This document provides an overview of superconductivity. It discusses key topics such as: 1. The discovery of superconductivity by Kamerlingh Onnes in 1911 and the properties of zero electrical resistance and the destruction of superconductivity by magnetic fields or currents. 2. The classification of Type I and Type II superconductors and their different responses to magnetic fields. 3. Theories that describe superconductivity such as the London equations, BCS theory, and Ginzburg-Landau theory. 4. Other properties like the Meissner effect, isotope effect, and persistent currents. Applications and the effect of variables like stress, frequency, and impurities are also covered

1. “Superconductivity is perhaps the most
remarkable physical property in the
Universe” David Pines
Superconductivity
1

2. 2
Topics covered
1. Introduction
2. Properties of superconductors – overview
3. Type I and Type II superconductors
4. Theories of superconductivity
5. Josephson’s effects and SQUIDS
6. Applications
7. Super fluidity

3. Discovery of Superconductivity
Discovered by Kamerlingh Onnes
in 1911 during first low temperature
measurements to liquefy helium ,
while measuring the resistivity of
“pure” Hg he noticed that the
electrical resistance dropped to zero
at 4.2K
In 1912 he found that the resistive
state is restored in a magnetic field
or at high transport currents
3

4. Resistivity()[x10-11Ohmm]→
T (K) →
10 20
5
10 Ag Sn
Resistivity()[x10-11Ohmm]→
T (K) →
5 10
10
20
00 Tc
Superconducting transition temperature
Superconducting transition
?
4

5. Superconductivity in alloys and oxides
5

6. High Tc superconductivity
Compound Tc Comments
Nb3Ge 23 K Till 1986
La-Ba-Cu-O 34 K Bednorz and Mueller (1986)
YBa2Cu3O7-x 90 K > Boiling point of Liquid N2
Tl (Bi)-Ba(Sr)-Ca-Cu-O 125 K
6

7. 7

8. Superconductors
8

9. 9

10. S.No. Alloy Critical temperature TC (K)
1. Niobium Titanium (NbTi) 10.0
2. Vanadium Gallium (V3Ga) 16.5
3. Vanadium Silicon (V3Si) 17.1
4. Niobium Aluminium (Nb3Al) 17.5
5. Niobium Tin (Nb3Sn) 18.1
6. Niobium Germanium (Nb3Ge) 23.2
PROPERTIES OF SUPERCONDCUTORS
1. Zero electrical resistance
The first characteristic property of a superconductor is its electrical
resistance.
The electrical resistance of the superconductor is zero below a transition
temperature (Tc.)
The variation of electrical resistivity of a normal conducting metal and a
superconducting metal as a function of temperature is shown in next slide
The sudden fall in resistance indicate transition to the superconducting state.
Table. Transition temperature of some intermetallic compounds.
10

11. 2. Effect of magnetic field
Below the transition temperature of a material (TC), its superconductivity can be
destroyed by the application of a strong magnetic field.
The minimum magnetic field strength required to destroy the superconducting
property at any temperature is known as critical magnetic field (HC).
H0 - critical magnetic field at absolute zero temperature (OK) of the material.
TC - superconducting transition temperature of the material
T - the temperature below TC of the superconducting material.















2
C
0C
T
T
-1HH
11

12. Table. Critical magnetic field at OK for some superconducting
materials
The critical magnetic field is zero at superconducting transition temperature,
i.e., at T = TC’ HC = 0. The variation of HC with temperature T (K) in a
superconductor is shown in fig.
S.N
o.
Element
Critical
magnetic field
at OK
(milli tesla)
1. Niobium (Nb) 198.0
2. Vanadium (V) 142.0
3. Lanthanum (La) 110.0
4. Lead (Pb) 80.3
5. Mercury (Hg) 41.2
6. Tin (Sn) 30.9
12

13. 3. Effect of electric current
The application of very high electrical current to a superconducting
material destroys its superconducting property.
Consider a wire made up of a superconductor as shown in fig. Let ‘I’ be
the current flowing through the wire.
The flow of current induces a magnetic field. This induced magnetic
field in the conductor destroys the superconducting property.
The critical current (iC) required to destroy the superconducting property
is given by
iC = 2  r HC
where HC is the critical magnetic field, and r is the radius of the
superconducting wire
13

