"Superconductivity" is a topic related to Physics, Chemistry and Engineering and Technology, anybody who would like to know about superconductor can read this article. This article explains about the fundamental's of superconductors, its various effects like Meissner effect, its theory and applications in MRI, Magneto encephalography, flying vehicle or levitating vehicles etc.

1. Engineering physics: Author: Praveen. N. Vaidya, S.D.M.College of Engg. and Tech. Dharwad.
1
SUPERCONDUCTIVITY
While conducting the experiments of electrical properties of metals in extremely low
temperatures In 1911, Dutch physicist, Heike Kammerlingh Onnes much to his surprise found
that at 4.2 K the resistance of the Mercury suddenly vanished. According to Onnes, "Mercury
has passed into a new state, which on account of its extraordinary electrical pr operties may be
called the superconductive state".
Material Critical temp.(K) Material Critical temp.(K)
====================== ======================
Aluminum 1.20 Thorium 1.37
Cadmium 0.56 Tin 3.72
Lead 7.2 Titanium 0.39
Mercury 4.16 Uranium 1.0
Niobium 8.70 Nb3Ge 23.2
Temperature dependence of resistivity of the superconductor (Matthiesen’s rule): At
temperature above zero k, the electrons gain sufficient energy and no more bound to atom. The
free electrons move randomly through the conductor leaving behind the positively charged
atoms or positive ions.
The ions oscillating about their mean positions due to thermal agitation, are called lattice
vibrations. The quantized lattice vibrations are called as PHONONS. When free electrons
interact with Phonons, they scatter from their paths and accelerate in random direction. This sort
of opposition to flow of electrons gives rise to the Resistance. Therefore in the absence of
electric field, current through the conductor is zero.
Under the influence of electric field the electrons overcome the opposition offered by the lattice
and move in the direction of field with a small velocity is called drift velocity and set up current
in conductor.
The property by virtue of which, the electric
resistance of some material disappear, at certain
temperature well below zero degree centigrade and sets
up long lasting current through the material is called
Superconductivity. The material that show zero
resistance is called as super conductor.
Critical Temperature: The temperature at which the
resistance of the material drops to zero is called as
critical temperature.
The Critical temperature is not same all the elements but it
is different for different materials. The critical temperatures
for few materials are given below.

2. Engineering physics: Author: Praveen. N. Vaidya, S.D.M.College of Engg. and Tech. Dharwad.
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If current I set up in the conductor due to the application of potential difference V, then
resistance of conductor is given by R = V/I.
ρ0
The resistivity of the conductor at constant temperature is the resistance offered by the conductor
of unit length and unit cross section area, therefore
l
RA


When temperature of go on decrease, intensity of lattice vibrations go on decrease as a
result resistivity of conductor also reduce. When temperature approaches to zero K, the
resistivity of typical conductor reaches to minimum value ρ0, but will not go to zero (as shown
in fig. 1). The ρ0 is called residual resistivity. This is due to defects in the conductor and also
due to the presence impurities. Therefore resitivity (ρ) of material at a temperature T is given by
according to mathiessen’s rule
ρ = ρ0 + ρ(T)
Where, ρ(T) is temperature dependent resitivity. This is called as Matthiessen's rule.
But in case many conductors and alloys the resitivity drops to zero abruptly to below
Critical Temperature (Tc) are superconductors (as in fig. 2)
BCS theory of Super conductivity:
The American Physicists, John Bardeen, Leon N. Cooper and John Robert Schrieffer in 1957,
for the first time successfully developed the theory of superconductivity, by giving quantum
mechanical treatment.
According to BCS theory the superconductivity is due to the collective or correlated motion
state of motion of assembly of electrons. The theory is based on the formation of Cooper pairs.
Formation of Cooper Pair:
The BCS theory argues that the current in superconductor is not due to independent motion of
electrons but it is due to the motions of ordered pair of electrons.
At normal temperatures when free electrons in metal approach the distorted or vibrating lattice
ion, as free electrons have sufficient energy, they scatters away; this phenomenon is called
electron phonon interaction. This results the resistivity in the metals.
If the temperature drops below Critical temperature, when an electron approaches an ion, ion
experience an attractive force due to opposite charge, as a result the lattice is distorted from its
Resistivity
Ab. Temperature
Variation of ρ w.r.t T in a typical conductor
Resistivity
Tc Ab. Temperature
Variation of ρ w.r.t T in a Super conductor

