A STUDY INTO ENERGY GAP IN SUPER CONDUCTORS


 A STUDY INTO ENERGY GAP IN SUPERCONDUCTORS   

ABSTRACT

The study of superconductors, their concept and the various theories are still a mystery in the field of Solid State Physics. Although a few theories try to explain the working principle (i.e. how and why it works) of super-conductors scientists believed that a full acknowledgement of its energy gap; its dependence on temperature and pressure and the effect of doping may finally unlock the door to a vast acknowledge of superconductivity.

          This project work brings all in one piece, the various principle and theories as derived by some renowned scientist working to ensure full understanding in this area of physics. It is believed that High-Temperature Superconductors (HTS) i.e. superconductors with considerable high critical temperature hold the key to the practical application of superconductors.

 CHAPTER ONE

1.1            INTRODUCTION

Superconductivity is a fascinating and challenging field of physics. Scientists and Engineers throughout the world have been striving to develop it for many years. For nearly 75 years superconductivity has been a relatively obscure subject. Until recently, because of the cryogenic requirement of low temperature superconductors, superconductivity at the high school level was merely an interesting topic occasionally discussed in a Physics class. Today however, superconductivity is being applied to many diverse areas such as: medicine, theoretical and experimental science, the military, transportation, power production, electronics, as well as many other areas. With the discovery of high temperature superconductor which can operate at liquid nitrogen temperature (77k), superconductivity is now well known within the reach of high school student. Unique and exciting opportunities now exist today for our student to explore and experiment with this new and important technological field of Physics. Major advances in low-temperature refrigerator were made during the late 19th century. (Bedornz, J and Muller, K; 1986). 

1.2            PROBLEM STATEMENT

It is not practical to transmit electric energy if you need liquid helium temperatures. The cooling costs are prohibitive. The current state of the art are cables using thin films of BSCCO. They can operate at 77 K without problems. The current world record for such a cable in a vacuum tube is several kilometers but after some distance you need a small building along the cable to cool the liquid nitrogen inside the cable again.

There is a tremendous research effort to find superconductors with higher critical temperatures and currents but that is not so easy. The usage for practical applications is increasing but the progress is rather slow. In more exotic applications such a CERN or ITER you absolutely need superconducting cables, if it is only for space reasons: Well, Is it really possible to maintain such low temperatures required for super-conductors (taking High-temperature superconductivity into account) over large distances? What I say is - Even if we were able to pass current through superconductors, we need to constantly cool them for maintaining the zero resistance. Hence to cool, we need power. Then, superconductors wouldn't be necessary in this manner if they don't have an advantage..? Or, are there any new approaches to overcome these disadvantages?

1.3            OBJECTIVES OF THE STUDY

The primary objective of the study is to examine the energy gap in superconductors. Specific objectives of the study are:

1. To critically examine the various types and properties of super conductors

2. To examine energy gaps in low temperature super conductors.

3. To examine energy gaps in high temperature super conductors.

1.4            SIGNIFICANCE OF THE STUDY

The study will give more insights into the various ways superconductors can be utilised and improved. Superconducting materials are in the forefront of current research because of their very rich and fascinating properties and their applications in electrical and electronics technology and energy-saving materials. Superconductivity is a unique characteristic of certain materials that appears when the system temperature is dropped below a specific critical value and under such conditions the materials can carry electrical current with absolutely zero resistance.

1.5            DISCOVERY OF SUPERCONDUCTORS

Superconductors were first discovered in 1911 by the Dutch physicist. Heike Kammerlingh Onnes.

          Onnes dedicated his scientific carriers to exploring extremely cold refrigerator He successfully liquefied helium by cooling it to 452 degree below zero Fahrenheit (4 Kelvin or 4K). Onnes produced only a few millilitres of liquid helium that day, but this was to be the new beginning of his exploration. The liquid helium enables him to cool other material closer to absolute zero (0 Kelvin)

          In 1911, Onnes began to investigate the electrical properties of metal in extremely cold temperature. It has been know for many years that the resistance of metal fell when cooled below room temperature, but it was not know what limiting value the resistance would approach if the temperature were reduced very close to Ok. Onnes, found that a cold wire’s resistance would dissipate. This suggested that there would be a steady decrease of electrical resistance allowing for better conductor of electricity.

