ohm’s law. The relationship drawn from these observations led to
notable figures in the field such as Dewar and Fleming postulating that there should be
immeasurable resistance at absolute zero.
In pursuit of an answer, and with the appropriate equipment at his disposal, in 1911 Heike
Kamerlingh Onnes was the first to discover the superconducting properties of mercury at a
temperature of 4.2K. Far from a simple linear decline to absolute zero, it was clear that for
some special substances the resistance reduces linearly with temperature until a certain
point, known as the critical temperature, at which there is an abrupt decrease to almost no
measurable electrical resistance (see figure 1); it was not long before many other substances
were also tested to see whether cooling had the same effect.
It followed from this, and was widely expected, that removing the power supply to a currentcarrying superconductor would result in the current continuing to flow without diminishing
in energy, a theory which was experimentally verified by Onnes in 1912.
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Figure 1 - Onnes' original resistance vs. temperature graph for Mercury
How does it work?
There are currently two classes of superconductor; the low temperature superconductors,
which can be explained by BCS theory, and high temperature superconductors, for which
there is currently no universally agreed-upon explanation. For this reason the latter class is
an area of highly active research.
An important step in understanding superconductors came from the work of Meissner and
Oschenfeld, who observed that above the critical temperature a magnetic field can
penetrate the material, but below the critical temperature the field is totally excluded by the
surface currents induced on the superconductor and no flux penetrates the interior (see
figure 2).
One well known example of this phenomenon can be seen in various popular science videos
of magnets ‘floating’ above liquid-Nitrogen cooled superconductors. If a sufficiently strong
magnetic field is used then the superconducting properties of the material may be destroyed
and the material will no longer repel the field.
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Figure 2 - The Meissner effect on a superconductor above and below the critical temperature
BCS theory was formulated by John Bardeen, Leon Cooper and John Schrieffer in 1957 and
successfully explains how superconductivity works for metals below around 77K. In this
theory electrons distort the lattice structure of the metal through which it is travelling,
creating a potential well which affects the electron directly following it so that the current is
carried by bound pairs of electrons, known as cooper pairs. The momentum of the cooper
pair is not changed throughout this process, resulting in a current that flows unimpeded for
an indefinite amount of time.
However, the energy maintaining the Cooper pairs is quite weak and can be broken up easily
with the addition of thermal energy. So only at low temperatures are a significant number
of the electrons in a metal in Cooper pairs, thus making this an idea which fitted observed
data but which would not work if superconductivity was found to happen at higher
temperatures, something which appeared to be inevitable given the continually rising critical
temperatures found in all subsequent superconductor experiments.
New discoveries of high temperature superconductivity
In 1986 scientists from IBM discovered superconducting properties of materials with critical
temperatures above 77K, the so-called ‘high temperature superconductors’. These materials
and subsequent similar ones were often ceramics, large compounds and alloys and behaved
in ways that could not be explained by BCS theory.
At low temperatures, the laws of quantum mechanics take precedence over classical
theories and just as in more familiar circumstances with changes of state in liquids and gases
there is a phase transition when the material can change abruptly from one state to another.
This collective behaviour at the atomic scale can also be applied to superconductivity and
the analogous changes observed at the critical temperature.
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Figure 3 - Graph showing resistance vs. temperature for two high-temperature superconductors
In these models proposed to describe the material structure there is a global change in
behaviour of the superconductor due to the local, short-range interactions of the electrons
with the positively charged lattice resulting in sudden phase changes from stable states.
However, this does not appear to be the case for high-temperature superconducting
materials.
Current knowledge and uses of superconductors
Superconductivity is known to occur in 26 metallic elements and in many compounds and
alloys although no unified theory has been produced to explain the phenomenon at high
temperatures.
Currently, superconductors can produce some of the most powerful electromagnets which
can be used in a wide range of fields including magnetic resonance imaging (MRI) in
hospitals, so that patients do not have to be exposed to radiation, to guiding beams around
particle accelerators. Mass spectrometry also makes use of the powerful electromagnets
afforded by superconductivity.
Superconductor (Chemical formula)
Critical Temperature (approx.) / K
(Sn5In)Ba4Ca2Cu11Oy
218
(Sn5In)Ba4Ca2Cu10Oy
212
Sn6Ba4Ca2Cu10Oy
200
(Sn1.0Pb0.5In0.5)Ba4Tm6Cu8O22+
195
(Sn1.0Pb0.5In0.5)Ba4Tm5Cu7O20+
185
Table 1 - Current highest temperature superconductors, all large-compound cuprates
Future applications of superconductivity
The ultimate goal of superconductor research is to find a material which behaves as a
superconductor at room-temperature (293K). This would have profound effects on industry
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and technology, where magnetic levitation vehicles such as trains will be able to travel faster
and more efficiently with greatly reduced friction; superconductors may become an efficient
way of storing power due to the way in which a current may flow unimpeded indefinitely.
However, engineering these will be more difficult to achieve for devices which do not use
direct currents, due to the fact that an alternating current can disrupt the magnetic field
around the superconductor. It is highly likely that superconductors will eventually replace
traditional conductors and improve efficiency and save money.
References
[1] John Daintith et al., Dictionary of Physics, Oxford University Press (2005)
[2] Jewett, Serway, Physics for scientists and Engineers, Thomson (2007)
[3] Philip Ball, Critical Mass, Arrow Books (2007)
[4] http://en.wikipedia.org/wiki/Superconductivity
[5] "On the sudden change in the rate at which the resistance of mercury disappears". Comm.
Leiden. 25 Nov, (1911)
[6] W. Meissner and R. Oschenfeld, Naturwiss. 21, 787 (1933)
[7] J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. 108, 1175 (1957)
[8] Figure 1 - http://nobelprize.org/nobel_prizes/physics/laureates/1972/schriefferlecture.html
[9] Figure 2 - http://www.thesuperconductor.info/images/untitled.bmp
[10] Figure 3 - http://www.imagesco.com/articles/superconductors/resistance-vstemperature.gif
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