3. Engineering physics: Author: Praveen. N. Vaidya, S.D.M.College of Engg. and Tech. Dharwad.
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position. In the mean time another electron also approaches the same atom and interacts with it.
As a result, energy of electrons reduces, and this reduction of energy of electron is considered as
interaction of electrons via lattice vibrations or phonons. The reduction of energy of electrons,
produce a weak attractive force between them, is shown by Leon N. Cooper.
If the two interactive electrons have equal and opposite spins, then attractive force goes to
maximum.
Therefore, bound pair of electrons formed by the interaction of between the electrons with
opposite spin and momenta in phonon field is called cooper pair.
At lower temperature the pairing is energetically advantageous, because the property of wave
function associated with a pair can be extended over a large volume with finite amplitude all
over the region. In a typical super conductor, the volume of given pair encompasses as many as
106
other pairs. This dense cloud of cooper pairs from a collective state results same drift
throughout conductor with identical velocity. Since the density of Cooper pairs is quite high,
even for large currents only a small velocity is sufficient.
The small velocity of cooper pairs combined with their precise ordering minimizes collision
process. The extremely rare collisions of cooper pairs with the lattice lead to vanishing
resistivity and current flows in superconductor without application of potential difference and
never diminish for an infinite time
Findings of BCS theory:
 Precise explanation of the phenomenon of superconductivity
 Reason for zero resistance or undiminishing current through the superconductor.
 Existence of Energy gap in superconductor: The energy gap of order 10-3
is existed in
superconductor, and energy gap is directly proportional to critical temperature.
 The magnetic flux enclosed by a superconducting loop is quantized and which not possible
in ordinary solenoid.
 Why the some noble metals like Gold, Silver and Copper are not super conductors: This is
because the electrons metal so energetic that they never form the cooper pairs. Hence
resistivity never goes to zero.
Persistence Current:
Below critical temperature, the current sets up in conductor will flow without resistance.
It is found that the current remain undiminished in a superconducting ring after two years.
Therefore, below critical temperature, flow of a steady current through a superconducting
material with undiminishing strength for long time is called Persistent current.
The calculations are shown that, magnitude of current remain same for more than 105
years,
without external field. As R = 0 in a super conductor, power dissipation (I2
R) is zero, hence it is
wattles current.
As the persistent current produces a magnetic field, a superconductor acts as a magnet. The
superconducting magnets are producing strong magnetic field without any external energy or
dissipation of power.
Meissner Effect:

4. Engineering physics: Author: Praveen. N. Vaidya, S.D.M.College of Engg. and Tech. Dharwad.
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a. S.C. sample above Tc, b. S.C. sample below Tc magnet hovering (black)on on superconductor (white),
flux is penetrating Flux expelled as super conductor expels flux of magnet.
A super conducting sphere is kept in a magnetic field. Above Tc, the magnetic flux penetrates
through the material (fig. a). When the temperature of sphere is dropped below Tc, suddenly the
magnetic flux lines are expelled from the sphere (fig. b), this shows the super conductor opposes
the magnetic flux, which is a property of diamagnetic material.
When the superconductor is kept in the magnetic field, the magnetic lines of force suddenly
expel from the superconductor and hence super conductor acts as perfectly diamagnetic
material, this property of the superconductor is known as Meissner Effect.
The maglev vehicles are working on the principle of meissner effect (in fig. if a magnet kept on a
super conductor is treated of coach of vehicle at above Tc, coach will remain on the surface of
conductor. Below Tc, suddenly the magnet will start levitating in the air above superconductor,
on giving acceleration it will move in the air). Let a super conductor is kept in a magnetic field
(H), A magnetic flux density ‘B’ through the conductor above Tc is given by,
 
M
H
B o 
  , Where M – is intensity of magnetization
When temperature is dropped below Tc,
 
M
H
o 
 
0 B = 0, because mag. Flux through conductor = 0
H = - M
But Susceptibility of material χ = M /H = M/-M = -1
Negative value of susceptibility signifies the superconductor shows the property of
diamagnetism
Effect of Magnetic field on superconductor:
A sufficiently strong magnetic field is applied can vanish the superconducting property of the
material. When a applied magnetic field exceeds the certain critical value Hc, the
superconducting state is destroyed and material goes into normal state.

