SUPERCONDUCTING PROPERTIES

Introduction
 Superconductivity is a state of matter exhibited usually at very low temperatures
where the resistivity of the material drops to zero.
 The superconducting state is influenced by temperature, current and magnetic field.
There exist critical values for these three parameters, above which the material
passes into normal state.
 Besides being of immense theoretical interest, the phenomenon has many possible
practical applications.
 Good superconducting materials like zinc and lead are not good electrical
conductors. Good electrical conductors like copper and gold are not good
superconductors.
 Addition of impurities destroys the superconducting property.
 A normal conductor is brought into a superconducting state by increasing its
pressure.
 Superconductivity was strictly a low temperature phenomenon till 1980’s, when
certain ceramic materials were found to exhibit superconductivity at higher
temperatures of about 120 K.

Superconductivity:
 H.K.Onnes was verifying the behaviour of metals at
very low temperatures and in 1911, he discovered
that the electrical resistance of highly purified
mercury dropped abruptly to zero at a temperature
of 4.15 K.
 The sudden drop in resistivity was quite unexpected
and Onnes recognized it to be an entirely new
phenomenon.
 Onnes also found that the transition was reversible.
When heated above the transition temperature 4.15
K, mercury regained its resistivity. Onnes named the
phenomenon as superconductivity.
 Subsequently, superconductivity was discovered in
lead, zinc, aluminium, and other metals as well as in a
number of alloys.
 Superconductivity is the phenomenon in which
electrical resistance of materials suddenly
disappears below a certain temperature. The
materials that exhibit superconductivity and which
are in the superconducting state are called
superconductors.
 Transition temperature
The temperature at which a normal material
abruptly changes into a superconductor is called
transition temperature or critical temperature TC.
 In a superconducting material at transition temperature, the following changes are
observed.
The electrical resistivity drops to zero.
The magnetic flux lines are expelled from the material.
There is a discontinuous change in the specific heat.
Further, there are also small changes in the thermal conductivity and the
volume of the materials.

Properties of Superconductors

1. Critical Temperature
 When a superconducting material is cooled below a certain temperature, it
goes into the superconducting state from normal state. The temperature at
which a material in normal state goes into superconducting state is known as the
critical temperature, TC.
 Different materials have different critical temperatures. The transition is
reversible. When the temperature of the material is increased above the critical
temperature, it passes into the normal state.
 A rearrangement of conduction electrons takes place leading to an increase in
the order at the transition from normal to superconducting state similar to the
case of thermodynamic phase transition, in which arrangement of atoms
increases at the transition of a material from liquid to solid state.
 The superconducting transition is sharp for a chemically pure and structurally
perfect specimen while the transition range is broad for specimens which are
structurally imperfect or which contain impurities.
2. Zero Electrical Resistance
 A super conductor is characterized by zero electrical resistivity. It is not
fundamentally possible to test experimentally whether the resistance is zero. A
method devised by Onnes consists of measuring the decrease of the current in a
closed ring of superconducting wire.
 The superconducting ring is kept in a magnetic field and it is cooled to below
the critical temperature so that it goes into the superconducting state. When the
external magnetic field is switched off, a current is induced in the ring.
 If the ring had a finite resistance, R, the current circulating in the ring would
decrease according to the equation
–
Where L is inductance of the ring
 The decay current is monitored by a change in the magnetic flux through a test
coil held close to the superconducting ring. Any change in the magnetic flux of
the superconducting ring will induce an emf in the test coil.
 Careful measurements established that the resistivity of superconductors could
be taken as zero.
3. Persistent Current
 Once a current is started in a closed loop of superconducting material, it will
continue to keep flowing, of its own accord, around the loop as long as the loop
is held below the critical temperature, Such a steady current, which flows
without diminishing in strength, is called a persistent current.
  The persistent current does not need external power to
maintain it because there do not exist I2R losses.
Calculations show that once the current flow is
initiated, it persists for more than 105 years. Persistent
current is one of the most important properties of a
superconductor.
 Superconductor coils with persistent current flowing
through them produce magnetic fields and can
therefore act as magnets. Such a superconducting
magnet does not require power supply to maintain its magnetic field.
4. Critical Magnetic Field
 Superconducting state depends on the strength of the magnetic field in which
the material is placed. Superconductivity vanishes if a sufficiently strong
magnetic field is applied.
 The minimum magnetic field, which is necessary to regain the normal
resistivity, is called the critical magnetic field, HC.
 When the applied magnetic field exceeds the critical value HC, the
superconducting state is destroyed and the material goes into normal state. The
value of HC varies with temperature.
 At temperatures below TC,
in the absence of
magnetic field, the
material is in
superconducting state.
When a magnetic field is
applied and as its strength
reaches the critical value
HC, the superconductivity
in the material disappears.
 At any temperature T < TC
the material remains
superconducting until a
corresponding critical
magnetic field is applied.
When the magnetic field exceeds the critical value, the material goes into
normal state.
 The critical field required to destroy the superconducting state decreases
progressively with increasing temperature. The dependence of critical field on
temperature is governed by the following relation.
 When T>TC Normal State
 When T<TC Superconducting State H<HC
 Normal State H> HC
 The dependence of critical field on temperature is governed by

[ ]

Where HC (0) is the critical field at 0 K.

