SUPERCONDUCTIVITY

Certain metals, alloys and compounds exhibit zero resisitivity and hence infinite
conductivity at a temperature above 0 K. These materials are called as superconductors and
the phenomenon is known as Superconductivity

Critical Temperature : Temperature at which the resistivity of the material drops to zero is
called as Critical Temperature(Tc) or Transition temperature
Ex : Hg = 4.2 K , Pb = 7.2 K, Nb = 4.5 K , Yitrium Barium Copper Oxide = 92 K etc
Meisner Effect (Effect of Magnetic field)
Statement : “When the weak magnetic field is applied to the superconducting material and
then cooled below the critical temperature, then magnetic flux will be expelled out of the
superconductor”
Thus the super conductor show perfect diamagnetism

B =0

We have the magnetic field inside the specimen

B = 0 ( H + M )
H = Applied magnetic field and
 M = Magnetisation in the specimen
According to Meisner effect, when the specimen is in superconducting state, it has B = 0

Thus H = -M  Magnetic susceptibility = (M/H) = -1. This is the indication for a perfect
diamagnetic material
Critical field OR Critical Magnetic field
It is defined as the magnetic field required to switch the material from superconducting state
to normal state and is denoted by HC
When once the applied magnetic field is removed, the material will regains its
superconducting property, provided T < Tc
Thus the material will remains in the superconducting state below HC and , above HC the
material will be in the normal state
Temperaturedependence of critical magnetic field HC :
• Magnitude of HC depends on temperature

• If H0 the critical magnetic field at T = 0 K and HC the critical magnetic field at T0K,
then

It can be seen that

 The curve of HC v/s T is almost parabolic

 If the superconductor is held at 0 K, then
higher magnetic field is required to destroy the superconducting property
 When the temperature of the superconductor is close to TC, then lesser magnetic
field is sufficient to destroy the superconducting property.

Types of Superconductors
• The Classification is based on the response shown by the super conductors in the
applied magnetic field
• The response curve of magnetisation v/s applied magnetic field show a different
nature of variation for different category of superconductors
• This classification provides useful information for the selection of superconductors in
the development of high field magnets
Type -1 superconductors (Soft superconductors):
• They exhibit complete Meisner effect
• Material in the superconducting state retains its diamagnetic nature, until the critical
 field is reached
• Once the critical field is reached, the material suddenly loses superconducting
property.
• Here onwards the flux starts penetrating the specimen
• These superconductors have low critical magnetic field.
• They are not useful for the construction of superconducting magnets
Ex : Hg, Pb, Nb, Sn etc

Response of Type1 superconductor against applied magnetic field

Type -2 Superconductors (Hard Superconductors):

• They do not exhibit complete Meisner effect
• They are characterised by two critical magnetic fields namely lower critical field HC1
and upper critical field HC2.
• For the applied field less than HC1 the magnetic field is completed expelled out of
the superconductor and it behaves as perfect diamagnetic.
• When the field is greater than HC1 and less than HC2, the flux starts penetrating the
specimen. In this region, the material is not perfect diamagnetic, but still retains zero
resistance. Hence it is called as mixed state or vortex state.
• When the applied field exceeds HC2, all the flux will penetrates the specimen and the
material becomes a normal conductor.
Ex : - Compounds like Y-Ba-Cu-O, Bi-Sr-Ca-Cu-O etc

Response of Type2 superconductor against applied magnetic field

 Difference between Type 1 and type 2 superconductors
Type 1 Type 2

1. Exhibits complete Meisner effect 1. Exhibits partial Meisner effect

2. Only one Critical field 2. Two critical fields namely lower and upper

3. No vortex state is present 3. Vortex state is present

4. Low critical temp. (<10K) 4. High critical temp (>10K)

5. Low critical magnetic field 5. High critical magnetic field

6. Cannot be used to prepare 6. Can be used to prepare high field magnets

high field magnets

BCS Theory of Superconductivity

• It is a quantum mechanical theory to explain superconductivity. According to this
theory, Superconductivity is due to the formation of cooper pairs
• “Cooper pairs are the pair of electrons formed by the interaction between electrons
with opposite spin and momentum in a phonon field”.
• Flow of current in a superconductor causes attraction between electron and positive
ions. Due to this, the positive ion gets displaced from its position.
• When a second electron reaches this distorted position, it also experience attractive
force.
• Thus we have attraction between two electrons takes place via lattice.
• This pair of electrons forms cooper pair.
• In a given superconductor,each cooper pair causes the formation of many number of
such pairs, causing the formation of cloud of cooper pairs
• Due to the orderly motion of these cooper pairs in group, and less collision with the
lattice, large current is produced.
• when the temperature exceeds Tc, there is no formation of cooper pairs and the
superconductivity destroys
High TemperatureSuperconductors

