Download Superconductivity Lesson Plan - GK

Superconductivity
GK-12 Program – Harvard University
[email protected]
December 9, 2003
Types of Materials:
Conductors: If the outer electrons in a material are weakly bound to their nucleus, they
behave as if they are nearly free and can move through the material nearly unimpeded.
Such materials are called conductors. Examples include metals such as copper and silver.
Superconductors: Some materials have electrons that move with no inhibition when they
are cooled to a sufficiently low temperature. These exciting materials are
superconductors, and will be the topic of today’s discussion.
Insulators: Materials with electrons that do not travel easily are called insulators. Glass
and rubber are two examples.
Semiconductors: Some materials, such as silicon and germanium, can be made into
insulators or conductors by controlling the electric forces on them or the temperature.
These materials play an important role in technology and are called semiconductors.
The Discovery of Superconductivity:
In the early 1900’s, Kammerlingh Onnes, an experimental physicist, was studying the
low temperature behavior of conductors. It was well known by this time that the
electrical resistance in metals decreases with decreasing temperature. Onnes predicted
that this behavior would continue until the resistance decreased to zero at 0 K. Others,
such as Lord Kelvin, thought that at absolute zero, the electrons would freeze in place,
causing the resistance to be infinite. What actually happened as temperature was lowered
was stunning and completely unpredictable at the time. The impurities in metals may
disturb the flow of electricity, so Onnes chose to work with mercury since he could get a
very pure sample. In 1911, he found that mercury losses ALL its resistance abruptly as
the temperature is lowered to a critical value of 4.1 K! Detailed measurements of a
superconducting ring with an induced current showed that after a year, no observable
decrease in current could be detected.
Below is a graph of Resistance vs. Temperature for a certain superconductor, with a
transition temperature of 90 K:
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Properties of Superconductors:
As we have discussed, superconductors have zero resistance below a critical temperature.
Superconductors have magnetic properties just as extraordinary as their electrical
properties. The electric field inside a superconductor is exactly zero, and interestingly
enough, the magnetic field inside is also zero. When a superconductor is placed inside a
magnetic field, surface currents are produced in the superconductor. These currents
produce a magnetic field which exactly cancels the external magnetic field. Below is a
picture of what happens when a sample is placed in a magnetic field (Tc stands for the
transition temperature).
T>Tc: Normal Metal
Magnetic Field Penetrates
T< Tc : Superconducting State
Magnetic Field Expelled
Theory of Superconductivity:
In a normal metal, positive ions form a lattice, and mobile electrons are responsible for
the current. As the electrons move, they collide with impurities or imperfections in the
lattice. See below. The large particles make up the lattice and the small particles are the
electrons:
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The lattice atoms vibrate, which causes scattering of the electrons, and thus resistance to
current flow. This vibration decreases with decreasing temperature, but always exists at
temperatures above 0 K. Thus, we see that superconductivity cannot be explained using
an extension of the theory of ordinary conductivity. The sharp disappearance of
resistance at a critical temperature suggests a transition to a completely different state of
matter.
Quantum mechanics is necessary to explain the superconducting phase. Classical
mechanics deals with matter, and can be used in everyday things like momentum
conservation in a collision, and gives you strategies in playing billiards, etc…
Electromagnetism, on the other hand, deals with fields (electric and magnetic fields).
Quantum mechanics blurs the distinction between matter and fields. An electron can be
thought of as a wave, as well as a particle. In classical mechanics, you can know both the
position and speed of an object (such as the speed of a baseball and where it is located).
In quantum mechanics, however, you cannot know both. The position of an electron and
its velocity cannot be known simultaneously. There always exists a certain degree of
uncertainty. A quantum mechanical world is a weird and exciting one!
In 1957, John Bardeen, Leon Cooper, and Robert Schrieffer satisfactorily explained
superconductivity with a theory now known as BCS theory. According to this theory, a
moving electron causes a slight distortion of the lattice (remember that the lattice atoms
are positively charged). See below:
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If this distortion remains for a finite amount of time, it can affect a second passing
electron. The effect of this phenomenon is for the current to be carried by pairs of
electrons (called Cooper pairs), as opposed to individual electrons.
The Cooper pairs move smoothly through the superconductor and there is no dissipation
of energy. As the superconductor is heated beyond the transition temperature, the lattice
vibrations cause the Cooper pairs to break, thus destroying superconductivity.
Applications of Superconductors:
Until 1986, 23 K was the highest known transition temperature for a material to become
superconducting. This low temperature is extremely costly to achieve, so until that point,
superconducting devices were used for only specialized applications, such as magnets for
particle accelerators or imaging machines in hospitals. In 1986, however, a new type of
material was discovered that had a much higher transition temperature. These materials
are called high-temperature superconductors. Some have transition temperatures above
120 K (-153 degrees C). These materials may be used in such things as switches in
supercomputers, and other small electrical devices.
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