The document summarizes key aspects of superconductivity. It describes how superconductivity was discovered in 1911 when the electrical resistance of mercury suddenly dropped to zero at 4.2 K. Some key properties discussed include the Meissner effect where magnetic flux is expelled from the superconductor below the critical temperature, and the distinction between type I and type II superconductors based on their behavior in magnetic fields. The document also provides an overview of the BCS theory of superconductivity and discusses some industrial applications of superconductors such as in MRI machines, maglev trains, and electricity transmission.

1. P.A. Nagpure
Department of Physics
Shri Shivaji Science College, Amravati
Superconductivity

2. Superconductivity
 The phenomenon was first discovered by Kamerling Onnes in
1911, while studying the electrical resistance of mercury at very
low temperatures close to 4.2 K.
 It was observed that the electrical resistance of mercury
decreases continuously from its M.P. (233K) to 4.2 K and then
for decrease of temperature by very small fraction of degree,
resistance suddenly drop to millionth of its original value.
 Similar results were obtained for other metals also such as Pb,
Sn and In.

3.  Thus the phenomenon of disappearance of electrical
resistance below certain temperature is called
superconductivity and the material in this state is called
superconductor.
 The temperature at which normal conductor becomes
superconductor is called critical temperature TC.
 Critical temperatures for some materials in kelvin : Al-1.18,
Hg-4.15, In-3.41, Pb-7.19, Sn-3.72, Zn-0.85.
In recent years many alloys and ceramic superconducting
materials are developed which have high critical
temperatures. For Example: Nb3Sn-18, Nb3Ge-23.2, Nb3Al-
20.7, etc.
P.A. Nagpure

4. Meissner Effect/ Perfect Diamagnetism
 Meissner discovered in 1933 that superconductor expelled
the magnetic flux as the specimen cooled below TC in an
external magnetic field. i.e it behaves as perfect diamagnet.
 This phenomenon of flux exclusion by the superconductor is
known as Meissner effect.
Cooled
below Tc
Field
removed
Normal
Conductor
T>Tc
Kept in
external
mag.
field
Super
Conductor
T<Tc
P.A. Nagpure

5. • Such flux exclusion is also observed if the superconductor first
cooled below Tc and then placed in the magnetic field.
• Thus it follows that the diamagnetic behaviour of
superconductor is independent of its history.
• Thus from figures, we can say, Meissner effect is a reversible
phenomenon.
Cooled
below Tc
Field
removed
Normal
Conductor
T>Tc
Super
Conductor
T<Tc
Super
Conductor
T<Tc
Kept in
external
mag.
field
P.A. Nagpure

6. Critical field Hc and Critical temperature TC
 In 1913, Onnes, observed that superconductors regains its normal
conducting state below its critical temperature TC if it is placed in
sufficiently strong magnetic field.
 The value of magnetic field at which superconductivity vanishes is
called critical field Hc.
 It is of the order of few hundred orested for most of pure
superconductors.
 The critical field Hc changes with temperature. Variation of Hc with
temperature for Pb is shown in figure. The curve can be expressed
by the relation
Where Hc(0) is critical field at 0 K.
 Thus at critical temperature Tc,
critical field Hc becomes zero.
2
2
(0) 1c c
c
T
H H
T
 
  
 
P.A. Nagpure

7. Type I and Type II Superconductors
Type I superconductor:
 The superconductors which strictly follow the Meissner effect are
called Type I superconductors.
 The typical magnetic behaviour of Pb, (HC=44x103Am-1) a type I
superconductor is shown in fig.
The superconductor exhibits perfect diamagnetism
below critical field Hc which for most of the cases is
of the order of 0.1 Tesla.
As the applied magnetic field increased beyond Hc,
the field penetrates material completely and the
material suddenly returns to their normal
conducting state.
Type I superconductors becomes normal conductors at relatively lower field
strengths and hence they are called soft super conductors.
These materials have very limited technical applications because of its low HC
value.
P.A. Nagpure

