Superconductivity PDF

Superconductivity Electrical conductivity of metals and alloys increases with decrease in temperature and of semiconductors increases with increase in temperature. So the electrical resistance of a conductor becomes zero only at absolute zero temperature. But H. Kammerlingh Onnes (1911) studied the...

Superconductivity Electrical conductivity of metals and alloys increases with decrease in temperature and of semiconductors increases with increase in temperature. So the electrical resistance of a conductor becomes zero only at absolute zero temperature. But H. Kammerlingh Onnes (1911) studied the properties of mercury at very low temperature using liquid helium and is found that the resistivity of mercury drops to zero at 4.2 K and changes into a superconducting material. The ability of certain metals, their compounds and alloys to conduct electricity with zero resistance at very low temperatures is called superconductivity. The materials which exhibit this property are called superconductors. The temperature at which electrical resistivity of the material suddenly drops to zero and the material changes from normal conductor to a superconductor is called the transition temperature or critical temperature (Tc). At the transition temperature the electrical resistivity drops to zero and hence conductivity becomes infinity. Superconductivity  Superconductivity Critical magnetic field (Magnetic Property) A very strong magnetic field applied to superconducting material it disappears super conducting property this is called as critical magnetic field.  Superconductivity Critical magnetic field when the temperature of a material increases, the value of critical magnetic field decreases. Therefore the value of critical magnetic fields are different for different materials. Meissener effect If a normal conducting material is placed in a magnetic field of flux density B, the magnetic lines penetrate through the material. Now the material is cooled below its transition temperature when T TC then the magnetic lines of forces are ejected out from the material. We know that, a diamagnetic material have the tendency to expel the magnetic lines of force. Since the superconductor also expels the magnetic lines of force and it behaves as a perfect diamagnet. This is known as Meissener effect. Superconductivity  Superconductivity TYPES OF SUPER CONDUCTORS Type I (or) Soft superconductors: In type I superconductor, the magnetic field is completely excluded from the material below the critical magnetic field and the material loses its superconducting property abruptly at Hc. These superconductors exhibit complete Meissner Effect. They have only one critical magnetic field value and below the material behaves as superconductor and above the material behaves as normal conductor.  Superconductivity Type II (or) Hard superconductors: In type II superconductor, the magnetic field is excluded from the material and the material loses its superconducting property gradually rather than abruptly. These superconductors do not exhibit a complete Meissner Effect. They have two critical magnetic field values. Lower critical magnetic filed [Hcl] and Higher critical magnetic field [HC2]. Below Hc1 the material behaves as superconductor and above the material behaves as normal conductor. The region in between [Hcl] and [Hc2] is called mixed state or vortex region.  Superconductivity BCS THEORY OF SUPERCONDUCTIVITY The properties of Type I superconductors were successfully explained by John Bardeen, Leon Cooper, and Robert Schrieffer which is called the BCS theory. According to BCS theory the pairing of electron close to the Fermi level into Cooper pairs through interaction with the crystal lattice. This pairing results form a slight attraction between the electrons related to lattice vibrations, the coupling to the lattice is called a phonon interaction. Pairs of electrons can behave very differently from single electrons which are fermions and must obey the Pauli Exclusion Principle. The pairs of electrons act more like bosons which can condense into the same energy level.  Superconductivity The electron pairs have a slightly lower energy and leave an energy gap above them on the order of 0.001 eV which inhibits the kind of collision interactions which lead to ordinary resistivity. For temperatures such that the thermal energy is less than the band gap, the material exhibits zero resistivity. Froehlich suggested that the electrons act as pairs coupled by lattice vibrations in the material. This coupling is viewed as an exchange of phonons, phonons being the quanta of lattice vibration energy. Experimental corroboration of an interaction with the lattice was provided by the isotopic effect on the superconducting transition temperature.  Superconductivity The BCS theory of superconductivity has successfully described the measured properties of Type I superconductors. It shows resistance-free conduction of coupled pairs of electrons called Cooper pairs. This theory of superconductivity was the realization that there must be a band gap separating the charge carriers from the state of normal conduction. A band gap was implied by the very fact that the resistance is precisely zero. If charge carriers can move through a crystal lattice without interacting at all, it must be because their energies are quantized such that they do not have any available energy levels within reach of the energies of interaction with the lattice.  Superconductivity A band gap is suggested by specific heats of materials like vanadium. The fact that there is an exponentially increasing specific hear as the temperature approaches the critical temperature from below implies that thermal energy is being used to bridge some kind of gap in energy. As the temperature increases, there is an exponential increase in the number of particles which would have enough energy to cross the gap. The critical temperature for superconductivity must be a measure of the band gap, since the material could lose superconductivity if thermal energy could get charge carriers across the gap.  Superconductivity The critical temperature was found to depend up on isotopic mass. It certainly would not if the conduction was by free electrons alone. The made it evident that the superconducting transition involved some kind of interaction with the crystal lattice.