The project report gives brief explanation of the phenomenon of superconductivity and also give introduction to superconducting materials and their types, properties and their applications.

1. NATIONAL INSTITUTE OF TECHNOLOGY
HAMIRPUR, HIMACHAL PRADESH
177 005

2. A
PROJECT REPORT
ON
SUPERCONDUCTING MATERIAL
AND
MEISSNER EFFECT
SUBMITTED
TO
Dr. VIMAL SHARMA
ASSOCIATE PROFESSOR
DEPARTMENT OF PHYSICS & PHOTONICS SCIENCE
BY
MRADUL SAXENA
ROLL NO. 198016
PROJECT GROUP: - G2

3. CONTENTS
1. Introduction to Superconducting Materials
1.1. History & Background
1.2. Phenomenon of Superconductivity
1.2.1. Definition of Superconductivity
1.2.2. BCS Theory
1.3. Types of Superconductor
1.3.1. Type I Superconductor
1.3.2. Type II Superconductor
2. Properties of Superconducting Materials
2.1. Thermal Properties of Superconductor
2.2. Magnetic & Electromagnetic Properties
2.2.1. Critical Field
2.2.2. Meissner Effect
2.2.3. Quantization of Magnetic Flux
2.2.4. Josephson effect
3. Applications of Superconducting Material
3.1. Wireless communication
3.2. Medical science
3.3. Nuclear magnetic Resonance (NMR)
3.4. Physics and research
3.5. Transportation

4. INTRODUCTION TO
SUPERCONDUCTING MATERIAL
1.1 HISTORY & BACKGROUND
Discovery of Superconductivity in 1911 by the Dutch physicist Heike
Kamerlingh Onnes is an outcome of research in the field of microscopic
source of electrical resistance of metal and alloys. It was found out in the
research the electrical resistance can be reduced by reducing the density of
impurity atoms as well as by lowering temperature. Heike Kamerlingh Onnes
uses mercury because of very low impurity levels in his experiment to see
how low resistance can go. He observed sudden jump to zero resistivity below
4 K and discover the phenomenon of Superconductivity and mercury become
the first superconducting material. For many years it was considered
superconducting material has same properties as metal until 1933 when two
German physicists Walther Meissner and Robert Ochsenfeld discover that
superconducting material are highly diamagnetic i.e. it is strongly repelled by
and tends to expel a magnetic field. The phenomenon is called Meissner
effect. In 1934, Fritz and Heinz London came up with the theory of the
electromagnetic properties of superconductors that predicted the existence of
an electromagnetic penetration depth, which was first confirmed
experimentally in 1939. Soon after mercury, Kamerlingh Onnes expanded the
list of SC materials to include tin (3.7 K) and lead (7.2 K). After the discovery
of superconductivity in thallium (2.4 K) and indium (3.4 K). Meissner
successfully continued the search through the periodic table finding in 1928
tantalum (4.2 K), 1929 thorium (1.4 K) and 1930 titanium (0.4 K), vanadium
(5.3 K) and niobium, the element with the highest critical temperature Tc =

5. 9.2 K. The extension to binary alloys and compounds in 1928 by de Haas and
Voogd was fruitful bringing in SbSn, Sb2Sn, Cu3Sn and Bi5Tl3. The initial
pure metals which show superconductivity are put in the class of type I
superconductors whose superconductivity is easily suppressed by magnetic
field. In 1950 Pippard introduce materials which are more tolerant to
magnetic field than type I superconductors. These materials are called type II
superconductors, they are alloys and intermetallic compounds. After 1930,
Superconducting materials research was more or less in a hiatus until Bernd
T. Matthias and John K. Hulm started in the early 1950s an extensive
systematic search that delivered a number of new compounds with high Tc
well above 10 K as well as technically attractive Bc2 well above 10 T. Having
generated some 3000 different alloys in the 1950s and 1960s Matthias
became a recognized wizard of the Superconducting materials science. He
condensed his huge practical knowledge into “rules” of how to prepare
“good” superconductors. More materials were discovered after 1957 when
BCS theory came, which is the theory for superconductivity explains many
properties of superconducting materials correctly. After these developments
next major development in superconducting material came in 1986, when
Swiss physicist Karl Alex Muller and his West German associate, Johannes
Georg Bednorz discovered high temperature superconducting material.
Before 1986 all the superconducting materials discovered show
superconductivity at very low temperatures less than 23 K but after Muller
materials which were discovered have critical temperature 134 K. These
superconductors contain lanthanum, oxygen, yttrium, copper, barium,
strontium, bismuth and thallium.