14. 4. Persistent current
When a superconductor in the form of a
ring is placed in a magnetic field, then
the current is induced in it by
electromagnetic induction.
The existence of persistent (i.e., with no energy dissipation) diamagnetic
currents on macroscopic scales has been considered a hallmark of
superconductivity in metals. The amplitude of the persistent current is a
periodic function of the magnetic flux quantum,
Φ0=h/e∼4.14×10−15Tm2
If the ring is in normal conducting state, the current
decreases quickly because of the resistance in the ring.
Since the ring is in superconducting state has zero resistance
and one the current is set up, it flows indefinitely without
any decrease in its value.
5. Meissner effect
When a bulk sample of a conducting material
is placed in a uniform magnetic field of flux
density B, the magnetic lines of force
penetrates through the material as
shown in fig. 14

15. However, when the material is cooled for the super-
conductivity below its transition temperature i.e., T < TC’
the magnetic flux originally present in the specimen
is pushed out from the specimen as shown in fig.
Thus, inside the bulk superconducting specimen, magnetic
induction (B) is zero.
This phenomenon is known as Meissner effect.
15

16. Meissner Effect
Normal
state
SuperC
state
B = 0 inside a
superconductor
For a long thin specimen with long axis // Ha,
H is the same inside & outside the specimen (depolarizing field ~ 0)
4 0a   B H M →
1
4a
M
H 
 
Caution: A perfect conductor (ρ = 0) may not exhibit Meissner effect.
E jOhm’s law → 0 0if  E
1
0
c t

  

B
E →
0
t



B (B is frozen, not
expelled.)
In this sense, a
superconductor is a perfect
diamagnet.
16

17. Applications of Meissner Effect
• Meissner effect is a standard test to prove whether a particular
material is a superconductor or not.
• Because of the diamagnetic property, the superconducting material
strongly repel external magnets. It leads to a levitation effect in
which a magnet floats above a superconducting material as shown
in fig.
6. Isotope Effect
Maxwell found that transition temperature are
inversely proportional to the atomic
masses of the isotopes of a single superconductor.
where α is called isotope effect coefficient.
In most of the cases, its value is taken as ½.
constantTM
M
constant
Tor
M
1
Ti.e.,
C
α
αC
αC



17

18. The atomic mass of mercury varies between 199.5 and 204.4. Due to
variation in atomic mass, the transition temperature of isotopes of
mercury varies between 4.185 K and 4.146 K.
7. Effect of pressure
By applying very high pressures, we can bring the TC of a material
nearer to room temperature, i.e., TC is directly proportional to pressure
at very high pressures.
8. Thermal properties
Experiments have shown that the transition between normal and
superconducting state is thermodynamically reversible.
• Entropy and specific heat decreases at transition temperature.
• Thermo-electric effect disappears in the super-conducting state.
constantTM C
1/2

18

19. Heat Capacity
S NS S
→ superC state is more
ordered
ΔS ~ 10–4 kB per atom
→ only 10–4 e’s participate in
transition.
Al
NC T N
T
S
T


 NS T→
Al
As dHc/dT is always
negative, Sn – Ss is always
positive.
19

20. Heat Capacity
20
From experiments, Sn – Ss is found to be approximately 10-7 eV per
atom.
Hence Un – Us is ~ 10 -7 eV, which is extremely small compared to the
band energies.
On substituting T = Tc, Hc = 0, in this equation we get the Ruger’s
formula for

21. 21
9. 9. General properties
• There is no change in the crystal structure in
the superconducting state as revealed by X-
ray diffraction studies. This suggests that
superconductivity is more concerned with
conduction electrons than with the atoms
themselves.
• There is no change in elastic and photo-
electric properties.
• In the absence of magnetic field, there is no
change in volume at the transition
temperature.

