What Is Superconductivity?

	by Loren Petrich

	Superconductivity was discovered in 1911 when physicist
Kamerlingh Onnes was measuring the resistance of mercury at low
temperatures. As the temperature was lowered, he found that it dropped
and dropped as expected, but below about 4.22 K, it dropped to below
measurement accuracy and stayed there. This was the first observation
of superconductivity, and later experiments have produced some very
strong upper limits to the resistivity of superconductive materials,
at least with respect to small, static currents.

	Since then, many other materials have been discovered to be
superconducting at sufficiently low temperature (the upper limit is
called the critical temperature, or Tc for short). These include about
30 elements, with Tc values of 0.01 K for tungsten to 9 K for niobium,
and several compounds, with the critical-temperature record holder
until 1986 being Nb3Ge at 23 K. Interestingly, the best conductors,
such as Cu, Ag, Au, and Pt, have never been observed to be
superconducting, while superconductors with relatively high Tc tend to
be poor "normal" conductors.

	But in 1986, K. Alex Mu"ller and J.  George Bednorz discovered
that a ceramic with composition La_1.85 Ba_0.15 CuO4 had a Tc of 35 K.
This was quickly followed by Paul C.W.  Chu and Maw-Kuen Wu's
discovery that a ceramic, YBa2Cu3O7 (YBCO for short) had a Tc of 95 K,
which is higher than the boiling point of liquid nitrogen, 77 K. This
caused a lot of excitement, because here was a superconductor that was
a lot easier to chill than any others available, even the commonly
used Nb3Sn, with a Tc of 18 K, which generally require liquid-helium
temperatures for effective operation.  The ceramic nature of the
material, however, would seem to fit the inverse relationship between
"normal" conductivity and Tc stated above.

	Superconductors have an additional property, which makes them
differ from idealized perfect conductors. They repel magnetic fields,
or at least relatively weak ones, which penetrate only to a fraction
of a micron. This property enables superconducting rings to trap
magnetic flux, which is produced by a steadily-flowing current in the
ring. This flux is quantized in multiples of (h/2e)*(one's favorite
units factor), which is critical for understanding the mechanism of
superconductivity, explained in more detail below. Suffice it to say
here that the electrons are correlated in a fashion which yields
macroscopic quantum behavior.

	Related to the quantization of magnetic flux is the "Josephson
effect", manifested at a "Josephson junction", which is a thin layer
of insulator (usually 10 A of metal oxide) separating two layers of
superconducting material. The frequency of current oscillation is
related to the voltage across the junction by: f = (2e/h)*V. A
Josephson junction can be used as a switch, because if it is slightly
heated or magnetized, its superconductivity can be destroyed at a
lower temperature that the Tc of the surrounding materials.


	* What can it be used for?

	The _very_ low resistance to electric current and the
macroscopic quantum properties are reasons to be interested in
applications of superconductivity. The main barrier, however, has been
the low Tc of most available materials, and the resultant requirement
of liquid-helium refrigeration. The interest in high-Tc
superconductors is simply because they need less refrigeration, to
liquid-nitrogen temperatures, or perhaps even to closer-to-normal
temperatures. However, YBCO and related materials are ceramics that
are difficult to form into wires and other useful shapes.

	Even existing low-Tc materials, like Nb3Sn, can be difficult
to work with. To make wire for magnets, it is necessary to clad
several Nb3Sn wires with copper, which is a good heat and "normal"
electric conductor, despite its being non-superconducting. Nb3Sn is a
poor "normal" conductor of electricity, and if some of it went from
superconducting to normal, it would heat up very quickly. The copper
serves as a heat and electric bypass. So given the difficulty with
working with many low-Tc materials, it should not be surprising that
high-Tc materials are even worse.

	Superconducting magnets are used in applications that call for
strong magnetic fields, like particle accelerators and NMR/MRI
devices. They also have been proposed for various other applications,
such as energy storage, improved motors and generators, and magnetic
propulsion of ships and trains.

	Magnets are necessary for ring-shaped particle accelerators,
to keep the particles' path confined to the evacuated ring. Magnets
are also for measuring the energies and electric charges of particles
emerging from interactions; the radius of curvature of a particle's
path is proportional to its momentum and inversely proportional to its
charge.

	For NMR/MRI (Nuclear Magnetic Resonance / Magnetic-Resonance
Imaging), magnetic nuclei precess in the field, and they can be
detected by exposing them to radio waves of the appropriate frequency.
Though expensive, it has become a common way of non-invasive probing
in medical examinations, since, unlike X-rays, it is non-ionizing and
it is sensitive to the details of soft tissues.

	For energy storage, a magnet is "charged" with electric
current, and later discharged. The energy is stored in the circulating
current and the magnetic field; if the energy is not dissipated
through electrical resistance, it can stay on a long-term basis. One
such system is currently being studied for the Bay Area Rapid Transit
system, to even the electricity supply to its trains as they pass
through a tunnel under the San Francisco Bay, where there are no
electricity substations. It would be charged when the trains are less
frequent, and discharged during rush hour, when the trains are more
frequent.

	Another possible place for superconducting magnetis is in
large motors and generators, to lessen the electricity and cooling
demands of at least some of their magnets. I'm not aware of any that
are planned or running, however; although they could be of use in
electric power plants and in ships.