6. 1.2 PHENOMENON OF SUPERCONDUCTIVITY
1.2.1 DEFINITION OF SUPERCONDUCTIVITY
Complete disappearance of electrical resistance in various solids when
they are cooled below a characteristic temperature. The phenomenon
is known as superconductivity. The characteristic temperature is called
the transition temperature (Tc).
1.2.2 BCS THEORY
It is the first microscopic theory given by American physicists John
Bardeen, Leon N. Cooper, and John Robert Schrieffer in 1957 for
superconductors explaining the phenomenon of superconductivity and
properties of superconductors. The main points of the theory are
1. Theory explains electron–electron attractive interaction (cooper
pairs).
2. Theory explains that there is the energy gap between the normal
state and superconductive state.
3. Theory explains superconductivity as phenomenon of ground state
with cooper pairs lies in ground state and excitation of electrons
from ground state to break cooper pair to the normal state by giving
energy equal to twice of energy gap.
4. It also explains properties of superconductors Meissner effect,
electromagnetic properties etc.
5. It also introduce some parameters like coherence length (ξ),
penetration depth (λ).
6. Coherence length (ξ): - It is the distance within which
superconducting electron concentration cannot change drastically
in a spatially varying magnetic field.

7. 7. Penetration depth (λL): - It is the length of penetration of magnetic
field in superconductor.
1.3 TYPES OF SUPERCONDUCTOR
The conventional superconductors excluding high temperature
superconductors (HTS) are classified in two types on the bases of their
magnetic properties.
1.3.1 TYPE I SUPERCONDUCTORS
These types of superconductors exclude magnetic field until
superconductivity destroys, and then the field penetrates completely.
They are mainly pure metals. The ratio of
λ
ξ
for these superconductors
lie in range 0 <
λ
ξ
<
1
√2
. E.g. Aluminium, Lead, Tin etc.
1.3.2 TYPE II SUPERCONDUCTORS
These types of superconductor exclude magnetic field completely until
a particular value of applied field (Hc1), above Hc1 they allow partial
penetration of magnetic field until a particular value of applied field
(Hc2). Above which complete penetration happens and
superconductivity destroys. They are mainly alloys and intermetallic
compounds. The ratio of
λ
ξ
for these superconductors lie in range
λ
ξ
>
1
√2
. E.g. Cuprate-perovskite, Yttrium barium copper oxide etc.

8. Image 1 variation of magnetization with applied field for Type I and Type II super
conductors.
Image 2 variation of magnetic field
and electron wave function y axis
with distance d x axis for type I
super conductor.
Image 3 variation of magnetic field and
electron wave function y axis with distance d
x axis for type II super conductor.

9. PROPERTIES OF
SUPERCONDUCTING MATERIAL
As superconductors are formed from normal conductors only by lowering
temperature, initially it was considered that properties of superconductors are
same as that of normal conductors but later it was proved that superconductors
have properties surprisingly different from normal metals.
2.1 THERMAL PROPERTIES OF SUPERCONDUCTORS
Superconductors have completely different thermal properties compared with
normal conductors. Transition temperature, variation of specific heat of
superconductor and thermal conductivity are some of its thermal properties.
Transition temperature: - It is the critical temperature for superconductors
above which they lose their superconductivity. The vast majority of the
known superconductors have transition temperatures that lie between 1 K and
10 K. of the chemical elements, tungsten has the lowest transition
temperature, 0.015 K, and niobium the highest, 9.2 K. The transition
temperature is usually very sensitive to the presence of magnetic impurities.
A few parts per million of manganese in zinc, for example, lowers the
transition temperature considerably.
Specific heat: - When a small amount of heat is put into a system, some of
the energy is used to increase the lattice vibrations (an amount that is the same
for a system in the normal and in the superconducting state), and the
remainder is used to increase the energy of the conduction electrons. The
electronic specific heat (Ce) of the electrons is defined as the ratio of that
portion of the heat used by the electrons to the rise in temperature of the

