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Superconductivity
Superconductivity
Superconductivity is an
electromagnetic phenomenon occurring in certain materials at low
temperatures, characterized by the complete absence of
electrical resistance and the damping of the interior
magnetic field (the
Meissner effect.)
Superconductivity occurs in a wide variety of materials,
including simple elements like
tin
and
aluminum, various metallic
alloys, some heavily-doped
semiconductors, and certain
ceramic compounds containing planes of
copper and
oxygen atoms.
The latter class of compounds, known as the
cuprates, are high-temperature superconducters. Superconductivity does not
occur in
noble metals like
gold
and
silver, nor in ferromagnetic metals such as iron
(although iron can be turned into a superconductor by subjecting it to very high
pressures).
In
conventional superconductors, superconductivity is caused by a
force of attraction between certain
conduction electrons arising from the exchange of
phonons, which causes the fluid of conduction electrons to exhibit a
superfluid
phase composed of correlated pairs of electrons. There also exists
a class of materials, known as
unconventional superconductors, that exhibit superconductivity but whose
physical properties contradict the theory of conventional superconductors. In
particular, the so-called
high-temperature superconductors superconduct at temperatures much higher
than should be possible according to the conventional theory (though still far
below
room temperature.) There is currently no complete theory of high-temperature
superconductivity.
Most of the physical properties of superconductors vary from
material to material, such as the
heat capacity and the critical temperature at which superconductivity is
destroyed. On the other hand, there is a class of properties that are
independent of the underlying material. For instance, all superconductors have
exactly zero resistivity to low applied currents when there is no
magnetic field present. The existence of these "universal" properties imply that
superconductivity is a
thermodynamic phase, and thus possess certain distinguishing properties
which are largely independent of microscopic details.
Suppose we were to attempt to measure the electrical
resistance of a piece of superconductor. The simplest method is to place the
sample in an
electrical circuit, in series with a voltage source V (such as a
battery), and measure the resulting current. If we carefully account for the
resistance R of the remaining circuit elements (such as the leads
connecting the sample to the rest of the circuit), we would find that the
current is simply V/R. According to
Ohm's law, this means that the resistance of the superconducting sample is
zero.
In a normal conductor, an electrical current may be
visualized as a fluid of electrons moving across a heavy
ionic
lattice. The electrons are constantly colliding with the ions in the lattice,
and during each collision some of the
energy carried by the current is absorbed by the lattice and converted into
heat
(which is essentially the vibrational
kinetic energy of the lattice ions.) As a result, the energy carried by the
current is constantly being dissipated. This is the phenomenon of electrical
resistance.
The situation is different in a superconductor. In a
conventional superconductor, the electronic fluid cannot be resolved into
individual electrons, instead consisting of bound pairs of electrons
known as Cooper pairs. This pairing is caused by an attractive
force between electrons from the exchange of phonons. Due to
quantum mechanics, the
energy spectrum of this Cooper pair fluid possesses an energy gap,
meaning there is a minimum amount of energy ΔE that must be supplied in
order to excite the fluid. Therefore, if ΔE is larger than the thermal
energy of the lattice (given by kT, where k is
Boltzmann's constant and T is the temperature), the fluid will not
be scattered by the lattice. The Cooper pair fluid is thus a
superfluid, meaning it can flow without energy dissipation. Experiments have
in fact demonstrated that currents in superconducting rings persist for years
without any measurable degradation.
(Note: actually, in a class of superconductors known as type
II superconductors, a small amount of resistivity appears when a strong magnetic
field and electrical current are applied. This is due to the motion of
vortices in the electronic superfluid, which dissipates some of the energy
carried by the current. If the current is sufficiently small, the vortices are
stationary, and the resistivity vanishes.)
In superconducting materials, the characteristics of
superconductivity appear when the temperature T is lowered below a
critical temperature Tc. The value of this
critical temperature varies from material to material. Conventional
superconductors usually have critical temperatures ranging from less than 1K to
around 20K. Solid
mercury, for example, has a critical temperature of 4.2K. As of
2001,
the highest critical temperature found for a conventional superconductor is 39K
for magnesium boride (MgB2), although this material displays enough
exotic properties that there is doubt about classifying it as a "conventional"
superconductor. Cuprate superconductors can have much higher critical
temperatures: YBa2Cu3O7, one of the first
cuprate superconductors to be discovered, has a critical temperature of 92K, and
mercury-based cuprates have been found with critical temperatures in excess of
130K. The explanation for these high critical temperatures remains unknown.