	Magnetic-induction ships are currently being worked on in
Japan, where a magnetic-induction ship has been tested. A magnetic
field in created in one direction, electric current is run through the
water in another direction, and the cross-product of the two yields
the water's motion. Currently, only 20 mph (30 kph) has been achieved
in salt water (which is more conductive than fresh water), but the
technology avoids the cavitation (low-pressure boiling) that happens
on propellers and is promising for high speeds.

	Another such possibility: magnetic-levitation (maglev) trains.
These would have large on-board magnets which maintain a separation of
the train from the track (specially designed; standard railroad tracks
will _not_ work!). The magnets can be underneath steel beams, in which
case the field must be continually adjusted, though the train can
maintain separation at low speeds. The magnets can be above a metallic
sheet or next to some coils in the track, in which case they work by
causing eddy currents as they move, producing magnetic repulsion. But
a train must be in motion, probably faster than about 60 mph (100
kmh), for this system to work. Though for the most part, maglev is
still in the testing stage, there is a go-ahead for a 250-mph maglev
line to be built connecting the Orlando Airport in Florida with an
area featuring some major hotels. However, maglev may not be
competitive with steel-wheel-on-steel-rail trains like the French TGV,
which reaches 180 mph (300 kph) in regular service, and 300 mph (500
kph) in tests, unless speeds reach as much 600 mph (1000 kph).

	Other applications exploit the quantum properties of
superconductivity. The SQUID (Superconducting Quantum Interference
Device) splits current, sends it through two Josephson junctions, and
recombines it. The superconducting field gets a different phase going
in different paths in the field, and when combined, may produce a
reduced current. A changing field will therefore cause an oscillating
current, and these oscillations can be translated into differences in
field values. In addition, the universal voltage-frequency
relationship that Josephson junctions have makes possible _very_
precise voltmeters, and in fact, it is now used as a _de facto_
voltage standard.


	* How does it work?

	In "normal" conductors, the travels of electrons are
interrupted by various obstacles: crystal defects, grain boundaries,
out-of-place ions, and even the thermal oscillations of the ion cores.
Thus, an electron set in motion will be slowed down, and this slowing
down will create electrical resistance.

	More precisely, in a conductor, the electrons fill up part of
a band of states, with states available for slightly more energetic
electrons. An electric current results from there being more electrons
going one way than the other. The interactions mentioned above tend to
scatter the electrons and even out their velocity distribution.

	How does superconductivity work? In what follows, I will
explain the Bardeen-Cooper-Schrieffer (BCS), which successfully
accounts for the properties of the metallic (low-Tc) superconductors,
but which may have to be modified for the high-Tc ones.

	An electron can interact with another one by pulling the ion
cores slightly out of place, which then interacts with the other
electron by the resulting nonuniform charge. This interaction is
essentially the transmitting of a sound wave between two electrons.
This mechanism successfully accounts for low-Tc superconductivity, but
there appear to be some different mechanisms for the high-Tc
superconductors.

	If this interaction is strong enough, then the electrons may
become slightly correlated in their motion. Electrons have spin 1/2,
which means that two electrons cannot occupy the exact same state.
However, a correlation between two electrons will have spin 0 or 1,
which means that the correlations can occupy the same state, meaning
that they will be highly correlated.  This correlation of correlations
is what produces superconductivity, since it extends over macroscopic
distances. These electron correlations, however, can be destroyed by
sufficiently high temperature or magnetic field, thus limiting the
superconductor's performance.

	This macroscopic correlation also brings about other effects,
like flux exclusion and flux quantization; from theory, the magnetic
flux trapped in current loops should be an integer multiple of
(h/q)*(one's favorite units factor), where q is the charge of the
charge carriers. Since the quantized flux is observed to be (h/2e),
one concludes that the superconducting charge carriers have charge 2e,
and are paired electrons.

	In similar fashion, the ac Josephson-junction
voltage-frequency relationship may be derived as follows: Treat the
correlation of correlations as a quantum field, obeying the
Schro"dinger equation: i*hbar*(d(Psi)/dt) = H(Psi), where H = qV in
this problem. The field (Psi) will oscillate: (Psi) ~ exp(i*phi),
where the phase (phi) = - iqVt/hbar + const. On two sides of a
Josephson junction, the fields on each side may oscillate at different
rates, and that will be manifested as current oscillations:

	I_12 = I_max * sin(phi_1 - phi_2)

where we can simplify the phase difference to q*(V_1 - V_2)*t/hbar +
const. The oscillation frequency is therefore given as qV/h (V =
voltage difference), which is observed to be 2eV/h.

	There is an interesting division in superconductor reactions
to high magnetic fields. Type I superconductors simply turn normal at
fields of 300 gauss or so, while Type II superconductors can have
critical fields of several thousand gauss. The difference lies in the
stability of thin tubes of magnetic flux. Each one is surrounded by a
current vortex, and inside, the material is normal
(non-superconducting). The tubes extend from one surface to to
another. For Type I, these tubes are unstable, while for Type II,
these tubes are unstable. As the magnetic field increases for Type II,
the tubes occupy more and more of the volume of the material, with the
critical field resulting from where too much of the material is inside
a flux tube.

  ===
/Loren Petrich, the Master Blaster
/lip@s1.gov