SUPERCONDUCTIVTY

The phenomenon by virtue of which certain materials exhibit zero resistivity or infinite
conductivity when cooled below a certain temperature is called ‘superconductivity’. The
materials which show the property of superconductivity are known as superconductor.

The best known conductors of electricity like silver and copper cannot be come superconductors.
Whereas compounds and alloys of some metals, non-metals and ceramics etc., become
superconductors when cooled below the critical temperature.

Example:

Elemental superconductor: Hg = 4.15K, Pb = 7.19K

Compound Superconductor : AlNb3 = 19K, GeNb3 = 23K

Ceramic Superconductor” HgBa2Ca2Cu2O8 = 133K, Ti2Ba2Ca2Cu2O11 = 125K

General properties of superconductors:

1) It is a low temperature phenomenon. Below the critical temperature transition from

normal state to super conducting state takes place. The transition temperature is different
for different materials.
2) Resistance of a superconductor is zero.
3) Superconductivity occurring in metals having valance electrons from 2 to 8. Mono
valence metals are not superconductors. E.g. Cu, Ag.
4) Superconducting elements generally lie in the inner columns of the periodic table.
5) Transition metals having odd number of valance electrons i.e. 3, 5, 7 are favorable to
exhibit superconductivity more than the metals having even number of valance electrons
2, 4, 6.
6) Ferromagnetic (Fe, Co, Ni) and anti ferromagnetic (Co O, Ni O) materials are not
superconductors.
7) Super conductors do not allow magnetic field through them. They are perfectly
diamagnetic in nature.
8) Superconductivity vanishes if the current in the superconductor increases beyond the
critical current IC.
9) Superconductivity disappears if the applied magnetic field exceeds the critical field HC.
10) Thermal conductivity of superconductors is very low which indicates that
superconducting electrons has no role in heat transfer.
11) Specific heat of superconductors increase discontinuously.
12) Prominent examples of superconductors include aluminium, niobium, magnesium
diboride, cuprates such as yttrium barium copper oxide and iron pnictides. These
 materials only become superconducting at temperatures below a certain value, known as
the critical temperature.
13) Some elements like Bismuth, Antimony etc., become superconducting under high
pressure.

Critical temperature (Tc)

The temperature below which a substance behaves

like a superconductor is known as ‘critical
temperature’ or ‘transition temperature’ (TC), it is
different for different materials.

If we draw a graph by taking temperature along X-

axis and corresponding resistivity along Y-axis the
nature of the graph will be like as in the figure.

From the figure it is clear that the resistivity drop

suddenly at Tc to zero. If we cool below Tc then the
material exist in superconducting state and above Tc the material exist in normal state.

Effect of magnetic field on superconductivity:

Superconductivity disappears by the application of strong magnetic field. The minimum

magnetic field required to destroy superconductivity is called critical field (HC). The value of
critical field depends on the temperature of the material.

At T = Tc, Hc = 0. At temperature below Tc, Hc increases. The dependence of critical field upon
the temperature is given by

T2
H C (T )  H C (0)(1  2
)
TC

Where HC(0) is the critical field at 00K

Hc(T) Critical field at T0C, Tc is the critical temperature

If we draw a graph by taking T along X-axis and H

along the Y-axis the nature of the graph will be like in figure.
Right to TC and above HC(0), the material exists in normal state
and below TC and HC(0), material in superconducting state.

From the figure it is clear that, If H <HC(0), the material is in

superconducting state. And if H> HC(0), the material is in
normal state.
Critical current density

The maximum current density at which the superconductivity disappears is called the critical
current density Jc. If the value of J is less than Jc then the current can sustain itself where as if j >
Jc the current cannot sustain itself.

A superconducting ring of radius r ceases to be a

superconductor when the current is

Effect of current IC = 2πr HC

As the temperature of the superconductor increases the current

carrying capacity decreases and falls to zero at transition
temperature. The variation of critical current Jc, critical
magnetic field Hc with temperature is shown in the figure.

Missner Effect:

If a superconducting material is placed in a magnetic field at H < H C and T < TC then the
magnetic flux inside the material is excluded from the material. This effect is known as ‘Missner
effect’.

From Missner effect it is clear that magnetic field inside a superconductor is zero i.e. a

superconductor is a perfect diamagnetic substance. Because the magnetic induction B inside a
material medium is given by
        
B  B0  0 M  0 H  0 M  0 ( H  M ) since ( B0  0 H )
   
Where B0 is the magnetic induction in free space. H is the applied magnetic field, M is the
intensity of magnetization.

Since B  0 inside a superconductor,
 
(H  M )  0
 
 H  M

M
But, M  r  1    1,  r  0 Hence, a superconductor is perfect diamagnetic.
H
Type – I superconductors:

Superconductors which can exhibit complete Missenr

effect or perfect diamagnetism are called type-I superconductors.
In such case when type –I superconductor is placed in a varying
magnetic field H < HC and on increasing magnetic field the
specimen suddenly changes to normal state at H = HC. i.e. above
the critical field (H>HC) the specimen is in normal state and
below the critical field (H<HC) the specimen in superconducting
sate. Type-I superconductors are also known as soft
superconductors.