22. 10. Stress
If istress s applied to a material, then there is an increase
in the dimension of the material. Due to stress, an
increase in transition temperature is observed and it also
affects critical magnetic field.
11. Frequency
At very high frequencies, the zero resistance of a
superconductor is modified. The transition temperature
is not affected by the frequency variation.
12. Impurity
The general properties especially the magnetic property
of superconducting state are modified by the addition of
impurities.
13.13. Size
If the size of the specimen is reduced below 10-4 cm, the
properties of superconducting state are modified.
22

23. 23
Energy gap in superconductors
Experiments show that a gap of forbidden energy exists just above the
Fermi level at absolute zero, in a superconductor. The energy gap in
superconductors is the gap between the energy bands which are fully
occupied by electrons, and the bands which are fully empty. That Eg is
one of the superconductors' properties that don't show in any other
materials. The size of the energy gap is about 1 eV, which is the
required energy to break the band between 2 electrons pairs. At zero
temperature, the electrons jump over the energy gap and create holes.
The width of the energy gap has been found to be about 3.5 kTc at 0 K.
The effective energy gap in
superconductors can be measured in
microwave absorption experiments.

24. Normal Conductor Superconductor
1.In a normal conductor, there is no band gap between the filled and
unfilled levels. Normal conductors to not exhibit macroscopic
quantum features.
2.In a superconducting material, there is a very tiny band gap ~10-4eV,
which is very small compared to the 1-2 eV occurring in
semiconductors. This tiny band gap would only be apparent at very
low temperatures.
24

25. Type I and Type II superconductors
25

26. Superconductor Types
The Type 1 category of superconductors is mainly comprised
of metals and metalloids that show some conductivity at room
temperature. They require incredible cold to slow down
molecular vibrations sufficiently to facilitate unimpeded
electron flow in accordance with what is known as BCS
theory.
The Type 2 category of superconductors is comprised of
metallic compounds and alloys. The recently-discovered
superconducting "perovskites" (metal-oxide ceramics that
normally have a ratio of 2 metal atoms to every 3 oxygen
atoms) belong to this Type 2 group. They achieve higher Tc's
than Type 1 superconductors by a mechanism that is still not
completely understood. Conventional theories suggest that it
relates to the planar layering within the crystalline structure
26

27. M→
H → Hc
Normal
Superconducting
Type I
Type I (Ideal or soft) superconductors
 Type I SC placed in a magnetic field totally repels the flux lines
till the magnetic field attains the critical value Hc






c
c
HH
HHH
M
0
27

28. M→
H → Hc
Normal
Type I
Type II (Hard) superconductors
 Type II SC has three regions









c2
c2c1
c1
HH0
)H,(HHH
HHH
M
Vortex
Vortex
Region
Gradual penetration of the
magnetic flux lines
Super
conducting
Hc1 Hc2
28

29. 29
In Type II superconductors
the magnetic field is not
excluded completely, but is
constrained in filaments
within the material. These
filaments are in the normal
state, surrounded by super
currents in what is called a
vortex state. Such
materials can be subjected
to much higher external
magnetic fields and remain
superconducting.
Vortex state

30.  As type II SC can carry high current densities (Jc) they are
of great practical importance
 The penetration characteristics of the magnetic flux lines
(between Hc1 and Hc2) is a function of the
microstructure of the material  presence of pinning
centres in the material
 Pinning centres:
 Cell walls of high dislocation density
(cold worked/recovery annealed)
 Grain boundaries
(Fine grained material)
 Precipitates
(Dispersion of very fine precipitates with interparticle
spacing ~ 300 Å)
 Jc ↑ as Hc2 ↑
30

31. Types of Superconductors
Type I
• Sudden loss of magnetisation
• Exhibit Meissner Effect
• One HC = 0.1 tesla
• No mixed state
• Soft superconductor
• Eg.s – Pb, Sn, Hg
Type II
• Gradual loss of magnetisation
• Does not exhibit complete
Meissner Effect
• Two HCs – HC1 & HC2 (≈30
tesla)
• Mixed state present
• Hard superconductor
• Eg.s – Nb-Sn, Nb-Ti
-M
HHC
Superconducting
Normal
Superconducting
-M
Normal
Mixed
HC1 HC
HC2
H
The London penetration length λ
· The coherence length ξ 31