8. Type II superconductor:
• These superconductors do not follow Meissner effect strictly i.e,.
the magnetic field does not penetrate these materials abruptly at
the critical field.
• The Typical magnetization curve for Pb-Bi alloy shown in figure.
• It follows from the curve that for fields less than HC1 , the material
exhibits perfect diamagnetism and no flux penetration takes
place.
• Thus for H< HC1 , material exists in
superconducting state. As the field
exceeds HC1 , the flux begins to
penetrate the specimen and for H >HC2 ,
the complete penetration occurs and
the material becomes normal conductor.
• HC1 and HC2 are called the lower and
upper critical fields respectively.P.A. Nagpure

9. • The region between HC1 and HC2 is called intermediate or
mixed or vortex state, which is complicated distribution of
superconducting and normal conducting state.
• Type II superconductors becomes normal conductors at
relatively large field strengths and hence they are called hard
super conductors.
For Pb-Bi alloy, values of HC1 and HC2 are about 20 x103Am-1 and
100 x103Am-1 respectively.
P.A. Nagpure

10. BCS Theory
• In 1957, Bardeen-Cooper-Scherieffer gave the satisfactory
explanation of phenomenon of superconductivity (type I
supeconductors).
• The isotope effect in superconductors suggests that the
current carrying electrons in superconductor do not move
independently of the ion lattice but they somehow
interacting with lattice.
• The nature of interaction became clear when Cooper
proposed that two electrons in superconductor form a
coupled pair despite their coulomb
repulsion.
• He explained the formation of
coupled pair of electrons as follows.
Scherieffer Bardeen CooperP.A. Nagpure

11. When electron moves through the lattice, lattice slightly deforms
such that the positive ions in the electron path being displaced
towards electron.
The deformation produces a region of increased positive charge and
another electron moving through this polarized region will be
attracted by the greater concentration of positive charge.
If attraction is stronger than the repulsion between the electrons,
they coupled together in pair called as Cooper pair.

12. • The binding energy of Cooper pair, called the energy gap Eg , is of
the order of 10-3 eV, hence superconductivity is low temperature
phenomenon.
• The BCS theory relates the energy gap of superconductor at 0 K
to its critical temperature TC by the formula Eg = 3.53 X kTC .
• The equation fairly agrees with observed values of Eg and TC.
• At temperature above 0K, some Cooper pair breaks up. Resulting
individual electrons interact with the remaining Cooper pairs
and reduce the energy gap. Finally at TC the energy gap
disappears, now there are no more Cooper pairs, and material
becomes normal conductor.
• The electron in Cooper pair have opposite spins, so the pair has
total spin zero. Hence Cooper pair in superconductor is boson
and any number of them can exists in same quantum state at
same time.
• A current in a superconductor involves the entire system of
electron pairs acting as unit.
P.A. Nagpure

13. Magnet applications:
There are a number of industrial applications based on the ability
of superconductors to provide very high field magnets.
• A high profile application of superconducting magnets is to
facilitate high speed levitating trains, where the advantages
include speed, safety and environmental benefits.
• High field magnets using superconductors are also of
importance in research fields such as high energy physics. Mass
spectrometers, Particle detector magnets and beam-steering
magnets used in particle accelerators.
• Magnets for Magnetic Resonance Imaging (MRI) machines,
used for medical diagnostics.
• Application in magnetic separation and filtration.
P.A. Nagpure

14. P.A. Nagpure

15. Electricity transmission and distribution
• One use of a superconducting wire is to produce a
transmission cable where high current density is required.
• The development of transformers, where superconducting
materials would have several advantages over those using
conventional materials.
Other applications
• Superconductors are used to build Josephson junctions,
which are the building blocks of SQUIDs the most sensitive
magnetometers known.
• The large resistance change at the transition from the
normal to the superconducting state is used to build
thermometers in cryogenic micro-calorimeter.
• Josephson junction can be used as a photon detector
P.A. Nagpure