The onset of superconductivity is accompanied by abrupt
changes in various physical properties, which is the hallmark of a
phase transition. For example, the electronic heat capacity is proportional
to the temperature in the normal (non-superconducting) regime. At the
superconducting transition, it suffers a discontinuous jump and thereafter
ceases to be linear. At low temperatures, it varies instead as e-α/T
for some constant α. (This exponential behavior is one of the pieces of evidence
for the existence of the energy gap.)
Behavior of heat capacity (C) and resistivity (ρ) at the superconducting
phase transition
The order of the superconducting phase transition is still a
matter of debate. It had long been thought that the transition is second-order,
meaning there is no
latent heat. However, recent calculations have suggested that it may
actually be weakly first-order due to the effect of long-range fluctuations in
the electromagnetic field.
When a superconductor is placed in a weak external
magnetic field H, the field penetrates for only a short
distance λ, called the penetration depth, after which
it decays rapidly to zero. This is called the Meissner effect.
For most superconductors, the penetration depth is on the order of a thousand
angstroms (10-7m.)
The Meissner effect is sometimes confused with the "perfect
diamagnetism" one would expect in a perfect electrical conductor: according to
Lenz's law, when a changing magnetic field is applied to a
conductor, it will induce an electrical current in the conductor that creates an
opposing magnetic field. In a perfect conductor, an arbitrarily large current
can be induced, and the resulting magnetic field exactly cancels the applied
field.
The Meissner effect is distinct from perfect diamagnetism
because a superconductor expels all magnetic fields, not just those
that are changing. Suppose we have a material in its normal state, containing a
constant internal magnetic field. When the material is cooled below the critical
temperature, we would observe the abrupt expulsion of the internal magnetic
field, which we would not expect based on Lenz's law.
The Meissner effect was explained by London and London, who
showed that the electromagnetic
free energy in a superconductor is minimized provided
-
where H is the magnetic field and λ is the
penetration depth. This equation, which is known as the
London equation, predicts that the magnetic field in a superconductor decays
exponentially from whatever value it possesses at the surface.
The Meissner effect breaks down when the applied magnetic
field is too large. Superconductors can be divided into two classes according to
how this breakdown occurs. In Type I superconductors,
superconductivity is abruptly destroyed when the strength of the applied field
rises above a critical value Hc. Depending on the geometry
of the sample, one may obtain an intermediate state consisting
of regions of normal material carrying a magnetic field mixed with regions of
superconducting material containing no field. In Type II
superconductors, raising the applied field past a critical value Hc1
leads to a mixed state in which an increasing amount of
magnetic flux penetrates the material, but there remains no resistance to the
flow of electrical current as long as the current is not too large. At a second
critical field strength Hc2, superconductivity is destroyed.
The mixed state is actually caused by vortices in the electronic superfluid,
sometimes called "fluxons" because the flux carried by these vortices is
quantized. Most pure
elemental superconductors (except
niobium) are Type I, while almost all impure and compound superconductors
are Type II.
Variation of internal magnetic field (B) with applied external magnetic
field (H) for Type I and Type II superconductors
Since the discovery of superconductivity, great efforts have
been devoted to finding out how and why it works. During the
1950s,
theoretical condensed matter physicists arrived at a solid understanding of
"conventional" superconductivity, through a pair of remarkable and important
theories: the phenomenological
Ginzburg-Landau theory (1950)
and the microscopic
BCS theory (1957).
Superconductivity was discovered in
1911
by
Onnes, who was studying the resistivity of solid
mercury at cryogenic temperatures using the recently-discovered liquid
helium as a refrigerant. At the temperature of 4.2K, he observed that the
resistivity abruptly disappeared. For this discovery, he was awarded the
Nobel Prize in Physics in
1913.
In subsequent decades, superconductivity was found in several
other materials. In
1913,
lead
was found to superconduct at 7K, and in 1941
niobium nitride was found to superconduct at 16K.