32. Superconductor Classifications
• Type I
– tend to be pure elements or simple alloys
–  = 0 at T < Tcrit
– Internal B = 0 (Meissner Effect)
– At jinternal > jcrit, no superconductivity
– At Bext > Bcrit, no superconductivity
– Well explained by BCS theory
• Type II
– tend to be ceramic compounds
– Can carry higher current densities ~ 1010 A/m2
– Mechanically harder compounds
– Higher Bcrit critical fields
– Above Bext > Bcrit-1, some superconductivity
32

33. Theories of Superconductivity
• London Equation
 

  

fieldm agnetic
ofenergy
2
currentperm anent
ofenergykinetic
s
2
0 rd
8π
H
rdnmv
2
1
FF  
  0HH0F 2


H λ
x
eH

• BCS Theory
• Ginzburg-Landau Theory
2/1
c MT 

•Electrons can attract via
phonons
•Attraction leads to energy gap
1.76Tc
isotope effect
EF EF
2
Normal Metal Superconductor
 
   
  A
mc
e4
m
ei
B
4
c
j
0A
c
e2
im2
1
T4
H,
T
T
TT
T
8
H
A
c
e2
i
m2
1
2
FF
2
2
**
s
2
2/12
c
2
c
c
0
22
42
n








































 
 
 
   
IItype21
Itype21
parameterGL
Te24
mc
T
Tm2
T
2/1
2
2
2/1
2


























33

34. London Theory – 1
• Newton’s law (inertial response) for applied electric field
 SJ
dt
d
E  2
en
m
s








en
J
dt
d
meE
s
S
 sv
dt
d
mF 
sss evnJ 
dt
dJ
m
Een Ss

2
dt
Jd
m
Een Ss





2
dt
Jd
dt
Bd
m
en Ss




2
0
2






 B
m
en
J
dt
d s
S

Supercurrent density is
B
m
en
J s
S
 2

We know B = 0 inside
superconductors
Faraday’s law
34

35. London Theory – 2
London Equations
 SJ
dt
d
E  2
en
m
s

B
m
en
J s
S
 2

t
E
JB





000 
JB 

0
  B
m
en
BB s
 2
0
2

B
m
en
B s
 2
0
2

Ampere’s
law
=0; Gauss’s law for
electrostatics
35
There are two London equations:
The first equation follows from
the Newton's second law for
superconducting electrons.

36. London Equation
    /
// // 0 Lx
x e

 B B
λL = London penetration length
2
2
4
L
mc
nq



This characteristic length, λ, is known as
the London penetration depth. A small value of the
penetration depth implies that the magnetic field is
effectively expelled from the interior of a macroscopic
sample. The number density of superconducting
electrons is dependent on temperature and and so is
the penetration depth. penetration depth rises
asymptotically as the temperature approaches Tc.
Thus the field penetrates further and further as the
temperature approaches Tc and does so completely
above Tc.
36

37. Coherence Length
Coherence length ξ ~ distance over which nS remains relatively uniform.
Spatial variation of ψ increases K.E.
→ High spatial variation of ψS can destroy superconductivity
Let
ik x
e 
 
 1
2
i k q x ik x
e e 
 
→ *
1  
 * 1
2
2
iqx iqx
e e  
   1 cosqx 
2
2 2
2
2
p
km
m
 
 

h
 
     
2
2
2 212
2 2
i k q x i k q xik x ik x
p
m dx e e k q e k e
m
 
   
       
 
h
 
2
2 21
2 2
k q k
m
    
 
h
 
/2
/2
2
1 cos sin
2
L
L
Lq
qx dx L
q
 

   
     
2
2 21
1 1
2 2
iqx iqx
dx k q e k e
m 
           

h
 
/2
/2
1
L
iq x
L
e dx

 
 
2
2
2
k kq
m
 
h
for q << k
 
2
. .
2
K E kq
m
 
h
37

38.  
2
. .
2
K E kq
m
 
h
→
2
0
2
gkq E
m

h
Critical modulation for destroying superC
is
Intrinsic coherence length:
2
0
2
F
g
k
mE
 
h
2
F
g
v
E

h
ξ in impure material is smaller than ξ0 . (built-in modulation)
ξ and λ depend on normal state mean free path length .
Impure sample:
0  l 0
L

 
l
L
 
l
→
ξ0 = 10 λL
Pure sample:
0  L  →
0
L

 
 
