A Study Into Energy Gap In Super Conductors

ENERGY GAP

In solid state physics and related applied field, an “ENERGY GAP” also known as “BAND GAP” is the energy ranged in a solid where no electron state exist for insulators and semiconductors the band gap or energy gap, generally refers to the energy different between the top of the valance band and the  bottom of the conduction band, but in superconductors, the energy gap is the energy required to break up a pair of electron usually referred to as cooper pairs or simply put, then energy require to disrupt the state. Energy gap depend on temperature because of ‘thermal expansion’. (Emslay, J ; 1991). Energy gap also depend on pressure. Energy gap can further be divided into two groups, depending on the band structure, they are

1. Direct energy gap
2. Indirect energy gap Figure: 3.2 Energy Vs momentum for an indirect energy gap                                               Showing that an electron cannot shift from the lowest potential in the conduction to the highest potential in the valance band without a change in momentum. An indirect band gap means that the minimum energy in the conduction band is shifted by a vector relative to the valence band. The vector difference represents a difference in momentum. Recombination occurs with the mediation of a third body, such as a “phonon” or a crystallographic defect, which allows for conservation of momentum. This recombination will often release the band gap energy as phonons; instead of photons, and thus do not emit light. 3.2    HOW THE ENERGY GAP AROSE The next big experimental discovery were done by two group. Goodman who was working on thermal conductivity and Brown Zemansky and Boorse who were making specific heat measurement. They discovered how and why the energy gap arose. Let us consider the way in which we build up the periodic table of elements. As one does this, one thinks of the orbits of an atom which one fills with electron. The unique chemical properties are associated with the extent to which one fills or empties an orbit. Here the electron can go only into  certain orbits. Here the electron can go only into certain orbits. And only one electron can go into any given orbit. This property of electron was first noted by Wolfgang Pauli, after whom the phenomenon is named ‘the Pauli exclusion principle’. (Paw, C.W.; 2002). Now, we talk about a metal and we think putting the electron in it, we can get a pretty good picture if we think of those electron as bouncing around inside the metal the metal being so to speak like a box we can also think of electron very much as one thinks of the atom of a gas, which are bouncing around inside what every container the gas in the fact is that when electron are in metal, they can posses certain orbits as the same way as electron in an atom. One way of thinking about these orbits is that some electron move slowly some move some what faster. In orbit which are possible can be specific by t he speed and direction in which the electrons are allowed to move if we then start putting electrons into a metal to achieve the situation at absolute zero. The first electron we put in would go into the lowest energy absolute zero. The fist electron we put in world go into the lowest energy orbits, the nest would into a somewhat higher energy orbit and so on unit we have put in the proper number of electrons. Those last ones we put in have a good deal more energy than the first ones. The energy which they have relative to the first ones is called the Fermi energy’ named after Enirico Fermi who fist calculated its value. Now suppose we heat this metal to give it a little more energy to all its parts. The electron are no expectation. Think of those electron which initially have a rather low amount of energy. If you try to give it more energy, there is a problem because the orbit of the somewhat higher enough are already occupied, and the Pauli principle does not let the electron switch over into an already occupied orbit. Now, let us talk about electron with the Fermi energy, those that were last added, and the one moving around most rapidly. Those electron have nearly energy orbit which are not occupied so if you heat up them. There is in  fact a continuous set of energies available to those electron of Fermi-energy, so they can gradually add energy at the metal is warmed. This bring   us to the point of the energy gap” Suppose instead of having the situation describe above, that they had to  pay so to speak, an entrance free to gain energy suppose no nearby orbital state were available an suppose you had to give them a really large chunk of energy before their motion change. Then one has described what is called a “gap” in the spectrum of the possible energy state. This is the situation which exist in superconductors
1.     ENERGY GAP IN SUPER CONDUCTOR AS A FUNCTION OF TEMPERATURE

The effective energy gap in superconductors can be measured in microwave absorption experiment the figure below offer the general confirmation of the BCS theory of superconductivity, the reduction of the energy gap as we approach the critical temperature can be taken as an indication that the change carries have some sort of collective nature. That is, the change carries must consist of at least two tins. Which are bound together and the energy is weaken as we approach the critical temperature. Above the critical temperature such collection does not exist and normal resistively prevails. This kind of evidence , along with the isotope effect, which shows that the critical lattices was  involved, helped to suggest the picture of paired electron bound together by phonon interaction with the lattice.

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