• Super conductors that exhibit high Tc are called as High temperature

superconductors
• Generally, those superconductors that can work at liquid Nitrogen temperature
(above 77K) are classified under High Tc superconductor.
• They are oxides of copper bearing pervoskite crystal structure
• Ex : Barium copper oxide, Yttrium barium copper oxide etc
• Recently developed high Temperaturesuperconductors are from ceramics
compounds
• All the high temperature superconductors are classified under Type 2, since they
have higher critical magnetic fields.
Quantum Tunnelling
• It is a quantum mechanical phenomenon in which an object such as an electron or
atom passes through a potential energy barrier. This concept is not
possible, according to classical mechanics
• Tunneling is a outcome of wave nature of matter and is found in low mass particles
like electrons, protons etc
• Probability of transmission of a wave packet through a barrier decreases
exponentially with the barrier height. When the quantum wave reach the barrier, its
amplitude will decrease exponentially

(E the energy of the particle and V the potential energy of the barrier)

Josephson Junction
• A Josephson junction is made by sandwiching a thin layer of a non superconducting
material between two layers of superconducting material. The non superconducting
barrier separating the two superconductors must be very thin.
• If the barrier is an insulator, it must be about 30 angstroms thick or less. If the barrier
is another metal , it can be as much as several nanometer thick.
• In this system, the cooper pairs tunnel through the barrier without resistance
• This phenomenon of flow of current between two pieces of superconductor
separated by a normal material is called as Josephson effect and the current is called
Josephson current. The current flows through the junction even in the absence of
 external DC voltage. Hence the Josephson current is present in the absence of supply
voltage
• If the external DC voltage is applied, current oscillates rapidly with a frequency of
several GHz, leading to the development of AC voltage.
DC Josephson Effect

• It is the phenomenon of flow of super current through the junction even in the
absence of external emf . If the voltage across the junction is measured, it gives zero.
• Consider a Josephson junction containing two superconducting films separated by
thin oxide layer. Here cooper pairs in the superconductor starts tunneling through the
oxide layer which are represented by wave function.
• During this process the oxide layer introduces the phase difference between input
and output wave functions.
• Due to this, super current flow through the junction, even in the absence of external
source.
• The super current through the junction is

Is = Ic sin 0

Ic = critical current at zero voltage, which depends on the thickness of the

junction layer and the temperature, 0 = Phase difference between the
wave functions of cooper pairs

AC Josephson Effect

 When dc voltage is applied across the Josephson junction, it leads to the

development of oscillating current. In other words an alternating emf of high
frequency is established across the junction. This effect is called as AC Josephson
effect.
• The oscillating current is because of the fact that, the application of dc voltage across
the junction causes the additional phase change for the cooper pairs
• The energy difference of cooper pairs on both sides is of the order of 2eV
• Thus the current

Is = Ic sin (0 +Δ)

Δ = phase difference, Ic is the critical current

The frequency of the generated AC is

f = 2eV / h
• Where 2eV is the energy difference between the cooper pairs on either side of the
junction
 Thus if a voltage of if a voltage of about 1V is applied, and AC frequency of about
484 MHz can be obtained.
SQUIDS
• Stands for Super conducting Quantum Interference Device
• It is an instrument used to measure extremely weak magnetic field of the order of
10-13 T

• Hence it is a sensitive magnetometer

• Heart of the SQUID is a super conducting ring containing one or more Josephson
junctions
• Two types of SQUIDS are available namely DC SQUID and RF SQUID.
• It works on the principle of Josephson effect
DC SQUID
It has two Josephson junctions connected in parallel and works on the interference of
current from two junctions. It works on the principle of DC Josephson effect which is
the phenomenon of flow of super current through the junction even in the absence
of external emf.
Construction and Working :

• The cross
sectional view of the
arrangement is shown
• P and Q are two
Josephson Junctions
arranged in parallel
• When current I flows through the point C, it divides into I1 and I2

Cross Sectional View

• Hence the wave function due to these super currents (cooper pairs) experience
a phase shift at P and Q
• In the absence of applied magnetic field, the phase difference between the wave
functions is zero. If the magnetic field is applied perpendicular to the current loop,
then phase difference between the wave functions will not be zero. This is identified
by the sum of the currents I1’ and I2’
• The magnitude of phase difference is proportional to applied magnetic field.
Hence, Even if there is a weak magnetic field in the region will be detected.

RF SQUID
• It works on the principle of AC Josephson effect - When dc voltage is applied across
the Josephson junction, it leads to the development of oscillating current.
• It has single Josephson Junction
• Magnetic field is applied perpendicular to the
plane of the current loop.
• The flux is coupled into a loop containing a
single Josephson Junction through an input coil
and an RF source. Hence when the RF current
changes, there is corresponding change in
the flux linked with the coil
• This variation is very sensitive and is
measured.
• It is also used in the detection of low magnetic field
• It is less sensitive compared to DC Squid
• Due to its low cost manufacturing, it is commonly used SQUID in many applications.