The ratio κ = λ/ξ is known as the Ginzburg–Landau parameter. It has
been shown that Type I superconductors are those with 0 < κ < 1/√2,
and Type II superconductors those with κ > 1/√2.
38

39. 39

40. Definition of London penetration depth: The London
penetration depth is the distance inside the surface of a
superconductor at which the magnetic field reduces to 1/e times
its value at the surface.
The London penetration depth depends strongly on the
temperature and becomes much larger as T approaches critical
temperature Tc. The relation is
λl(T)/ λl(0)= [1 – T/Tc)4]-1/2
where λl(T) and λl(0) are the London penetration depths at
temperature T kelvin and 0 k respectively.
We can estimate a value for λ by assuming that all of the free
electrons are superconducting. If we set ns = 1029 m−3, a typical
free electron density in a metal, then we find that it is of the order
a few nm.
40

41. Bardeen Cooper Schreiffer Theory
BCS theory requires:
(a) low temperatures - to minimise the number of
random (thermal) phonons (ie those associated
with electron-ion interactions must dominate)
(b) a large density of electron states just below EF
(the electrons associated with these states are
those that are energetically suited to form pairs)
(c) strong electron phonon coupling
BCS theory is an effective, all encompassing
microscopic theory of superconductivity from
which all of the experimentally observed results
emerge naturally
41

42. THE BCS THEORY
According to BCS theory, as an electron passes by positively charged ions
in the lattice of the superconductor, the lattice distorts. This in turn causes
phonons to be emitted which forms a trough of positive charges around
the electron. Before the electron passes by and before the lattice springs
back to its normal position, a second electron is drawn into the trough. It is
through this process that two electrons, which should repel one another,
link up and form Cooper pairs. The electron pairs are coherent with one
another as they pass through the conductor in unison. The electrons are
screened by the phonons and are separated by some distance. When one
of the electrons that make up a Cooper pair and passes close to an ion in
the crystal lattice, the attraction between the negative electron and the
positive ion cause a vibration to pass from ion to ion until the other
electron of the pair absorbs the vibration. The net effect is that the electron
has emitted a phonon and the other electron has absorbed the phonon. It
is this exchange that keeps the Cooper pairs together. It is important to
understand, however, that the pairs are constantly breaking and reforming.
Because electrons are indistinguishable particles, it is easier to think of
them as permanently paired. 42

43. THE BCS THEORY OF SUPERCONDUCTIVITY
BCS Theory suggests that superconductors have zero electrical
resistance below their critical temperatures because at such
temperatures the electrons pass unimpeded through the crystal
lattice and therefore lose no energy. The theory states that the
super current in a superconductor is carried by many millions of
bound electron pairs, called Cooper pairs. 43

44. BCS Theory of Superconductivity
BCS wavefunction = Cooper pairs of electrons k and –k (s-wave pairing)
Features and accomplishments of BCS theory :
• Attractive e-e interaction –U → Eg between ground & excited
states. (Frohlich interaction)
• Eg dictates HC , thermal & EM properties.
• –U is due to effective e-ph-e interaction.
• λ , ξ , London eq. (for slowly varying B ), Meissner effect, …
• Quantization of magnetic flux involves unit of charge 2e.
 
1
1.14 expC
F
T
U D


 
  
 
θ = Debye
temperature
U D(εF) << 1 :
 Higher ρ → Higher TC (worse conductor → better superconductor
 0 3.528g B CE k T
44

45. 45
BCS Theory contd..
Bardeen Cooper and Schrieffer derived two expressions that
describe the mechanism that causes superconductivity,
where Tc is the critical temperature, Δ is a constant energy
gap around the Fermi surface, N(0) is the density of states
and V is the strength of the coupling.
 
1
2 exp
0
D
N V

 
   
 
h
 
1
1.14 exp
0
B c Dk T
N V

 
  
 
h

46. • Experimental Support of BCS Theory
– Isotope Effects
– Measured Band Gaps
corresponding to Tcrit predictions
– Energy Gap decreases as Temp 
Tcrit
– Heat Capacity Behavior
46

47. 47
Ginzburg-Landau Theory
Ginzburg and Landau (G-L) postulated a Helmholtz energy
density for superconductors of the form:
where α and β are constants and ψ is the wavefunction. α
is of the form α’(T-TC) which changes sign at TC
High magnetic fields penetrate superconductors in units of
quantised flux (fluxons)!