10. system. The specific heat of the electrons in a superconductor varies with the
absolute temperature (T) in the normal and in the superconducting state. The
electronic specific heat in the superconducting state (designated Ces) is
smaller than in the normal state (designated Cen) at low enough temperatures,
but Ces becomes larger than Cen as the transition temperature Tc is approached,
at which point it drops abruptly to Cen for the classic superconductors. Precise
measurements have indicated that, at temperatures considerably below the
transition temperature, the logarithm of the electronic specific heat is
inversely proportional to the temperature. This temperature dependence
suggests the energy gap in the distribution of energy levels available to the
electrons in a superconductor.
Thermal Conductivity: - Thermal conductivity of normal conductor Kn
approaches thermal conductivity of superconductor Ks as the temperature (T)
approaches the transition temperature (Tc) for all materials, whether they are
pure or impure. This suggests that the energy gap (Δ) for each electron
approaches zero as the temperature (T) approaches the transition temperature
(Tc).
Image 4 Variation of specific heat
with temperature for normal
conductor or superconductor.

11. 2.2 MAGNETIC AND ELECTROMAGNETIC PROPERTIES
As thermal properties superconductors have totally different magnetic
properties they show highly diamagnetic behaviour which is totally opposite
For normal conductor. Electromagnetic properties of superconductor show
absorption of electromagnetic radiation by superconductors.
2.2.1 CRITICAL FIELD
The superconductors are highly diamagnetic and exclude magnetic
field completely. The smallest value of applied magnetic field for
which magnetic field starts penetrating and superconductivity destroys
is called Critical field (Hc).
Critical field increase with decrease in temperature.
Hc(T) = Hc(0)(1 − (
T
TC
)
2
)
Where Hc(T) is critical field at
temperature T.
Hc(0) is critical field at absolute zero
0 K.
TC is critical temperature.
2.2.2 MEISSNER EFFECT
If a Type I superconductor of a symmetrical shape kept in a magnetic
field at a constant temperature with magnetic field less than Critical
field (Hc), complete exclusion of magnetic field from superconductor
is observed. Now consider a normal conductor of a symmetrical shape
lying in a magnetic field, keeping magnetic field constant we cool the
normal conductor till the transition temperature. It is found that the
Image 5 variation of critical field
with temperature for Type I and Type
II superconductor.

12. normal conducting sample expels the
magnetic flux as it becomes
superconducting the effect is known as
Meissner effect. Complete expulsion
of the magnetic flux (a complete
Meissner effect) occurs in this way in
type I superconductors.
Magnetic behaviour of Type II semiconductors is completely different
from type I semiconductors.
London equations: - London equations are modified form of Maxwell
equation of electromagnetism, which are applicable for
Superconductors. London equations describe the electromagnetic
behaviour of superconductor and also explains the Meissner effect and
penetration depth.
For superconductor
𝐵
⃗ = 𝜇𝑜(𝐻
⃗
⃗ + 𝑀
⃗⃗ )
Where B= net magnetic field H= applied magnetic field
M= magnetization
Image 6 experiment showing
Meissner effect.
Image 7 phenomenon of Meissner effect.