5. Critical Current Density
 The critical magnetic field required to destroy superconductivity need not be
necessarily applied externally.
 The application of a large value of electric current to a superconducting
material destroys the superconducting property. Let i be the current flowing
through the wire.
 The application of
the current induces
a magnetic field.
Thus, the induced
magnetic field in the conductor destroys the superconducting property.
 The induced critical current (Ic) required to destroy the superconducting
property is given by IC = 2πrHc
Where Hc is the critical magnetic field required
r the radius of the superconductor
 The maximum current density at which the superconductivity disappears is
called the critical current density, JC.
 For any value of J < JC, the current can sustain itself whereas for values J > JC,
the current cannot sustain itself. This effect was observed in 1916 by Silsbee and
is known as Silsbee effect.

 The maximum current that a

superconductor can carry
decreases as the temperature
is raised and falls to zero at
the transition temperature of
the material. Since the critical
current falls with
temperature, the critical
magnetic field will also
decrease as the transition
temperature is approached.
6. Perfect Diamagnetism (Meissner Effect)
 In 1933 W.Hans Meissner and Robert Ochsenfeld found that when
superconductors are cooled below their critical temperature in the presence of
a magnetic field, the magnetic flux is expelled from the interior of the specimen
and the superconductor becomes a perfect diamagnetic.
 This phenomenon is known as Meissner effect.
 Meissner and Ochsenfeld found that as the temperature of the specimen is
lowered to TC, the magnetic flux is suddenly and completely expelled from it.
The flux expulsion continues for T < TC. The effect is reversible.
 When the temperature is raised from below TC, the flux suddenly penetrates
the specimen at T = TC and the material returns to the normal state.
 The specimen is therefore diamagnetic and the state in which magnetization
cancels the external magnetic field completely is referred to as perfect
 diamagnetism.
 The essential properties of superconductivity
1. Zero resistivity
2. Perfect Diamagnetism (Meissner Effect)

For perfect diamagnetism B= 0

So, B = μ0(H+M) = 0 = H+M=0 =.> M= -H
So, χ = −1
μr = 0
7. Effect of Pressure
 When we apply high pressure the transition temperature TC also increases, so if
by increasing the pressure on the material the critical temperature for which the
material makes transition into superconducting state can be increased.
 Additional to this, Certain materials are brought into the superconducting state
by increasing the pressure.
 For example, cesium is a normal conductor at atmospheric pressure. While
increasing the pressure of Cs, it is converted into a superconductor at 110 kbar
(Tc = 1.5 K).
8. Isotopic Effect
 In 1950, C.A.Reynolds and E.Maxwell found that the critical temperature
decreases with increasing isotopic mass M. The variation is given by the
relation.
–

Where is constant whose value is ½ and M is Molecular weight

9. Variation in Heat Capacity
 The transition of a metal from its normal state to superconducting state does not
involve a change of crystallographic structure. It is only a thermodynamic phase
transition where the specific heat changes discontinuously at the transition
temperature TC.
 The specific heat of a normally conducting metal is composed of a lattice part
and an electronic part. The electronic contribution varies smoothly at low
temperatures.
  In superconductors it is found that the electronic part decreases exponentially

Type-I and Type-II superconductors

 Superconductors are classified into two types. They are type I superconductors
and type II superconductors. Type I superconductors are known as soft
superconductors and type II superconductors are known as hard
superconductors.
Type-I Superconductors
 In type I superconductors, the transition from superconducting state to normal
state in the presence of magnetic field occurs sharply at the critical value of HC.
 Type I superconductors are perfectly diamagnetic below HC and completely
expel the magnetic field from the interior of the superconducting phase.
 Ex-Sn Hg, Nb, V, C0.1 T0.3 V0.6

Characteristics
They are perfectly diamagnetic and exhibit complete Meissner effect.
They have only one critical field. At the critical field the magnetization drops
to zero.
The maximum critical field for type I superconductor is of the order of 0.1
Wb/m2.
The transition at HC is reversible. Below HC the material behaves as a
superconductor, and above HC it behaves as a normal conductor.

