SUPERCONDUCTIVITY

The electrical resistivity of many metals and alloys drops suddenly to zero when their specimens are cooled to a sufficiently low temperature, offer a temperature in the liquid helium range. This phenomenon is called superconductivity. This was first observed by Kamerlingh Onnes in 1911 while measuring the resistivity of mercury at low temperatures.
Transition temperature
The transition temperature (Tc) is the critical temperature at which the resistivity of the material suddenly changes to zero.

Properties of superconductors

Critical field (Hc)
When the superconducting materials are subjected to a strong magnetic field, it will result in the destruction of the superconducting property. i.e, they return to the normal state. The minimum field required to destroy the superconducting property is called the critical field (Hc). The variation of Hc with temperature is as shown.

Critical current density (Jc)
The application of a large value of electric current to a superconducting material destroys its superconducting property. The current required for this is called critical current (Ic) and corresponding current density is called critical current density (Jc).
Specific heat
Specific heat of superconductors undergoes a discontinuous change below transition temperature.

Isotope effect
It has been observed that the superconducting transition temperature for various isotopes of a superconductor is different. This effect is known as isotope effect. This effect was discovered in isotopes of mercury by Maxwell and Reynolds in the year 1950.
Meissner effect
Meissner and Ochsenfeld in 1933 found that if a superconductor is cooled in a magnetic field below the transition temperature, the magnetic flux lines are pushed out of the body of the superconductor as shown:

This phenomenon is called Meissner effect which establishes that a superconductor is a perfect diamagnet.Therefore inside the specimen B=0

But B=H+4PM

Therefore H+4PM=0

H=-4PM

Susceptibility=M/H=-1/4P
TypeI and typeII Superconductors
In type I superconductors, magnetization curve is as shownThey are completely diamagnetic or exhibits complete Meissener effect up to critical field Hc. They are also called soft superconductors. Eg: Al, In, Sn, Pb etc.

In type II superconductors, magnetization is as shown

For applied fields below Hc1 the specimen is diamagnetic, exhibiting complete Meissner effect. Hc1, the flux begins to penetrate the specimen and the penetration increases until Hc2 is related. Here Meissner effect is incomplete and the specimen is said to be in a vertex (mixed) state. At Hc2, the specimen becomes a normal conductor. Hc2 is called upper critical field. They are also called hard superconductors. Eg: Nb3Sn, Nb3Ge, Nb3H etc.
BCS Theory of Superconductivity
This theory was developed by Bardeen, Cooper and Schrieffer in 1957 based on electron- lattice- electron interaction. According to this theory, an electron attracts lattice ions towards itself, so that it is surrounded by a region of positive charges. Another gets attracted to this region at high positive ion concentration. Thus an electron- lattice- electron interaction results in an electron pair formation. These pairs are called cooper pairs. They can be scattered only if the energy involved is sufficient to break it up into two single electrons.
Copper pair electrons are of opposite momenta and spin (K­ and –K¯). In addition, a cooper pair does not obey Pauli’s exclusion principle and hence any number of cooper pairs can be accommodated into a single quantum state.
Since an electron pair has a lower energy than the two normal electrons, there is an energy gap between the paired and the two single electrons.
As long as Cooper pair electrons remain in Cooper pair states, they do not suffer scattering and hence resistivity will be zero. When the temperature is raised, to overcome the energy gap, Cooper pair electrons gets separated to normal single electrons which may undergo scattering due to the presence of imperfections in the crystal or lattice vibrations which leads to a finite resistivity.

Josephson effect
This effect was first predicted by Josephson in 1962. The experimental arrangement was a Josephson junction which consists of a thin insulator sandwiched between two superconductors as shown:
If the insulator layer is very thin, of the order of 10-50 Å in thickness, a tunneling phenomenon called Josephson tunneling (Josephson effect) takesplace through the insulator. Thus the insulator turns into a superconductor.
I-V characteristics of a Josephson junction is as shown:
With no applied voltage, a dc current (ic) will flow across the junction. This is called dc Josephson effect. When a small voltage is applied across the junction, current oscillates with a frequency w = 4peV/h. This is called ac Josephson effect. If the applied voltage is increased beyond the critical voltage (vc), the current attains an ohmic behaviour.
Applications of superconductors
For the production of high magnetic fields.
In high energy physics experiments.
In NMR imaging.
In magnetohydrodynamic power generation.
In magnetic separation for refining ores and chemicals.
As memory storage element in computers.
In superconducting generators and motors.
In superconducting fuses, switches and cables.
In Superconducting Quantum Interference Device (SQUID).
In levitating trains.