13. Inside super conductor B=0
𝜇𝑜(𝐻
⃗
⃗ + 𝑀
⃗⃗ ) = 0
𝑀
⃗⃗ = −𝐻
⃗
⃗
For outside superconductor
𝐵
⃗ = 𝜇𝑜𝐻
⃗
⃗
From Maxwell 3rd
and 4th
equations
∇
⃗
⃗ × 𝐸
⃗ = −𝜇0
𝜕𝐻
⃗
⃗
𝜕𝑡
∇
⃗
⃗ × 𝐻
⃗
⃗ = 𝐽𝑠
⃗⃗ + 𝐽𝑑
⃗⃗⃗
Where Js and Jd are super conduction or displacement current density
respectively. We can neglect Jd Maxwell 4th
equation becomes
∇
⃗
⃗ × 𝐻
⃗
⃗ = 𝐽𝑠
⃗⃗
Now, consider ns no. of electrons per unit volume out of total no. of
electrons per unit volume responsible for supercurrents in the
superconductor. As we know electric field cause acceleration of these
electrons we can write as
𝑚
𝑑𝑣𝑠
𝑑𝑡
= −𝑒𝐸
⃗
𝑑𝑣𝑠
⃗⃗⃗⃗
𝑑𝑡
= −
𝑒𝐸
⃗
𝑚
Negative sign indicates that force is in opposite direction of electric
field. Where m is mass of electrons, e is charge on electron E is electric
field, vs is drift velocity of superconducting electrons. Super
conduction current density is given by
𝐽𝑠
⃗⃗ = −𝑛𝑠𝑒𝑣𝑠
⃗⃗⃗

14. Negative sign indicates flow of current is opposite to the flow of
electrons. Differentiate above equation w.r.t. time we get
𝑑𝐽𝑠
⃗⃗⃗
𝑑𝑡
= 𝑛𝑠𝑒
𝑑𝑣𝑠
⃗⃗⃗⃗
𝑑𝑡
Substituting
𝑑𝑣𝑠
𝑑𝑡
, we get
𝑑𝐽𝑠
⃗⃗
𝑑𝑡
=
𝑛𝑠𝑒2
𝐸
⃗
𝑚
(𝑖)
𝐸
⃗ =
𝑚
𝑛𝑠𝑒2
𝜕𝐽𝑠
⃗⃗
𝜕𝑡
Substitute E in Maxwell’s 3rd
equation
∇
⃗
⃗ × (
𝑚
𝑛𝑠𝑒2
𝜕𝐽𝑠
⃗⃗
𝜕𝑡
) = −𝜇𝑜
𝜕𝐻
⃗
⃗
𝜕𝑡
𝑚
𝑛𝑠𝑒2
(∇
⃗
⃗ ×
𝜕𝐽𝑠
⃗⃗
𝜕𝑡
) = −𝜇𝑜
𝜕𝐻
⃗
⃗
𝜕𝑡
∇
⃗
⃗ ×
𝜕𝐽𝑠
⃗⃗
𝜕𝑡
= −𝜇𝑜
𝑛𝑠𝑒2
𝑚
𝜕𝐻
⃗
⃗
𝜕𝑡
𝜕
𝜕𝑡
(∇
⃗
⃗ × 𝐽𝑠
⃗⃗ ) = −𝜇𝑜
𝑛𝑠𝑒2
𝑚
𝜕𝐻
⃗
⃗
𝜕𝑡
Integrate above equation w.r.t. time
∇
⃗
⃗ × 𝐽𝑠
⃗⃗ = −𝜇𝑜
𝑛𝑠𝑒2
𝑚
𝐻
⃗
⃗ (𝑖𝑖)
Now
𝜆𝐿 = √
𝑚
𝜇𝑜𝑛𝑠𝑒2
Where λL is penetration depth substituting it in equation (i) and (ii)