48. Salient properties of superconductors:
Type I and type II superconductors are distinguished by
their behavior in a magnetic field.
In a type II S/C there are 2 critical fields.
At intermediate fields, the material has both
superconducting and normal regions
Electrodynamics of superconductors is described by
London equations
BCS theory – microscopic mechanism for
superconductivity through the formation of e-e Cooper
pairs via electron-phonon interaction.
A Cooper pair has a lower energy than 2 individual
electrons
48

49. Salient properties of superconductors:
 Superconductivity is observed usually only for those
metallic materials for which the number of valence
electrons lies between 2 and 8
 In the case of transition metals, the variation of Tc with
the number of valence electrons shows sharp maxima
for Z = 3, 5 and 7
 For a given Z, certain crystal structures are more
favourable than others. Ex β tungsten and α manganese
 The current in a superconductr persists for a very long
time (persistent currents)
 Monovalent metals are generally not superconductors
 Good conductors like copper at room temperature are
not superconductors, and superconducting materials are
not very good conductors at normal temperatures.
49

50. Salient properties of superconductors contd…:
Ferromagnetic and anti ferromagnetic materials are not
superconductors.
Bismuth antimony an tellurium become superconducting under high
pressure
Superconductivity occurs in materials having high normal resistivity.
The condition n ρ> 106 is a good criterion for the existence of
superconductivity where n is the number of valence electrons per c.c.
and ρ is the resistivity in electrostatic units at 20˚C.
The Meissner effect is the expulsion of a magnetic field from
a superconductor during its transition to the superconducting state.,
observed in 1933
 Superconductors in the Meissner state exhibit perfect diamagnetism,
or super diamagnetism, meaning that the total magnetic field is very
close to zero deep inside them .
The transition from superconducting state to the normal state is
observed to be a second order phase transition. In such a transition,
there is no latent heat but a discontinuity in the heat capacity
50

51. One other property of superconductors is that when two of them
are joined by a thin, insulating layer, it is easier for the electron pairs
to pass from one superconductor to another without resistance .
This is called the Josephson Effect. This effect has implications for
superfast electrical switches that can be used to make small, high-
speed computers.
51
The standard volt is now defined in terms of a Josephson junction
oscillator.
The oscillation frequency of a Josephson junction is given by
so the relationship between frequency and voltage across the
junction depends only upon the fundamental constants e and h. For
one microvolt applied to the junction the frequency is
The standard volt is now defined as the voltage required to produce a
frequency of 483,597.9 GHz.

52. Principle: persistent current in d.c. voltage
Explanation:
• Consists of thin layer of
insulating material placed
between two
superconducting materials.
• Insulator acts as a barrier to
the flow of electrons.
• When voltage applied
current flowing between
super conductors by
tunneling effect.
• Quantum tunneling occurs
when a particle moves
through a space in a
manner forbidden by
classical physics, due to the
potential barrier involved
52

53. DC Josephson Effect
1
2i T
t





h h 2
1i T
t





h h T = transfer
frequency
ji
j jn e

 
→ 11 1
1
1
1
2
n
i
t n t t
 

  
  
   
2i T  
2
1
in
i T e
n

 
22 2
2
2
1
2
n
i
t n t t
 

  
  
   
1i T  
1 1 2
1 1
1
2
n
i i T
n t t
 

 
  
 
2 1   
2 2 1
2 2
1
2
n
i i T
n t t
 

 
  
 
1
2
i
n
i T e
n

 
Real
parts:
1 2
1 1
1
sin
2
n n
T
n t n




2 1
2 2
1
sin
2
n n
T
n t n


 

Imaginar
y parts:
1 2
1
cos
n
T
t n



 

2 1
2
cos
n
T
t n



 

→
1
1 22 sin
n
T n n
t




1 2n n
t t
 
 
 
2
1 22 sin
n
T n n
t


 


 1 2
1 2
1 1
cosn n
t n n


 
     