5. Engineering physics: Author: Praveen. N. Vaidya, S.D.M.College of Engg. and Tech. Dharwad.
5
As soon as magnetic field attains the critical field (HC), the
diamagnetic behavior vanishes (it is shown that at Hc, – M
drops to zero) and superconductor converts into normal state.
 The types of super conductors are usually of low critical
temperature materials, such as metals and metal alloys.
 Examples are Aluminum, Lead, Indium, Nb3Ge etc. are
Type I superconductor.
 These superconductors have only one critical field (HC) at
which it converts into normal state
The minimum magnetic field which is necessary to destroy the superconductivity (regain
it’s resistivity), below Tc is called as Critical field (Hc).
HC2
In fig. Hc(0) is critical field (magnetic field that destroy superconductivity) when temperature is
0k, HC1 and HC2 are the critical fields at temperature TC1 and TC2 , below TC
(the temperature at which a super conductor converts into normal state without application of
magnetic field)
The relation between the critical temperature and critical field can be written as
  









C
C
C
T
T
H
H 1
0
Type of superconductors:
There are two types of superconductors, Type I and Type II superconductors depending upon the
its behaviour in the applied magnetic field.
Type I superconductors:
The super conductors those converts into normal state abruptly at the critical field below
critical temperature are called Type I super conductors.
In fig. the negative magnetization i.e. diamagnetic behaviour go on increases in a typical type I
superconductor with in crease in magnetic field, below critical temperature.
 Type I super conductors are poor carriers of current. The magnetic field can penetrate only
the surface layer and current can only flow in this layer.
 The critical field for such superconductor is very low; it is of the order of .01 to 0.2Wb/m2
.
 This type of superconductors also called soft superconductors as superconductivity destroys
by the application small field
The value of Hc varies with the temperature. The graph
(fig.) shows the dependence of Hc on temperature of the
typical superconductor. At any temperature T < Tc, the
material remain superconducting until a corresponding
critical field applied. If it exceeds certain value
superconductivity will destroy.
Magnetic field(H) HC
Magnetisation(
-
M
)
Temperature TC1 TC2
Tc
Magnetic
field
H
c1
H
C
(0)
0

6. Engineering physics: Author: Praveen. N. Vaidya, S.D.M.College of Engg. and Tech. Dharwad.
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-
Magnetization
Type II Super conductors: a super conductor whose diamagnetic property go on increases
with applied magnetic field up to (HC1) and slowly go on decreases after and drops to zero
at magnetic filed HC2 and super converts completely into normal state, such
superconductors are called as type II Super conductors. .
HC1 HC2
But this property goes on decreases till the magnetic field attains the value HC2. At HC2 super
conductivity vanishes completely. Hence the type II superconductors have two critical fields
Type two super conductors are characterized by,
Usually ceramic superconductors are type II superconductors.
High critical temperature
High critical current, good carrier of electricity
Two critical fields, below HC1, acts as complete superconductor, between HC1 and HC2acts as
partial superconductor.
HC2 is very high it is about 10 to 20 Wb/m2
These superconductors also called as hard superconductors.
APPLICATIONS OF SUPERCONDUCTORS
Superconducting QUantum Interference Device (SQUID)
Superconducting Quantum Interference Devices (SQUID) are very sensitive magnetometers
used to measure extremely small magnetic fields, based on superconducting loops
containing Josephson junctions.
The superconducting quantum interference device (SQUID) consists of two superconductors
separated by thin insulating layers to form two parallel Josephson junctions. The device may be
configured as a magnetometer to detect incredibly small magnetic fields -- small enough to
measure the magnetic fields in living organisms.
Threshold for SQUID: 10-14
T
Magnetic field of heart: 10-10
T
Magnetic field of brain: 10-13
T
The great sensitivity of the SQUID devices is associated with measuring changes in magnetic
field associated with one flux quantum (0.5 Gauss = 0.5 x 10-4
Tesla – Horizontal field of earths’
magnetic field).
H
Fig. shows the behavior a type II super conductor
w.r.t applied magnetic field. In the beginning
negative magnetization (diamagnetism) go on
increases with applied magnetic field upto HC1,
and material acts as perfect superconductor.
Above HC1 the decrease in the value of
magnetization shows the magnetic flux start
penetrating the superconductor, but material will
retain its superconducting property.