15. We get
𝑑𝐽𝑠
⃗⃗
𝑑𝑡
=
𝐸
⃗
𝜇𝑜𝜆𝐿
2
This equation is called London 1st
equation.
∇
⃗
⃗ × 𝐽𝑠
⃗⃗ = −
𝐻
⃗
⃗
𝜆𝐿
2
This equation is called London 2nd
equation
Now from Maxwell 4th
equation and London 2nd
equation we get
∇
⃗
⃗ × (∇
⃗
⃗ × 𝐻
⃗
⃗ ) = −
𝐻
⃗
⃗
𝜆𝐿
2
(∇
⃗
⃗ . 𝐻
⃗
⃗ )∇
⃗
⃗ − (∇
⃗
⃗ . ∇
⃗
⃗ )𝐻
⃗
⃗ = −
𝐻
⃗
⃗
𝜆𝐿
2
From Maxwell 2nd
equation ∇
⃗
⃗ . 𝐻
⃗
⃗ = 0 we get
−∇2
𝐻
⃗
⃗ = −
𝐻
⃗
⃗
𝜆𝐿
2
∇2
𝐻
⃗
⃗ =
𝐻
⃗
⃗
𝜆𝐿
2
This equation is seen to account for Meissner effect because it does not
allow solution for uniform magnetic field in space so that a uniform
magnetic field cannot exist in a superconductor. The solution of this
equation implies that magnetic field is exponentially screened out from
the interior of superconductor with penetration depth (λL).
High frequency electromagnetic properties: - The energy gap in a
superconductor has a direct effect on the absorption of electromagnetic
radiation. At low temperatures, at which a negligible fraction of the
electrons are thermally excited to states above the gap, the

16. superconductor can absorb energy only in a quantized amount that is at
least twice the gap energy (at absolute zero, 2Δo). In the absorption
process, a photon (a quantum of electromagnetic energy) is absorbed,
and a Cooper pair is broken; both electrons in the pair become excited.
The photon’s energy (E) is related to its frequency (ν) by the Planck
relation, E = hν, in which h is Planck’s constant (6.63 × 10-34
joule
second).Hence the superconductor can absorb electromagnetic energy
only for frequencies at least as large as 2Δo /h.
2.2.3 QUANTIZATION OF MAGNETIC FLUX
The laws of quantum mechanics dictate that electrons have wave
properties and that the properties of an electron can be summed up in
what is called a wave function. If several wave functions are in phase
are said to be coherent. The theory of superconductivity indicates that
there is a single, coherent, quantum mechanical wave function that
determines the behaviour of all the superconducting electrons. As a
consequence, a direct relationship can be shown to exist between the
velocity of these electrons and the magnetic flux (Φ) enclosed within
any closed path inside the superconductor. Indeed, inasmuch as the
magnetic flux arises because of the motion of the electrons, the
magnetic flux can be shown to be quantized; i.e., the intensity of this
trapped flux can change only by units of Planck’s constant divided by
twice the electron charge.

17. 2.2.4 JOSEPHSON EFFECT
If two superconductors are separated by an insulating film that forms a
low-resistance junction between them, it is found that Cooper pairs can
tunnel from one side of the junction to the other. This flow of electrons
called Josephson current, which is generated and related to the phase
of coherent quantum mechanical wave function of superconducting
electron on either sides of junction. Several phenomenon which were
observed are collectively called Josephson Effect. Two of these
phenomenon are
DC Josephson Effect: - The flow of DC current in the super conductor
when no external voltage is applied.
AC Josephson Effect: - The flow of oscillating current in the super
conductor when a fixed voltage is applied.

18. APPLICATIONS OF
SUPERCONDUCTING MATERIAL
Superconducting materials since from discovery become of great importance due
to their vast applications in field of engineering & science. They are responsible
for many great inventions and technological advancements. Many of these
inventions today are making our life easier. Superconductors are used in wireless
communication. Superconducting materials application are also seen in the
medical science as Magnetic resonance imaging (MRI),
magnetoencephalography (MEG), and magnetocardiography (MCG) are based
on properties of superconductors. In pharmaceuticals, nuclear magnetic
resonance (NMR) is used for various purposes, also based on properties of
superconducting material. Superconductors have a great application in high
energy physics and other area of research. Transportation is also a field of
application of superconductors.
3.1 WIRELESS COMUNICATION
Superconductors have unique property of ultra-low dissipation and distortion
as well as intrinsic (quantum) accuracy. These advantages helps in making
superconductors filters which helps in increasing the range of communication
and in avoiding overlap of channels. Superconductors are also used to make
analog- digital converters which revolutionise communication industry
weather it is cellular or television communication.