1n
J
t


 → 0 sinJ J  n1  n2 → DC current up to iC while V =
0.
1 2 0n n    
53

54. AC Josephson Effect
11 1
1
1
1
2
n
i
t n t t
 

  
  
   
2 1
eV
i T i   
h
22 2
2
2
1
2
n
i
t n t t
 

  
  
   
1 1 2
1 1
1
2
i
n n eV
i i T e i
n t t n
 
   
  h
2 12
2 2
1
2
i
n n eV
i i T e i
n t t n
 
 
   
  h
Real
parts:
1 2
1 1
1
sin
2
n n
T
n t n




2 1
2 2
1
sin
2
n n
T
n t n


 

Imaginar
y parts:
1 2
1
cos
n eV
T
t n



  
 h
2 1
2
cos
n eV
T
t n



  
 h
→
1
1 22 sin
n
T n n
t



 1 2n n
t t
 
 
 
2
1 22 sin
n
T n n
t


 



0 sinJ J 
V across junction: 1
2 1i T eV
t

 

 

h h 2
1 2i T eV
t

 

 

h h 2q e 
1 2
eV
i T i   
h
1 2
1 2
1 1 2
cos
eV
n n
t n n


 
       h
AC current
with
1 2 0
2 eV
n n t    
h
0 0
2
sin
eV
J t
 
  
 h
2 eV
 
h
483.6 Mhz for V = 1 μV 54

55. Macroscopic Quantum Interference
Around closed loop enclosing flux
Φ:
2 s  
For B = 0, 2 1 2 1a a a b b b         
For B  0,
0b
e
c
   
h
2
b a
e
c
   
h
or 0a
e
c
   
h
tot b aJ J J  0 0 0sin sin
e e
J
c c
 
    
         
    h h
0 02 sin cos
e
J
c



h
periodicity = 39.5
mG Imax = 1 mA
periodicity = 16 mG
Imax = 0.5 mA
Junction area = 3 mm  0.5
mm
2
q
h c
 
2e
c
 
h
55

56. 56
To sum up,
The phenomenon in which the function permits current to
flow without any net loss of energy even if the p.d. across it
is zero, is called DC Josephson effect. It results from the
familiar tunneling phenomenon of quantum mechanics.
But, if we apply a dc voltage V across the junction the
result is an alternating current . i.e. a dc voltage generates
an oscillating current. The frequency of the oscillating
current is directly proportional to the voltage !
The frequency is given by
This is called AC Josephson effect.

57. Uses of Josephson devices
• Magnetic Sensors
• Gradiometers
• Oscilloscopes
• Decoders
• Analogue to Digital converters
• Oscillators
• Microwave amplifiers
• Sensors for biomedical, scientific and defence purposes
• Digital circuit development for Integrated circuits
• Microprocessors
• Random Access Memories (RAMs)
57

58. SQUIDS
(Super conducting Quantum Interference Devices)
58

59. Discovery: The DC SQUID was invented in 1964 by
Robert Jaklevic, John Lambe, Arnold Silver, and James
Mercereau of Ford Research Labs
Principle :
Small change in magnetic field, produces variation in the
flux quantum.
Construction:
The superconducting quantum interference device
(SQUID) consists of two superconductors separated by
thin insulating layers to form two parallel Josephson
junctions.
59

60. How it works
Phase change due to
external magnetic field
Current flow
Voltage
change
Due to B field Due to junctions Must be quantized
60

61. Types
Two main types of SQUID:
(1) RF SQUIDs have only one Josephson junction
(2)DC SQUIDs have two or more junctions.
more difficult and expensive to produce.
much more sensitive.
SQUIDs have been used for a variety of testing purposes
that demand extreme sensitivity, including engineering,
medical, and geological equipment. Because they
measure changes in a magnetic field with such
sensitivity, they do not have to come in contact with a
system that they are testing.
61

62. An area where superconductors can perform a life-
saving function is in the field of biomagnetism. Doctors
need a non-invasive means of determining what's going
on inside the human body. By impinging a strong
superconductor-derived magnetic field into the body,
hydrogen atoms that exist in the body's water and fat
molecules are forced to accept energy from the magnetic
field. They then release this energy at a frequency that
can be detected and displayed graphically by a
computer. Magnetic Resonance Imaging (MRI) was
actually discovered in the mid 1940's. But, the first MRI
exam on a human being was not performed until July 3,
1977. And, it took almost five hours to produce one
image! Today's faster computers process the data in
much less time.
62

