SUPERCONDUCTORSS

INTRODUCTION
The phenomenon of superconductivity, in which the electrical resistance of
certain materials completely vanishes at low temperatures, is one of the most
interesting and sophisticated in condensed matter physics. It was first
discovered by the Dutch physicist Heike Kamerlingh Onnes, who was the first
to liquefy helium (which boils at 4.2 Kelvin at standard pressure). In 1911
Kamerlingh Onnes and one of his assistants discovered the phenomenon of
superconductivity while studying the resistance of metals at low temperatures.
They studied mercury because very pure samples could easily be prepared by
distillation. In 1933, Walter Meissner and Robert Ochsenfeld discovered a
magnetic phenomenon that showed that superconductors are not just perfect
conductors. Imagine that both the ideal conductor and superconductor are
above their critical temperature, Tc. That is, they both are in a normal
conducting state and have electrical resistance. A magnetic field, Ba, is then
applied. This results in the field penetrating both materials. Both samples are
then cooled so that the ideal conductor now has zero resistance. It is found
that the superconductor expels the magnetic field from inside it, while the
ideal conductor maintains its interior field. Note that energy is needed by the
superconductor to expel the magnetic field. This energy comes from the
exothermic superconducting transition. Switching off the field induces currents
in the ideal conductor that prevent Figure 2. The critical temperatures of some
superconductors. changes in the magnetic field inside it – by Lenz’s law.
However, the superconductor returns to its initial state, i.e. no magnetic field
inside or outside it
Following his discovery that electric current can be transported through a
superconductor without electrical resistance, Kamerlingh Onnes soon
considered technical plans to utilize the phenomenon of superconductivity in
cables for the distribution and delivery of electrical power. However, to his
great disappointment, during his first experiments he found that the
superconducting property is reduced in a magnetic field, and that it
completely disappears above a distinct value of the magnetic field, the “critical
magnetic field” HC. Here an external magnetic field acts in exactly the same
way as the “self-field”, which is generated by the transported electric current in
the superconductor itself. The critical magnetic field HC(T) vanishes at the
critical temperature TC and increases with decreasing temperature below TC. It
reaches its maximum value at a temperature of zero Kelvin (Fig. 8.3). In many
classical superconductors this maximum value ranges between the 100-fold
value up to the 5000-fold value of the earth’s magnetic field. Because of the
self-field of the transported electric current, the maximum current value, up to
which superconductivity is maintained, is limited. This maximum current in a
superconductor is referred to as the critical current IC. In the simplest case the
critical current is reached when the magnetic self-field of the current is equal
to the critical field HC. This relationship is also called Silsbee’s rule, named
after Francis Briggs Silsbee. For many years, this severe restriction on the
possibility of transporting electric currents in superconductors has hindered
the technical application of superconductivity. This only changed in the 1960s,
when new superconducting materials were found with more favorable
properties and relatively high values of the critical magnetic field and the
critical current.
THEORY OF SUPERCONDUCTORS
It has taken nearly 50 years since the discovery of superconductivity,
until for the first time a microscopic theory was proposed which could explain
satisfactorily the underlying mechanism. In the year 1957 the three Americans
John Bardeen, Leon Cooper, and Robert Schrieffer achieved the long-expected
theoretical breakthrough. Their theory, the “BCS theory”, quickly became very
famous. The question why it took so long to produce a theoretical explanation
of superconductivity, can be answered relatively simply. The energy difference
of the electrons between their normal and their superconducting state is
extremely small and much smaller than the Fermi energy. On the other hand,
the uncertainty in the calculation of the different individual contributions to
the energy of the electrons in the crystal is much larger than the energy gain
during the transition into the superconducting state. Hence, the theory had to
find the exact point leading to superconductivity. The BCS theory is based on
the central idea that, at low temperatures, a specific attractive force is acting
between two electrons. Because of this attraction, two electrons combine into
pairs in a distinctive way and experience an energy reduction in the form of
binding energy. Such a formation of pairs accompanied by a reduction in
energy had been theoretically derived by Leon Cooper in 1956. Therefore, the
electron pairs are referred to as “Cooper pairs”. According to the BCS theory,
the attractive force leading to the formation of the Cooper pairs is due to the
distortions of the crystal lattice near the individual electrons, i.e., due to the
phonons. In this way, the otherwise expected repulsive force between two
