BCS theory of Superconductivity and types of Superconductors - Civil Engineering (CE) PDF Download

BCS theory of Superconductivity
Bardeen,Cooper and Schrieffer explained the phenomenon of superconductivity in the year 1957. The essence of the BCS theory is as follows.We know that resistance of the conductor is due to the scattering of electrons from the lattice ions. Consider an electron moving very close to a lattice ion. Due to coulomb interaction between electron and ion, the ion core gets distorted from its mean position. It is called lattice-distortion. Now another electron moving close to this lattice ion interacts with it. This results in the reduction in the energy of the electron. This interaction can be looked upon as equivalent to the interaction between two electrons via lattice. During the interaction exchange of phonon takes place between electron and the lattice. This interaction is called electron-lattice-electron interaction via the phonon field. Because of the reduction in energy between the two electrons, an attractive force comes into effect between two electrons. It was shown by Cooper that, this attractive force becomes maximum if two electrons have opposite spins and momentum. The attractive force may exceed coulombs repulsive force between the two electrons below the critical temperature, which results in the formation of bound pair of electrons called cooper pairs.

At temperatures below the critical temperature large number of electron lattice electron interaction takes place and all electrons form a cloud of cooper pairs. Cooper pairs in turn move in a cohesive manner through the crystal, which results in an ordered state of the conduction electrons without any scattering on the lattice ions. This results in a state of zero resistance in the material.

 Figure 6.5: Dependence of magnetic moment on H for type I super conductors

Types of Superconductors
Type I or Soft Superconductors:
Superconducting materials, which exhibit, complete Meissner effect are called Soft superconductors. We know that below critical temperature, superconductors exhibit perfect diamagnetism. Therefore they possess negative magnetic moment.

Ex: Sn, Hg, Nb.

The graph of magnetic moment Vs magnetic field is as shown in the Fig 4.5. As field strength increases material becomes more and more diamagnetic until H becomes equal to H_c. At H_c , material losses both diamagnetic and superconducting properties to become normal conductor. It allows magnetic flux to penetrate through its body. The value of H_c is very small for soft superconductors. Therefore soft superconductors cannot withstand high magnetic fields. Therefore they cannot be used for making superconducting magnets. They are used fro making superconductiong switches.

Type II or Hard Superconductors 
Superconducting materials, which can withstand high value of critical magnetic fields, are called Hard Superconductors.
Ex: Nb₃, Sn, Nb₃Ge, YBa₂Cu₃O₇

The graph of magnetic moment Vs magnetic field is as shown in the Fig.
Hard superconductors are characterized by two critical fields H_c1 and H_c2 .When applied magnetic field is less than H_c1 material exhibits perfect diamagnetism. Beyond H_c1 flux penetrates and fills the body partially. As the strength of the field increases further, more and more flux fills the body and thereby decreasing the diamagnetic property of the material. At H_c2 flux fills the body completely and material losses its diamagnetic property as well as superconducting property completely.

BetweenH_c1 and H_c2 material is said to be in vortex state. In this state though there is flux penetration, material exhibits superconducting property. Thus flux penetration occurs

through small-channelised regions called filaments. In filament region material is in normal state. As H_c2 the field strength increases width of the filament region increases at they spread in to the entire body, and material becomes normal conductor as a whole. The value of H_c2 is hundreds of times greater than H_c of soft superconductors. Therefore they are used for making powerful superconducting magnets.

High Temperature Superconductivity 
Superconducting materials, which exhibit superconducting property at higher temperatures, are called high temperature superconductors. Thus high temperature superconductors possess higher value of critical temperature compared to conventional superconductors. Most of the high temperature superconductors are found to be non-metals and intermetallics compounds, but are oxides, that fall into the category of ceramics. In 1986 a compound containing barium, lanthanum, copper, and oxygen having T_c = 30K was developed. In 1987, scientists developed a compound which is an oxide of the form Y Ba₂Cu₃O₇ often referred to as 1 − 2 − 3 compound having T_c = 77K.

All high temperature superconductors are oxides of copper, and bear a particular type of crystal structure called Perovskite crystal structure. Such crystal structures are characterized by large number of copper-oxygen layers. It was found that addition of extra copper-oxygen layer pushes the critical temperature T_c to higher values.

It was also found that formation of super currents in high superconductors is direction dependent. The super currents are strong in the copper-oxygen layer and weak in the direction perpendicular to the planes.