1.6            BCS THEORY OF SUPERCONDUCTIVITY

The properties of type-1 superconductor were modelled successfully by the effort of John Bardeen, Leon Cooper, and Robert Schrieffer in what is commonly called the BCS theory(Bardeen et al;1957). A key conceptual element in this theory is the pairing of electron close to the Fermi level into cooper pairs through interaction with the crystal lattices. The pairing result from a slight attraction between the electrons related to lattice vibration. The coupling of this lattice is called Phonon. Interaction pair of electron can behave very differently from single electron which one fermions and must obey the Pauli Exclusion Principle. The pair of electron acts more like Boson which can condense into the same energy level. The electron pair has a slightly lower energy and leave an energy gap above them on the order to 0.001 eV, which inhibit the kind of collision interaction which lead to ordinary resistivity. For temperature such that the thermal energy is less than the band gap, the material exhibit zero resistivity (Wu,J; 2002).      

1.7                      COOPER PAIRS

 The behaviour of superconductors suggest that electron pairs are coupling over a range of hundred of nanometres, there orders of magnitude larger that the lattice spacing called cooper pairs. This coupled electron can take the character of a boson and condense into the ground state.

          Cooper pairs are the pairing caused by the attractive forces between electronic from the exchanges of phonons.

Figure: 1.1 Cooper pairs

1.4     ANALYTICS OF SUPERCONDUCTIVITY

Materials that have no resistance to the flow of electricity are one of the last great frontiers of scientific discoveries. Not only have the limits of superconductivity not yet reached but the theories that explain superconductivity behaviours seem to be constantly under review.(Betil,S; 2007).

          In general, superconductors become superconducting only below a certain transition temperature Tc, which is usually within a few degree of absolute zero. Currently, in   a ringed shape superconducting material, electric current has been observed to flow for years in the absence of a potential difference with no measurable decrease. Measurement show that the resistivity superconductors is less than 4x10-25Ωm, which is over 1016 times smaller than that for copper (cu) and is considered to be zero in practice.

Figure 1.2 - A superconducting material

A superconducting materials has zero resistivity when it is below its critical temperature (Tc). At Tc, the resistivities jump to neither ‘normal’ nor zero value and increase with temperature as most material do

ρT = ρo [1+∞ (T-T0)]                                                                                      (1.1)

          Much research has been done on superconductivity to try and understand why it occurs. And to find materials that super conduct as higher more accessible temperature to reduce the cost and inconvenience of refrigerator at the require very low temperature. Before 1986, the highest temperature at which a material was found to super conduct was 23K, and this required liquid helium to keep the material cold(Charles, J; 2003). 

          In 1987, a compound of Yttrium, barium, copper and oxygen (YBCO) was developed that can be superconducting at 90K. Since this is above the boiling temperature of liquid nitrogen, 77K which is sufficiently cold to keep the material superconducting.

          This is an important break through since liquid Nitrogen was much more easily and cheaply obtained than the liquid helium needed for conventional super conductors. Since the superconductivity at temperature as high as 160 or 16K has been reported, through the fragile compound considerable research is being done to develop high Tc superconductors as wires that can carry current strong enough to be practical. Most application today use a Bismuth-Strontium-Calcium-Copper Oxide (BSCCO) known how to make a useable bendable wire out of it, which is of course very brittle. One solution is to embed tiny filaments of high Tc superconductor in a metal alloy matrix with the superconducting wire wrapped around a tube carrying liquid nitrogen to keep the BSCCO below Tc. The wire cannot be resistance less, because of the silver connections, but the resistance is much less than that of the conventional copper cable. (Gracho,D.C; 2005).

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 bandgap 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

Direct energy gap 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 bandgap 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 bandgap 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 possess 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 somewhat faster. In orbit which are possible can be specified by the 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 as 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 fee 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    

ENERGY GAP IN SUPERCONDUCTOR 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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A STUDY INTO ENERGY GAP IN SUPER CONDUCTORS



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