electrons is overcompensated. Already by the early 1950s strong indications
for the important role of the crystal lattice in the mechanism of
superconductivity were obtained, based on experimental observations of the
“isotope effect”. One generally speaks of an isotope effect, when the result
depends on the mass of the atomic nuclei at constant electric charge of the
nuclei, i.e., on the number of neutrons in the atomic nuclei. By careful study of
the different and specially prepared pure isotopes of various superconducting
materials such as, for example, lead, mercury, and tin, it was found, that the
critical temperature TC is inversely proportional to the square-root of the mass
of the lattice atoms:
 TC 1=Ma
with the exponent a = 0.5. Hence, the crystal lattice must play some role
in superconductivity. During pair formation, two electrons with opposite spin
always combine with each other. Therefore, the total spin of an individual
Cooper pair is zero, and the Pauli principle does not apply in this case. Hence,
all Cooper pairs can occupy the same quantum state, which is described in
terms of a macroscopic quantum mechanical wave function. However, not all
electrons participate in the formation of Cooper pairs and in the macroscopic
quantum state. Instead, only the electrons from a distinct small energy interval
near the Fermi surface are involved. We see again, how the concept of the
Fermi surface plays a central role. Mathematically, the subject of
superconductivity confronts us with a “manybody problem”, requiring special
techniques for its theoretical treatment. The development of these necessary
new methods started about 60–70 years ago in conjunction with quantum
field theory. The first steps of this theory can be found in a paper published in
the year 1928 by the German Pascual Jordan and Eugene Paul Wigner from
Hungary. One main result of the BCS theory was the prediction that, in the
superconducting state, a gap appears in the energy spectrum of the electrons
at the Fermi energy, in which no energy states exist which can be occupied by
electrons. The energy gap vanishes above the critical temperature TC. Below
TC the energy gap increases with decreasing temperature in a distinct way and
reaches its maximum value at a temperature of zero Kelvin. In the year 1960,
Ivar Giaever presented an impressive proof of this energy gap by means of his
famous tunneling experimentFor some time he had been fascinated by the
quantum-mechanical tunneling effect. Giaever was born in Norway and as a
young mechanical engineer was employed at General Electric in Schenectady
in the American Federal State of New York. At the Rensselaer Polytechnic
Institute near the location of his employment, he had heard in a lecture about
the new BCS theory and its prediction of a gap in the energy spectrum of the
electrons. On his way home after the lecture he had the idea that the energy
gap must directly affect the electric current flow between a superconducting
and a normal electrode, if the two electrodes are separated from each other
by a thin, electrically insulating barrier. Because of this barrier, the electric
current flow is possible only by means of the quantum mechanical tunneling
process. Hence, this arrangement is referred to as a tunnel junction. During
the propagation of particles, the tunneling effect is caused by the fact, that the
wave function of the particle can still seep through a high wall and can reach
an appreciable value at the other side. However, in our tunnel junction the
tunneling current cannot flow as long as no allowed energy states in the
superconductor are available for the electrons coming from the other
electrode, because of the energy gap. Only when the potential difference
between both electrodes has reached the value of the energy gap because of
the applied electric voltage does the electric current flow become possible. We
have a similar result, if both electrodes are superconducting. Hence, it should
be possible to determine the superconducting energy gap just by means of a
simple measurement of the electric voltage and the electric current in a tunnel
junction. Giaever’s experiments have impressively confirmed these
expectations. After this pioneering step, tunneling experiments with
superconductors have become an important source of information about the
physics of superconductors. The BCS theory has been confirmed by many
further experiments and has quickly found wide acceptance. There exists a
long list of physicists, who had tried before without success to construct a
microscopic theory of the mechanism of superconductivity. Among others, this
list includes the names Felix Bloch, Niels Bohr, Léon Brillouin, Jakov I. Frenkel,
Werner Heisenberg, Ralph Kronig, Lew Dawidowitsch Landau, and Wolfgang
Pauli. The fact that it is the formation of Cooper pairs occupying a
macroscopic quantum state, which leads to superconductivity, is also visible in
the magnitude of the magnetic flux quantum discussed above. Since the
Cooper pairs are composed of two elementary charges, the magnetic flux
quantum (h/2e) is only half as large as would be the case if the underlying
elementary particles carried only a single elementary charge, leading to (h/e).
TYPES OF SUPERCONDUCTORS

