Download Chapter_Superconductivity

Prof. Harvinder Kaur
Govt College for Girls
Outline
 Introduction
 Mechanism of Superconductors
 Meissner Effect
 Type I and Type II superconductors
 Characteristic
superconductors
properties
 BCS theory of Superconductivity
 Applications of Superconductivity
of
INTRODUCTION
For some materials, the resistivity vanishes at some low temperature:
they become superconducting.
Superconductivity is the ability of
certain
materials
to
conduct
electrical
current
with
no
resistance. Thus, superconductors
can carry large amounts of current
with little or no loss of energy
In July 1909, Heike Kamerlingh Onnes found that the resistance of mercury dropped suddenly to an
immeasurable small value when it is cooled below 4.2K. Onnes termed the new electrical state that
the mercury had entered the superconducting state.
PROPERTIES VIS-A-VIS
SUPERCONDUCTIVITY
Properties not affected :
 Elastic properties
 Thermal expansion behaviour
 Photoelectric properties
 Internal arrangement of crystal lattice as confirmed by X-ray diffraction pattern before and after
such a transition
Properties affected :
 Magnetic properties change
 Electrical properties : as the electrical resistivity tendo to zero at T=Tc
 All thermo electric effects disappear for T  Tc
 Specific heat shows a discontinuous change
 Some latent heat of transition may also be involved
 The transition in zero magnetic field from the superconducting state to the nornal state is not
exactly involving latent heat , though there is discontinuity in the heat capacity – temp2 graph
 Entropy shows a decrease for T  Tc
NON SUPERCONDUCTOR
SUPERCONDUCTOR
Bint = 0
Bint = Bext
MESSINER EFFECT
MEISSNER EFFECT : Meissner and Ochsenfeld discovered that when a
superconductor is cooled in a magnetic field to below the value of transition
temperature corresponding to that field, then the lines of magnetic induction
B are pushed out of the bulk superconductor.
TYPE I SUPERCONDUCTORS
Type I superconductors : These are superconductors which exhibit
Complete Meissner effect.
 There are 30 pure metals which exhibit
zero resistivity at
low temperature.
 They are called Type I superconductors
(Soft
Superconductors).
 The superconductivity exists only below
their critical temperature and below a
critical magnetic field strength.
Type I
Superconductors
Mat.
Be
Rh
W
Ir
Lu
Hf
Ru
Os
Mo
Zr
Cd
U
Ti
Zn
Ga
Tc (K)
0
0
0.015
0.1
0.1
0.1
0.5
0.7
0.92
0.546
0.56
0.2
0.39
0.85
1.083
Mat.
Gd*
Al
Pa
Th
Re
Tl
In
Sn
Hg
Ta
V
V
La
Pb
Tc
Nb
Tc (K)
1.1
1.2
1.4
1.4
1.4
2.39
3.408
3.722
4.153
4.47
5.38
6.00
7.193
7.77
9.46
TYPE II SUPERCONDUCTORS
Type II superconductors : These are superconductors which do not
exhibit Meissner effect strictly
 Starting in 1930 with lead-bismuth alloys, were found which exhibited
superconductivity; they are called Type II superconductors (Hard
Superconductors).
 They were found to have much higher critical fields and therefore could carry
much higher current densities while remaining in the superconducting state.
Type II
Superconductors
CHARACTERISTICS PROPERTIES OF A
SUPERCONDUCTOR : FACTOR AFFECTING
Temperature : If a ring made of superconducting material is cooled in a magnetic field from
ordinary temeprature to a value below its critical temperature and then the magnetic field is removed,
an induced current is set up in the ring. The resistance in the superconducting state being practically
zero, the decay of thie induced current will take infinitely long time.
Magnetic field : Application of magnetic field to a superconducting specimen brings a stage
when for H=Hc, the critical field, the superconductor behaves like a normal material i.e., the
superconductivity disappears.
Current : If the magnetic field around the superconductor is increased beyond the critical field the
superconductivity is destroyed and the sample behaves as a normal material. Therefore the
supercurrent will flow only up to its critical value .Once the field exceeds Hc(T) the current becomes just
the ordinary current.
Stress : Application of stress increases the transition temperature. As Hc(T) is temperature
dependent, increased stress is found to result in a slight change of Hc(T).
Size : Size of specimen exhibiting superconductivity is an important parameter for its behaviour.
Impurity : The presence of impurities changes almost all properties of a superconductor especially
its magnetic behaviour.
Isotopic Constitution of the Specimen : The critical temperature of a specimen
depends on the isotopic mass. The presence of various isotopes in a given specimen decided what its
average isotope mass will be. The dependence of Tc on such a mass is also called Isotope Effect.
MaTc = constant or Tc  M-1/2
THERMODYNAMICAL PROPERITES
OF SUPERCONDUCTING STATE
Entropy : Going from Normal state to superconducting state the entropy decreases, so the superconducting state
is more ordered than the normal state.
Specific Heat : The specific heat of the normal metal obeys the relation ship, Cn(T) =  T + βT3 where as for
the superconducting state the specific heat is Ces(T) = A exp (-/kβT) where A is some constant and  is
superconducting energy group which is equal to one half of the minimum value of energy for destroying a cooper
pair.
Energy Gap : The energy gap of superconductors is of entirely different nature than the energy gap in insulators.
In superconductor the energy gap is due to electron-electron interaction in fermi gas whereas in insulator or
semiconductor the energy gap is caused by electron lattice interaction. In insulators the gap prevents the flow of
electrical current. Energy must be added to lift electrons from the valence band to conduction band before the
current can flow. In a superconductor, on the other hand, the current flows despite the presence of energy gap . In
a superconductor the electrons in the excited state above the gap behave as normal electron. The transition in zero
magnetic filed from superconducting state to normal state is observed to be a second–order phase transition.
BCS THEORY OF SUPERCONDUCTIVITY
The microscopic theory put forward by Bradeen , Cooper and Schruffier (BCS) forms the
basis of quantum theory of Superconductivity. The fundamental postulate of BCS theory
is that when an attractive interaction between two electrons by means of phonon
exchange dominates the repulsive coulomb interaction then the superconducting state
is formed.
Electron-phonon-electron interaction : During an interaction of an electron with a positive ion
of the lattice through electrostatic coulomb force, some electron momentum get transferred. As
a result, these ions set up elastic wave in the lattice due to distortion. If another electron
happens to pass through this region then the interaction between two occurs which in its effect
lowers the energy of the second electron. The two electrons interact via the lattice distortion or
the phonon field resulting in the lowering of energy of the electron which implies the force
between two electrons is attractive. This interaction is strongest when two electrons have equal
and opposite moments and spin and this pair is known as cooper pair.
COOPER PAIR
When the temperature of the specimen is lowered, if the attractive
force between two electrons via a phonon exceeds coulomb repulsion
between them, then a weakly bound cooper pair is formed having the
binding energy of the order of 10-3 eV. The energy of Cooper pair is
less than the energy of the pair in free state. The binding energy of
cooper pair is called energy bang gap, Eg. When h  Eg strong
absorption occurs as the cooper pairs break apart.
The electrons in cooper pair have opposite spins so the total spin of
the pair is zero. As a result cooper pairs are bosons whereas electrons
are fermions.
APPLICATIONS OF SUPERCONDUCTIVITY
Superconductors are used to make the powerful electromagnets,
including those used in MRI machines, beam steering magnets used in
particle accelerators.
 Superconductors have also been used to make digital circuits and
microwave filter for mobile phone base stations.
 Promising future applications include high performance transformers,
power storage devices, electric power transmission, electric motors and
magnetic levitation devices.