E.g. Zn, Hg, Sn, Ga etc.

Type – II superconductors:

For these superconductors there are two critical fields HC1 & HC2 when H < HC1 the
specimen is in superconducting state. When
HC1 < H < HC2 the specimen is in a mixed state
i.e. it has both superconducting and normal
conducting properties. When H > HC2 the
specimen lost superconducting properties
completely and it is in normal state.

Superconductors which exhibit above

phenomenon are called type – II
superconductors. Here HC1 < H < HC2. These
are also called as hard superconductors. These
are most useful in commercial purpose.
Comparison between Type-I and Type II Superconductor

Type-I superconductor Type-II superconductor

1. They exhibit complete meissner effect. 1. They do not exhibit complete meissner effect.
2. They show perfectly diamagnetic behavior. 2. They do not show perfectly diamagnetic
3. They have only one critical magnetic field behavior.
Hc. 3. They have two critical magnetic field, lower
4. There is no mixed state or intermediate critical magnetic field HC1 and upper critical
state in case of these materials. magnetic field HC2.
5. The material loses magnetization abruptly 4. Mixed state or intermediate state is present.
6. Hiest value of Hc is about 0.1 Wb/m2. 5. The material loses magnetization gradually.
7. They are known as soft superconductors, 6. Upper critical field is of the order of
Example- Lead, tin, Mrcury etc 30Wb/m2.
7. They are known as hard super conductors
Example- Nb-Sn, Nb-Ti, Nb-Zr etc

B C S Theory:

This theory is developed by Bardeen, Cooper and Schrieffer. They explained the
superconductivity and its properties successfully which involves electron – electron interaction
via lattice deformation.

According to BCS theory superconductivity is due to the domination of attractive

interaction between two electrons by means of phonon exchange over usual repulsive interaction.

Electron – electron interaction:

Let us consider an electron approaching the lattice of positive

ions. Positive ions attract towards the electron and form a positive ion
core. Due to the attraction between the charge and the positive ion
core the lattice is deformed.

The electron is screened by the positive ion core by which the charge
of the electron reduces. Suppose another electron approaches the
assembly of the electron and the ion core, it is attracted towards the
assembly and interacts with the first electron via lattice deformation.
This interaction is due to exchange of virtual phonon ‘q’ between two electrons. In terms of
wave vector the interaction may be expressed as

k1  q  k1 And k2  q  k2

k k k k 
1 2 1 2
i.e. the net wave vector is conserved.
The pair of electrons called ‘Cooper pair’ and the electrons are known
as ‘Cooper electrons’.

According to Fermi Dirac distribution

F E  
1
1  exp ( E  E F ) / KT 

At T = 0oK and E < EF all the energy states below the Fermi level are filled and all the energy
states above the Fermi level are empty. So due to the addition of cooper electron they are forced
to occupy the energy states above the Fermi level. Due to attraction between the electrons they
form a bounded state whose total energy is less than the energy of the pair in the Free State i.e.
less than 2EF. The difference in the two energy states is the binding energy of the cooper pair. To
break cooper pair in to two separate electrons the energy equivalent to binding energy of the
cooper pair should be supplied. The binding energy is generally of order 10-3eV.The binding
energy of cooper pair is strongest when the electrons forming the pair have opposite moment and
opposite spins i.e. k  , k  . The cooper electrons are the super electrons which are responsible
for the superconductivity.

Josephson Effect:

The tunneling of cooper pairs between two superconductors separated by a thin insulating
layer is known as ‘Josephson Effect’. The tunneling current is very less since the two
superconductors are weakly coupled to thin insulating layer. Tunneling of cooper pairs take place
even in the absence of applied voltage as well as when a voltage is applied to the super
conductors.
D.C Josephson Effect:

According to this effect a d c

current flows across the junction of
two superconductors separated by a
thin insulating layer in the absence
of any external electric or magnetic
field. The tunneling current is

I  I 0 sin0  ,

I0 is the maximum current flow

through the junction. It depends up
on the thickness of the junction and
temperature. Φ0 is the phase
difference between the two parts of
the junction. The magnitude of the current varies from +I0 to - I0

A.C Josephson Effect:

According to this effect when a d c voltage is applied across the junction of the two
superconductors separated by a thin insulating layer, R.F current oscillations are generated across
the junction.