Depending upon the behavior in an external magnetic field, superconductors

are divided into two categories: 1. Type-I superconductor or soft
superconductor 2. Type-II superconductor or hard superconductor

TYPE-1
The Type 1 category of superconductors is mainly comprised of metals and
metalloids that show some conductivity at room temperature. They require
incredible cold to slow down molecular vibrations sufficiently to facilitate
unimpeded electron flow in accordance with what is known as BCS theory.
BCS theory suggests that electrons team up in "Cooper pairs" in order to help
each other overcome molecular obstacles - much like race cars on a track
drafting each other in order to go faster. Scientists call this process phonon-
mediated coupling because of the sound packets generated by the flexing of
the crystal lattice.
Type 1 superconductors - characterized as the "soft" superconductors -
were discovered first and require the coldest temperatures to become
superconductive. They exhibit a very sharp transition to a superconducting
state ] and "perfect" diamagnetism - the ability to repel a magnetic field
completely. Soft superconductors are those which can tolerate impurities
without affecting the superconducting properties. Only one criticial frields
exists for these. They exhibit perfect and complete Meissner effect.the current
flows through the surface only. These materials have limited technical
application because of very low field strength value.
Eg pb,hg,zn etc

TYPE-2
Except for the elements vanadium, technetium and niobium, the Type 2
category of superconductors is comprised of metallic compounds and alloys.
The recently-discovered superconducting "perovskites" (metal-oxide ceramics
that normally have a ratio of 2 metal atoms to every 3 oxygen atoms) belong
to this Type 2 group. They achieve higher Tc's than Type 1 superconductors by
a mechanism that is still not completely understood. Conventional wisdom
holds that it relates to the planar layering within the crystalline structure (see
above graphic). Although, other recent research suggests the holes of
hypocharged oxygen in the charge reservoirs are responsible. (Holes are
positively-charged vacancies within the lattice.) The superconducting cuprates
(copper-oxides) have achieved astonishingly high Tc's when you consider that
by 1985 known Tc's had only reached 23 Kelvin. To date, the highest Tc
attained at ambient pressure for a material that will form stoichiometrically (by
direct mixing) has been 147 Kelvin. And the highest Tc overall is 216 Celsius for
a material which does not form stoichiometrically (see below list). It is almost
certain that other, more-synergistic compounds still await discovery among
the high-temperature superconductors.
The first superconducting Type 2 compound, an alloy of lead and bismuth,
was fabricated in 1930 by W. de Haas and J. Voogd. But, was not recognized
as such until later, after the Meissner effect had been discovered. This new
category of superconductors was identified by L.V. Shubnikov at the Kharkov
Institute of Science and Technology in the Ukraine in 1936(1) when he found
two distinct critical magnetic fields (known as Hc1 and Hc2) in PbTl2. The first of
the oxide superconductors was created in 1973 by DuPont researcher Art
Sleight when Ba(Pb,Bi)O3 was found to have a Tc of 13K. The superconducting
oxocuprates followed in 1986.
Type 2 superconductors - also known as the "hard" superconductors -
differ from Type 1 in that their transition from a normal to a superconducting
state is gradual across a region of "mixed state" behavior. Since a Type 2 will
allow some penetration by an external magnetic field into its surface, this
creates some rather novel mesoscopic phenomena like
superconducting "stripes" and "flux-lattice vortices". They cannot tolerate
impurities and has 2 critical fields. The critical field value is very high . they
don’t exhibiti perfect and complete meissner effect. Current flows throughout
the material. These materials have wider technology of very high field strength
value.
E.g. Nb3Ge, Nb3Si

