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 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
1.8 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 = 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).
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