The expression for R.F current is given by

I  I 0 sin 0  t   I 0 sin 0   

d 2eV h
  
Now from quantum mechanics dt  Where 2
 2eV 2eV
So    
dt 

t C

Where C is the constant of integration. When t = 0 then φ = φ0 so C = φ0

2eV 2eV
Hence φ =    
dt 

t  0

Hence the R.F current is

 2eVt 
 0   I 0 sin0   
2eV 2eV
I    dt  t  C  I 0 sin   I 0 sin
    

 2eVt 
   
Where  

  2eVt    2eVt 
     I 0 sin 0  2
So I = I0sin  0    h 

2eVt 2eV
ωt  2π  ω  2π  2π f
So h h

2eV
The current represents an alternating current with frequency f=
h
Applications of Josephson Effect:

1. It is used to generate microwave of frequency

2eV
f=
h
2. It is used to define standard volt by national Bureau of Standards.
3. It is used to measure very low temperature. For this A C Josephson effect is used.
4. It is used as a switching device with a switching time of 1 Pico second.

High TC Superconductors

Based on transition temperature superconductors are divided into two categories as low TC and
high TC superconductors. The materials having TC below 24K are regarded as low TC
superconductors and those having TC above 27K are regarded as high TC superconductors.

Examples

1. LBCO- Mixed metallic oxide of lanthanum-barium-copper (La1Ba2Cu3O7) exhibited

super conductivity at about 30K.
 2. YBCO-Mixed metallic oxide of Yittrium-barium-copper (Y1Ba2Cu3O7) exhibited super
conductivity at about 95K.
3. BSCCO- Mixed metallic oxide of Bismuth, strontium, calcium and copper
(Bi2CaSr2Cu2O10+x) exhibited super conductivity at about 110K.

The oxygen vacancies are found to play a key role in the superconducting behavior of
ceramic oxide. When the cell contains one atom of rare earth metal, two barium atoms, three
copper atoms have seven oxygen atoms then such compounds are called 1-2-3
superconductors.

Properties of High TC Superconductors

1. High TC Superconductors are brittle in nature.

2. The properties of the normal state of these materials are highly anisotropic.
3. The Hall coefficient is positive indicating that the charge carriers are holes.
4. Their behavior can not be explained by BCS theory.
5. The isotope effect is almost absent in these materials.
6. The magnetic properties of these materials are highly anisotropic.

Applications of superconductors:

1. Transformers and electrical Machines: The transformers and electrical machines with
superconducting coils generate stronger magnetic field hence the size of the motors and
generators will be drastically reduced. In this case the eddy current loss is very less therefore
they are having 99% efficiency.

2. Magnetic levitation: (MagLev Trains)

Since superconductors are diamagnetic substances and magnetic field inside them is zero,
therefore hey can be suspended in air against the repulsive force from a permanent magnet.
This effect is known as ‘magnetic levitation’.
The basic idea of this is to levitate it with magnetic fields so that there is no physical contact
between the trains and the guide ways. Consequently the MagLev train can travel at high
speed.
Principle
Maglev trains work on the principle of magnetic repulsion between the cars and the track.
Operation-

In case of MagLev train, the train has superconducting magnets built into the base of its
carriages. An aluminium guide-way is laid on the ground and carries electric current. The
repulsion between the two powerful magnetic fields, namely the field produced by the super
conductor magnet and the field produced by the electric current in the aluminum guide-way
causes magnetic levitation of the train. A levitation of about 10 to 15cm is achieved so that the
train floats in air.

3. SQUIDS (Super conducting quantum interference devices)- SQUID is a device used to

measure extremely weak magnetic flux.
There are two main types of SQUIDS. DC SQUID AND AC SQUID.
Fabrication.
SQUIDS are fabricated by depositing a thin niobium layer on an alloy having 10% gold or
indium. It act as the basic electrode of the SQUID and the tunnel barrier is oxidized onto this
niobium surface. The top electrode is a layer of lead alloy deposited on top of the other two. The
entire device is cooled to nearly absolute zero with liquid helium.
A two junction DC SQUID consists of two Josephosons arranged in parallel so that electron
tunneling through the junctions demonstrate the quantum interference.
Working
As DC super current is applied to the SQUID which is the bias current, it enters the device
through the arm C. It is divided along two paths a and b and again merge into one and leaves
through the arm D. P and Q are the Josephson junctions and. I1 and I2 are the currents tunneling
through the junction P and Q respectively.
When a magnetic field is applied perpendicular to the loop, the flux passes through the loop
changes the quantum mechanical phase difference across each of the two junctions. Then the
wave functions at the two Josephson
junctions interferer with each other.
Then the total current through two parallel
Josephson junction is
2 e
IT = 2(I0sin  0)cos
hC

The above relation indicates that a

progressive increase or decrease of
magnetic flux, causes the current to oscillate
between a maximum and a minimum value.
The period of the oscillation is one flux
h
quantum  0  = 2.06 x 10-15 Weber
2e
Uses of SQUID.
1. SQUIDS are used to study tiny magnetic signals from the brain and heart.
2. SQUID magneto meters are used to detect the paramagnetic response in the liver. This
gives the information about the amount of iron held in the lever of the body accurately