High magnetic fields destroy superconductivity and restore the normal

conducting state. Depending on the character of this transition, we may
distinguish between type I and II superconductors. The graph shown in Figure
4 illustrates the internal magnetic field strength, Bi, with increasing applied
magnetic field. It is found that the internal field is zero (as expected from the
Meissner effect) until a critical magnetic field, Bc, is reached where a sudden
transition to the normal state occurs. This results in the penetration of the
applied field into the interior. Superconductors that undergo this abrupt
transition to the normal state above a critical magnetic field are known as type
I superconductors. Most of the pure elements in Figure 2 tend to be type I
superconductors. Type II superconductors, on the other hand, respond
differently to an applied magnetic field, as shown in Figure 5. An increasing
field from zero results in two critical fields, Bc1 and Bc2. At Bc1 the applied field
begins to partially penetrate the interior of the superconductor. However, the
superconductivity is maintained at this point. The superconductivity vanishes
above the second, much higher, critical field, Bc2. For applied fields between
Bc1 and Bc2, the applied field is able to partially penetrate the superconductor,
so the Meissner effect is incomplete, allowing the superconductor to tolerate
very high magnetic fields. Type II superconductors are the most
technologically useful because the second critical field can be quite high,
enabling high field electromagnets to be made out of superconducting wire.
Most compounds shown in Figure 2 are type-II superconductors. Wires made
from say niobium-tin (Nb3Sn) have a Bc2 as high as 24.5 Tesla – in practice it
is lower. This makes them useful for applications requiring high magnetic
fields, such as Magnetic Resonance Imaging (MRI) machines. The advantage of
using superconducting electromagnets is that the current only has to be
applied once to the wires, which are then formed into a closed loop and allow
the current (and field) to persist indefinitely – as long as the superconductor
stays below the critical temperature. That is, the external power supply can be
switched off. As a comparison, the strongest permanent magnets today may
be able to produce a field close to 1 Tesla. However, it is possible to obtain up
to 24.5 Tesla from a niobium–tin superconductor. There is a misconception
amongst some non-specialists that the term "Type II" refers to the copper
oxide based high temperature superconductors discovered in the late 1980s.
While these are type II superconductors, so are many superconductors
discovered before that time.
PROPERTIES OF SUPERCONDUCTORS
Below a critical temperature, the resistance of a superconduction material
almost becomes zero causing current to flow indefinitely and with no power
loss. No voltage difference is needed to matain a current. Above a current
density, superconductivity is lost in the material. A supercurrent can flow
across an insulating junction in what is called the josephon effect. The
current in the superconductors persists for a very long time. This is
demonstrated by placing a loop of the superconductor in a magnetic
field, lowering its temperature below transition temperature Tc, and then
removing the field. The current which is setup is found to persist over a
period longer than a year without any attenuation. The magnetic field
does not penetrate into the body of the superconductor. The property
known as the Meissner effect, is the fundamental characterization of
superconductivity. However, when the magnetic field H is greater than a
critical field Hc, the superconductor becomes a normal conductor.When a
current through the superconductor is increased beyond critical value
Ic(T), the superconductor again becomes a normal conductor,
i.e., the magnetic field which causes a superconductor to become normal
from a superconducting state is not necessarily an external magnetic field,
it may arise as a result of electric current flow in the conductor.
The superconductivity may be destroyed when the current exceeds the
critical value which at the surface of the wire will produce a critical field :
Hc given by
I=2pirHc
This is known as Silsbee’s rule.
The specific heat of the material shows an abrupt change at T =
Tc jumping to a large value for T < Tc. In all cases involving transition
metals, the variation of Tc, with number of valence electrons shows
sharp maxima for Z = 3, 5 and 7. A rather striking correlation exists
between Tc and Z2 for elements Hg, La, Pb, Nb, Zn, in, In, Sn, V, Tc, Cd,
Ga and Al.For a given value of Z, certain crystal structures seem more
favourable than others, e.g., β-tungsten and α-Mn structures are
conducive to the phenomenon of superconductivity. Tc increases with a
high power of the atomic volume and inversely as the atomic mass and
is known as isotope effect. Superconductivity occurs in materials
having high normal resistivities.

The condition nρ > 106 is a good criterion for the existence of

superconductivity, where ‘n’ is number of valence electrons per cc and
‘ρ’ is the resistivity in use at 20°C.
ADVANTAGES

