ENERGY GAP IN SUPERCONDUCTOR

ABSTRACT

The study of superconductors, it concept and the various theories are still a mystery in the field of Solid State Physics. Although a few theories tries to explain the working principle (i.e. how and why it works) of super-conductors scientists believed that a full acknowledgment of its energy gap; is 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 super conductors.

TABLE OF CONTENTS

CHAPTER ONE

1.1            INTRODUCTION

1.2            PROBLEM STATEMENT

1.3            OBJECTIVES OF THE STUDY

1.4                      SIGNIFICANCE OF THE STUDY

1.5            DISCOVERY OF SUPERCONDUCTORS

1.6            BCS THEORY OF SUPERCONDUCTIVITY

1.7                      COOPER PAIRS

1.4     ANALYTICS OF SUPERCONDUCTIVITY

CHAPTER TWO

2.2            THEORIES OF SUPERCONDUCTIVITY

2.2.1    GINZEBURG – LANDAU THEORY

2.2.2    THE COMPLETE MICROSCOPIC THEORY 

2.3            MEISSNER EFFECT

2.4            JOSEPHSON EFFECT 

2.5        CRITICAL TEMPERATURE

3.1       ENERGY GAP

3.1.1    Direct Energy Gap

3.1.2    INDIRECT ENERGY GAP

3.2    HOW THE ENERGY GAP AROSE

3.3                      ENERGY GAP IN SUPER CONDUCTOR AS A FUNCTION OF TEMPERATURE

3.2       EXPERIMENT AL OBSERVATION

3.3       ENERGY GAP IN SEMI CONDUCTORS

CHAPTER THREE

CALCULATIONS AND METHODS

3.1     CALCULATION OF ENERGY GAP IN LOW TEMPERATURE SUPERCONDUCTORS (LTS) AND HIGH TEMPERATURE SUPERCONDUCTORS (HTS)

3.2     COMPARISON OF DATA VALUE

4.3.1    The Scenario Of Performed Pairs                       

4.3.2  The Scenario of a Non-Superconducting Related Pseudo Gap.

4.4     EFFECT OF IMPURITY

4.5     CO-EXISTENCE OF ANTI FERROMAGNETISM AND SUPERCONDUCTIVITY, A STRONG COUPLING-PERSPECTIVE.

CHAPTER FOUR

CONCLUSION

5.1                 GENERAL CLASSIFICATION OF SUPER CONDUCTORS.

5.2     APPLICATIONS

REFERENCES

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 19^th 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

1.8     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 = ρ_o [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). 

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