63. 63
APPLICATIONS OF SUPERCONDUCTORs

64. Current Applications of Superconductors
• Superconducting magnets – NMR, MRI
• magnetic shielding devices
• superconducting quantum interference
devices (SQUIDS) used to detect extremely small changes in
magnetic fields, electric currents, and voltages.
• infrared sensors
• analog signal processing devices
• microwave devices
• Maglev trains
64

65. Emerging Applications
• power transmission
• superconducting magnets in generators
• energy storage devices
• particle accelerators
• levitated vehicle transportation
• rotating machinery
• magnetic separators
65

66. Maglev Train
The first MagLev train was developed in Japan in 1972 and Japan has been the leaders in
levitated transport since. In 1990, the Yamanashi MagLev test line opened and has been
operating ever since. The test line is an 18.4 km stretch of track that runs solely on the
technology of superconductors. The MagLev trains are much safer, faster and
environmentally friendly than their traditional counterparts. Japan is leading the way,
continually investing more money into the further research of levitated vehicles. The MagLev
trains that run on the Yamanashi test line have been clocked at speeds up to 581 km h-1. 66

67. Maglev Train
The train runs in a concrete guide way on sides of which there are three systems of copper
coils. One system serves for the train levitation, another one for the train propulsion, and
the third one for lateral stability in the guideway. The left figure demonstrates the
principle of the train levitation. The superconducting coils on the cars produce high
magnetic field of about 5 Tesla. At sufficiently high speed (above 130 km/h) this field
induces magnetic field in the stable copper coils on the bed sides that is high enough to
keep the train safely above the bottom. Below the critical speed the train is driven by a
conventional electrical motor and runs on rubber wheels. Electric current passing through
the copper coils on the ground produce alternating magnetic field that attracts the
superconducting magnets of the train and propells the train forward.
67

68. Potential Applications
 Strong magnetic fields → 50 Tesla
(without heating, without large power input)
 Logic and storage functions in computers
Josephson junction → fast switching times (~ 10 ps)
 Magnetic levitation (arising from Meissner effect)
 Power transmission
68

69. 69

70. SUPERFLUIDITY – helium ii – fountain effect
This phenomenon was first observed in helium at a
temperature below 2.17K. Helium at these low
temperatures was seen to flow quite freely, without any
friction, through any gaps and even through very thin
capillary tubes.
Once set in circular motion, it will keep on flowing forever
- if there are no external forces acting upon it.
Unlike all other chemical elements helium does not solidify
when cooled down near absolute zero. Physicists explain
this phenomenon by extremely weak attractive forces
between the almost "perfectly round" atoms and by their
rapid motion which is due to Heisenberg's Uncertainty
Principle
Bulk super fluid helium has many unusual properties - it
can flow up walls and through narrow pores without
resistance. Helium-4 and Helium-3 become super fluid
below 2.12 and 0.003 Kelvin respectively. However, only a
proportion of the Helium becomes super fluid at the
transition temperature. 70

71. 71
Helium II is a super fluid, a quantum mechanical state of matter with
strange properties.
 when it flows through capillaries as thin as 10−7 to 10−8 m it has no
measurable viscosity. However, when measurements were done
between two moving discs, a viscosity comparable to that of gaseous
helium was observed.
Current theory explains this using the two-fluid model for helium II. In this
model, liquid helium below the lambda point is viewed as containing a
proportion of helium atoms in a ground state, which are super fluid and
flow with exactly zero viscosity, and a proportion of helium atoms in an
excited state, which behave more like an ordinary fluid
The thermal conductivity of helium II is greater than that of any other
known substance, a million times that of helium I and several hundred
times that of copper
Helium II also exhibits a creeping effect. When a surface extends past
the level of helium II, the helium II moves along the surface, against the
force of gravity. Helium II will escape from a vessel that is not sealed by
creeping along the sides until it reaches a warmer region where it
evaporates. It moves in a 30 nm-thick film regardless of surface material.

72. 72

73. 73