19. 3.2 MEDICAL SCIENCE
In medical science the major
breakthrough comes with introduction
of medical imaging and diagnostics,
as it helps doctors to diagnose patient
by seeing inside his or her body from
outside by various imaging techniques
MRI, MEG and MCG. These all
imaging techniques uses
superconductor magnets. Due to superconductor magnets these techniques
not only safe but energy efficient and also continuing on advancing. MRI
provides enormous increase in diagnostic ability, clearly showing soft tissue
feature not visible in X ray imaging. MEG which is based on SQUIDs which
is a magnetometer based on Josephson Effect helps in pre surgical mapping
of eloquent brain areas, brain tumour. MCG provides functional imaging of
heart are also based on SQUIDS.
3.3 NUCLEAR MAGNETIC RESONANCE (NMR)
NMR is critical tool for genomics, drug
discovery, biotechnology and material science.
Low temperature superconductor materials
enables the stable magnets required for precision
NMR spectroscopy. NMR spectroscopy is used
in structure determination of proteins and drug
discovery. NMR spectroscopy is also used in
material science, the determination of chemical
Image 8 MRI machine
Image 9 NMR
spectrometer

20. structure of extra-terrestrial matter in meteorites and the effect of various
trace element additions on melt chemistry and matter flow in variety of
material are some examples of use of NMR in material science.
3.4 PHYSICS AND RESEARCH
Superconducting material has played a key role throughout the past century
in expanding the frontiers of human knowledge. Today these materials
continue to offer important new tools to expand our understanding of the
natural world and potentially foster new energy technologies. Scientist spent
the last half of the century putting together what is called the scientist model
of particle physics. The standard
model, which explains the basic
interactions of fundamental particles
that make up everything we see in the
most complete physical theory in
theory, yet it leaves 95% of universe
unexplained. Physicists use particle
accelerators to recreate the condition of the early universe in an attempt to
piece together the complex puzzle of how we got to where we are today.
These huge machines are used to accelerate particles to very high energies
where they are brought together in collisions that generate particles that only
existed a few moments after the Big bang that created universe 15 billion
years ago.
The largest machine on earth is located underground in a circumference of 27
km near Geneva, Switzerland called “large hydron collider” biggest particle
Image 10 large hydron collider

21. accelerator on earth will generate
conditions that existed 20 billionths of
second after Big Bang.
The superconducting magnets are used
to make rings of particle accelerator. In
“large hydron collider” two concentric
rings are made of thousands of
superconductor. Detectors in “large
hydron collider” are also made of superconductors use to measure properties
of particle.
International thermonuclear experimental
reactor (ITER) is a global project
With aim to use fusion energy for
peaceful purpose. The superconductors
play a critical enabling role in this project
by generating the high magnetic fields
needed to confine and shape the high
temperature plasma.
Superconductors are under development for range of space related projects.
Space telescopes and other space based instruments require about minimal
power budgets and low loss natures of superconductors make them ideal for
these applications. These application includes magnetic actuators, magnetic
assisted propulsion, magnetic refrigeration and space based magnetic plasma
confinement.
Image 11 tunnels of large hydron
collider.
Image 12 ITER project fusion reactor.

22. 3.5 TRANSPORTATION
Transportation system faces new challenges today like changes in fuel
market economics, demand for improved performance. In response to these
challenges some transportation are electrified. Superconductors can leverage
the advantages of electrified transportation in various ways ranging from high
speed trains to advance ship propulsion system. Incorporation of
superconductors in transportation system improve efficiency and
performance, reduce weight and fuel consumption. Some main examples of
use of superconductor in transportation are electric ship propulsion system
which uses superconductor motors or generator which is much smaller and
lighter and also have high efficiency. Maglevs are magnetically levitated
trains which is direct application of Meissner effect property of
superconductor. It is found that maglev provide high performance and great
efficiency.
Image 13 Maglev train.