The next important step in understanding superconductivity
occurred in
1933,
when
Meissner and
Oschenfeld discovered that superconductors expelled applied magnetic fields,
a phenomenon which has come to be known as the Meissner effect. In 1935,
F. and H. London showed that Meissner effect was a consequence of the
minimization of the electromagnetic
free energy carried by superconducting current.
In
1950,
the phenomenological
Ginzburg-Landau theory of superconductivity was devised by
Landau and
Ginzburg. This theory, which combined Landau's theory of second-order
phase transitions with a
Schrödinger-like wave equation, had great success in explaining the
macroscopic properties of superconducters. In particular,
Abrikosov showed that Ginzburg-Landau theory predicts the division of
superconductors into the two categories now referred to as Type I and Type II.
Abrikosov and Ginzburg were awarded the Nobel Prize for these works in 2003.
Also in
1950,
Maxwell and Reynolds et. al. found that the critical temperature of a
superconductor depends on the
isotopic mass of the constituent
element. This important discovery pointed to the electron-phonon interaction
as the microscopic mechanism responsible for superconductivity.
The complete microscopic theory of superconductivity was
finally proposed in
1957
by
Bardeen, Cooper, and Schrieffer. This
BCS theory explained the superconducting current as a superfluid of "Cooper
pairs", pairs of electrons interacting through the exchange of phonons. For this
work, the authors were awarded the Nobel Prize in 1972.
The BCS theory was set on a firmer footing in 1958,
when Bogoliubov showed that the BCS wavefunction, which had originally been
derived from a variational argument, could be obtained using a canonical
transformation of the electronic
Hamiltonian. In
1959,
Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close
to the critical temperature.
In
1962,
the first commercial superconducting wire, a niobium-titanium alloy, was
developed by researchers at Westinghouse. In the same year, Josephson made the
important theoretical prediction that a supercurrent can flow between two pieces
of superconductor separated by a thin layer of insulator. This phenomenon, now
called the Josephson effect, is exploited by superconducting devices such as
SQUIDs. It is used in the most accurate available measurements of the
magnetic flux quantum h/e, and thus (coupled with the
quantum Hall resistivity) for
Planck's constant h. Josephson was awarded the Nobel Prize for this
work in 1973.
In
1986,
Bednorz and Mueller discovered superconductivity in a
lanthanum-based cuprate perovskite material, which had a transition
temperature of 35K (Nobel Prize in Physics, 1987).
It was shortly found that replacing the lanthanum with
yttrium raised the critical temperature to 92K, which was important because
liquid
nitrogen could then be used as a refrigerant (at atmospheric pressure, the
boiling point of nitrogen is 77K.) Many other cuprate superconductors have since
been discovered, and the theory of superconductivity in these materials is one
of the major outstanding challenges of theoretical
condensed matter physics.
Some technological innovations benefiting from the discovery
of superconductivity include sensitive magnetometers based on SQUIDs, digital
circuits (e.g. based on the RSFQ logic),
Magnetic Resonance Imaging, beam-steering magnets in particle accelerators,
electric power transmission cables, and
microwave filters (e.g., for mobile phone base stations). Promising future
industrial and commercial applications include
transformers, power storage,
electric motors, and
magnetic levitation devices. Most applications employ the well-understood
conventional superconductors, but it is expected that high-temperature
superconductors will soon become more cost-effective in many cases.
See also:
Timeline of low temperature technology.
-
H.K. Onnes, Commun. Phys. Lab. 12,
120 (1911)
-
W. Meissner and R. Oschenfeld, Naturwiss.
21, 787 (1933)
-
F. London and H. London, Proc. R. Soc. London
A149, 71 (1935)
-
V.L. Ginzburg and L.D. Landau, Zh. Eksp. Teor. Fiz.
20, 1064 (1950)
-
E.Maxwell, Phys. Rev. 78, 477
(1950)
-
C.A. Reynolds et. al., Phys. Rev. 78,
487 (1950)
-
J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys.
Rev. 108, 1175 (1957)
-
N.N. Bogoliubov, Zh. Eksp. Teor. Fiz. 34,
58 (1958)
-
L.P. Gor'kov, Zh. Eksp. Teor. Fiz. 36,
1364 (1959)
-
B.D. Josephson, Phys. Lett. 1,
251 (1962)
-
J.G. Bednorz and K.A. Mueller, Z. Phys.
B64, 189 (1986)
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