Superconductivity brings sensitivity, accuracy and performance advantages

beyond the theoretical limits of conventional electronics technology.
Additionally, in large scale superconducting systems, when all the necessary
cryogenic components are included, size and weight reductions of 50-70% are
achieved versus conventional equipment.
Mine Protection: As steel hulled ships at sea move through the magnetic field
of the earth they develop a low level magnetic charge which can be used as a
homing signature in mine warfare. Most naval vessels are therefore equipped
with large copper degaussing coils running around the ship which are used to
“neutralize” the magnetic signature. Superconducting degaussing coils are
20% the weight of copper based coils as they carry higher currents at lower
voltages which translates into smaller footprints and improved efficiency. High
Temperature Superconductor (HTS) coils were retrofitted on the guided-
missile destroyer USS Higgins (DDG 76) in 2008 and have performed
extremely well in sea trials since that time. Use of this demonstrated superior
and potentially life-saving technology should be retrofitted on all current Navy
vessels and incorporated into all new construction.
Electric Power Distribution: High Temperature Superconducting (HTS) power
cables have significantly higher power density capability than copper
counterparts, thus providing weight and size savings and making room for
other war fighting equipment on board Navy vessels. Bridging various loads
and sources of electric power with HTS cables will ensure uninterrupted power
with minimal waste. HTS cables also offer tunable power density by adjusting
the operating temperature. With investments in research and development,
the HTS technology advancements that are under development for utility
power grid applications can be extended to defense. CCAS recommends that
the Administration and the Congress continue funding ongoing programs and
new proposals in HTS cables and related cryogenic technology development
for military use.
Superconducting magnets: Probably the biggest use of superconductors is in
making magnets. Back in the 19th century, Michael Faraday had discovered
that if you pass a current down a wire, there is a magnetic field which exists
around the wire. As you pass more electrical current, the magnetic field gets
stronger. Winding the wire into a helical coil allows this magnetic field to be
concentrated inside the coil, andhey presto you have an electromagnet, a
magnet whose strength can be controlled using electrical current. Such an
electromagnet is used in old-fashioned electric doorbells, and in relays and
tape recorders. They are also used to make many laboratory magnets. But to
produce a really large magnetic field, you need a lot of electric current, and an
enormous amount of electrical power. Onnes was sure that superconductors
provide the answer. However, it was only after Hulm, Matthias, Kunzler, and
others in the 1960s discovered new materials with large critical magnetic fields)
that superconducting magnets became a realistic possibility. The large critical
magnetic fields available meant that it was going to be possible to replace the
copper windings in electromagnets with superconducting wire. Although the
new superconducting coils would have to be cooled with liquid helium, which
is quite expensive, the current would flow with no dissipation and so the
ruinous electricity costs involved with conventional magnets could be avoided.
From that time onwards, various companies began to form and begin the
manufacture of commercial superconducting magnets.
Niche applications The examples quoted so far are all fairly large-scale
engineering applications of superconductors. But there is a lot you can do on
the smaller scale. Superconductors find their way into certain applications
where high frequencies are needed, for example in antennas, filters, and
mixers in microwave circuits, and often in Tunnel or Josephson junctions
APPLICATION
The first large scale commercial application of superconductivity was in
magnetic resonance imaging (MRI). This is a non-intrusive medical imaging
technique that creates a two-dimensional picture of say tumors and other
abnormalities within the body or brain. This requires a person to be placed
inside a large and uniform electromagnet with a high magnetic field. Although
normal electromagnets can be used for this purpose, because of resistance
they would dissipate a great deal of heat and have large power requirements.
Superconducting magnets on the other hand have almost no power
requirements apart from operating the cooling. Once electrical current flows in
the superconducting wire, the power supply can be switched off because the
wires can be formed into a loop and the current will persist indefinitely as long
as the temperature is kept below the transition temperature of the
superconductor. Superconductors can also be used to make a device known
as a superconducting quantum interference device (SQUID). This is incredibly
sensitive to small magnetic fields so that it can detect the magnetic fields from
the heart (10-10 Tesla) and even the brain (10-13 Tesla). For comparison, the
Earth’s magnetic field is about 10-4 Tesla. As a result, SQUIDs are used in non-
intrusive medical diagnostics on the brain. The traditional use of
superconductors has been in scientific research where high magnetic field
electromagnets are required. The cost of keeping the superconductor cool are
much smaller than the cost of operating normal electromagnets, which
dissipate heat and have high power requirements. One such application of
powerful electromagnets is in high energy physics where beams of protons
and other particles are accelerated to almost light speeds and collided with
each other so that more fundamental particles are produced. It is expected
that this research will answer fundamental questions such as those about the
origin of the mass of particles that make up the Universe. Levitating trains
have been built that use powerful electromagnets made from
superconductors. The superconducting electromagnets are mounted on the
train. Normal electromagnets, on a guideway beneath the train, repel (or
attract) the superconducting electromagnets to levitate the train while pulling
it forwards. A use of large and powerful superconducting electromagnets is in
a possible future energy source known as nuclear fusion. When two light
nuclei combine to form a heavier nucleus, the process is called nuclear fusion.
This results in the release of large amounts of energy without any harmful
waste. Two isotopes of hydrogen, deuterium and tritium, will fuse to release
energy and helium. Deuterium is available in ordinary water and tritium can be
made during the nuclear fusion reactions from another abundantly available
element – lithium. For this reason it is called clean nuclear energy. For this
reaction to occur, the deuterium and tritium gases must be heated to millions
of degrees so that they become fully ionized. As a result, they must be
confined in space so that they do not escape while being heated. Powerful
and large electromagnets made from superconductors are capable of
confining these energetic ions. An international fusion energy project, known
as the International Thermonuclear Experimental Reactor (ITER) is currently
being built in the south of France that will use large superconducting magnets
and is due for completion in 2017. It is expected that this will demonstrate
energy production using nuclear fusion. An electronic instrument used today
in many different ways is the “SQUID” (abbreviated from Superconducting
Quantum Interference Device). It is based on the magnetic flux quantization
and the Josephson effect.