Type-II Superconductors
 In type II superconductor, the magnetic field is expelled out of the material and
the material loses its superconducting property gradually rather than abruptly.
 Type II superconductors are characterized by two critical fields HC1 and HC2.
 The transition from superconducting state to normal state occurs gradually as the
magnetic field is increased from HC1 to HC2.
 At HC1 the magnetic field lines begin penetrating the material. At the upper
critical field HC2 superconductivity completely vanishes.
 Ex- Nb3 Sn, Nb3 Ge, YBa2 Cu3 O7

Characteristics
They have two critical magnetic fields, HC1 and HC2.
The material is perfect diamagnetic below the lower critical field, HC1.
Meissner effect is complete in this region. Above the upper critical field,
HC2, magnetic flux enters the specimen.
Above HC1 they do not show complete Meissner effect and therefore do
not behave as perfect diamagnetic materials.
They exist in an intermediate state in between the critical fields, HC1 and
HC2. The intermediate state is a mixture of the normal and
superconducting states, magnetically but electrically the material is a
superconductor.
At HC2 the magnetization vanishes and the specimen returns to normal
conducting state.
The upper critical field is very high and is of the order of 30 Wb/m2.
 S.No. Type-I Superconductors Type-II Superconductors
They do not exhibit complete Meissner
1 They exhibit complete Meissner effect
effect
They show perfect diamagnetic They do not show perfect diamagnetic
2
behaviour behaviour
They have two critical magnetic fields,
They have only one critical magnetic
3 lower critical magnetic field, HC1 and
field, HC
upper critical magnetic field, HC2
There is no mixed state or
Mixed state or intermediate state is
4 intermediate state in case of these
present in these materials
materials
The material loses magnetization The material loses magnetization
5
abruptly gradually
Highest value for HC is about 0.1 Upper critical field is of the order of 30
6
Wb/m2 Wb/m2
They are known as soft They are known as hard
7
superconductors superconductors
Nb-Sn, Nb-Ti, Nb-Zr, Va-Ga are
8 Lead, tin, mercury are examples
examples

BCS theory
 In 1957, the American physicists J. Bardeen, L.N. Cooper and J.R. Schrieffer
developed the quantum theory of superconductivity, which came to be known as
BCS theory.
 This theory involves the electron interaction through phonon as mediators.
 The main idea behind the BCS theory is the experimental results of the two
effects, namely, isotope effect and variation of specific heat with temperature.
 It successfully explained the effects like zero resistivity, Meissner effect etc.
 A phonon is a quantum mechanical description of an elementary vibration motion
in which a lattice of atoms or molecules uniformly oscillates at a single frequency.
 The two principal features of BCS theory are
 Electrons form pairs, called Cooper pairs, which propagate
throughout the lattice
 Such propagation is without resistance because the electrons move
in resonance with phonons.
 If we consider two electrons, when they get very close to each other in the
region between ions, they repel each other due to Coulomb force.
 The electron is repelled from other electrons due to their negative charge, but it
also attracts the positive ions that
make up the rigid lattice of the
metal.
 This attraction distorts the ion
lattice, moving the ions slightly
toward the electron, increasing the
positive charge density of the lattice in the vicinity.
 This positive charge can attract other electrons. At long distances, this attraction
between electrons due to the displaced ions can overcome the electrons'
repulsion due to their negative charge, and cause them to pair up.
 The rigorous quantum mechanical explanation shows that the effect is due to
electron–phonon interactions.
 In an equilibrium condition, a balance between attraction and repulsion is
established and the two electrons combine to form a Cooper pair.
 In a typical superconductor, the dense cloud of Cooper pairs forms a collective
state and the motion of all the Cooper pairs is correlated.
 As such the pairs drift cooperatively through the material. Thus, the
superconducting state is an ordered state of the conduction electrons.
 Since the density of Cooper pairs is very high, even large currents require only
a small velocity. The small velocity of ordered Cooper pairs minimize collision
processes and leads to zero resistivity.
 When an electron of wave vector k
emits a virtual phonon, which
absorbed by k1, then the wave vector
is scattered as K–q and K1+q
 Thus, for attractive interaction, the
wave vector and spin are represented
as K↑and K↓.

Applications of superconductors
The most obvious application of superconductors is in power transmission. If the
national grid were made of superconductors rather than aluminium, then the
savings would be enormous.
Superconducting coils in transformers and electrical machines generate much
stronger magnetic fields than magnetic circuits employing ferromagnetic
materials produce. The normal eddy current losses and hysteresis losses will
not be present in superconducting devices and hence the size of motors and
generators will be drastically reduced.
Superconducting solenoids produce very strong magnetic fields. They are small
in size and are less cumbersome. They do not need either large power supplies
or the means of removing heat.
Type II superconductors can be used as very fast electronic switches due to the
way in which a magnetic field can penetrate into the superconductor.
Cryotrons: The application of a magnetic field greater than its critical magnetic
field changes the superconducting state of a superconducting material to
normal state and removal of the field brings the material back from normal state
to the superconducting state. This fact is used in developing cryotron switches.
MagLev Trains: The most spectacular application would be the so-called
‘MagLev’ trains. The coaches of the train do not slide over steel rails but float on
a four inch air cushion above the track using superconducting magnets; this
eliminates friction and energy loss as heat, allowing the train to reach high
speeds of the order of 500 km/hr. Such magnetic levitation trains would make
train travel much faster, smoother, and more efficient due to the lack of friction
between the tracks and train.
A superconducting quantum interference device (SQUID) is a device used to
measure extremely weak magnetic flux. Thus, it is basically a sensitive
magnetometer. The heart of a SQUID is a superconducting ring, which contains
one or more Josephson junctions.