7. Engineering physics: Author: Praveen. N. Vaidya, S.D.M.College of Engg. and Tech. Dharwad.
7
There are two main types of SQUID: DC and RF. RF SQUIDs can work with only one
Josephson junction, which might make them cheaper to produce,
but are less sensitive.
If a constant biasing current is maintained in the SQUID device,
the measured voltage oscillates with the changes in phase at the
two junctions, which depends upon the change in the magnetic
flux. Counting the oscillations allows you to evaluate the flux
change which has occurred.
The traditional superconducting materials for SQUIDs are pure
niobium or a lead alloy with 10% gold or indium, as pure lead is unstable when its temperature
is repeatedly changed. To maintain superconductivity, the entire device needs to operate within a
few degrees of absolute zero, cooled with liquid helium.
"High temperature" SQUID sensors are more recent; they are made of high temperature
superconductors, particularly YBCO, and are cooled by liquid nitrogen which is cheaper and
more easily handled than liquid helium. They are less sensitive than conventional "low
temperature" SQUIDs but good enough for many applications
APPLICATION of SQUIDS
The use of high sensitivity magnetic field detection is of interest in many fields. Two of these
are listed below:
 Biomedicine. In diagnosing heart and/or blood circuit problems the use of magneto
cardiograms is an important supplement to conventional electro cardiograms. Such
diagnostic equipment is now feasible with the application of the new SQUID sensors.

 Non-destructive testing. In monitoring internal faults or wear especially in metal
containing structures, magnetic field detection is an advantageous alternative to ultra
sound or X-ray methods.

 Surveillance. Any man-made body will have an influence on the magnetic field of the
surroundings. Hence, SQUIDs may be applied in military or other surveillance tasks.
MAGLEV VEHICLES:
In Maglev—which is short for MAGnetic Levitation—high speed vehicles are lifted by
magnetic repulsion, and propelled along an elevated guide way by powerful magnets attached to
the vehicle. The vehicles do not physically contact the guide way, do not need engines, and do
not burn fuel. Instead, they are magnetically propelled by electric power fed to coils located on
the guide way.
Maglev moves passengers and freight at much lower cost, and in much greater volume. The
reduction of friction in a maglev system provides a comfortable, smooth ride, eliminates
noise, and can lower maintenance costs. Most important of all, the lack of friction allows
maglev vehicles to travel at speeds over 300 miles per hour.
Maglev systems have many safety and health impacts. The vehicles cannot derail due to the
track design. The vehicle is "locked" onto the guide way. They also do not carry on-board

8. Engineering physics: Author: Praveen. N. Vaidya, S.D.M.College of Engg. and Tech. Dharwad.
8
fuel, therefore, it should be safer in the event of a crash. Because the vehicle does not touch the
guide way, accidents related to weather and wear will be minimized. A health concern is that
people must be shielded from the magnetic field radiation.
The first practical Maglev system was proposed and published by us in 1966. It was based on
Maglev vehicles carrying lightweight superconducting magnets that induced currents in a
sequence of ordinary aluminum loops mounted along a guide way. These induced currents
interacted with the superconducting magnets on the vehicle, levitating it above the guide way.
The levitated vehicle is inherently and passively stable against all external forces, including
cross-winds, and the centrifugal forces on curves, whether horizontal or vertical. If a cross-wind
tries to push the vehicle sideways, an opposing magnetic force is automatically generated that
holds the vehicle on the guide way. If the vehicle is pushed down towards the guide way, the
levitation force automatically increases, preventing contact. If an external force lifts the vehicle
away from the guide way, the levitation force decreases, and the vehicle drops back towards its
equilibrium suspension height.
The levitation process is automatic, as long as the vehicle moves at a speed above its lift-off
speed. Below this speed, which is in the range of 20 to 50 mph depending on design, the finite
electrical resistance of the aluminum loops on the guide way decreases the induced currents to
the point where the magnetic force is too weak to levitate the vehicle. The vehicle is supported at
low speeds by auxiliary wheels, or by locally powering the guide way. These lower-speed
sections of guide way are very short and are needed only when a vehicle accelerates out of a
station or decelerates into it.
Apart from this the super conductors have numerous industrial and scientific applications, but
only hurdle is that, it are not available at room temperature.
Questions:
1. Define Superconductivity. Using Matthiesen’s rule. Describe how a superconductor
is different from the normal metallic conductor.
2. Give an account of formation of cooper pairs below critical temperature. What is
persistent current?
3. With neat labeled diagram explain the Meissner’s effect of superconductor. Write any
five differences between Type I and Type II Superconductors.
4. What you mean by Squid? How a Squid is constructed? Write any three applications of
Squids.
5. On which principle the Maglev vehicles work? Write a note on maglev vehicles.
6. Give an account of High temperature Superconductivity.