Superconductivity

Course: B.Tech

Subject: Engineering Physics

Unit: III

Chapter: 2

Introduction of superconductivity

• Electrical resistivity ↓ Temp. ↓

• 0 º K Electrical resistivity is 0 for perfectly pure

metal

• Any metal can’t be perfectly pure.

• The more impure the metal Electrical resistivity ↑

• Certain metals when they cooled their electrical

resistivity decreases but at Tc resistivity is 0 this

state of metal is called __________.

• Finder – K Onnes 1911

Properties of Superconductors

Electrical Resistance

• Zero Electrical Resistance

• Defining Property

• Critical Temperature

• Quickest test

• 10-5Ωcm

1

Effect of Magnetic Field

Critical magnetic field (HC) –

Minimum magnetic field

required to destroy the

superconducting property

at any temperature

H0 – Critical field at 0K

T - Temperature below TC

TC - Transition

Temperature

Element HC at 0K

(mT)

Nb 198

Pb 80.3

Sn 30.9

Superconducting

Normal

T (K) TC

H0

HC

2

0 1C

C

TH H

T

Effect of Electric Current

• Large electric current – induces magnetic field – destroys superconductivity

• Induced Critical Current iC = 2πrHC

Persistent Current

• Steady current which flows through a superconducting ring without any decrease in strength even after the removal of the field

• Diamagnetic property

i

Meissner effect

• When Superconducting material cooled bellow its Tc it

becomes resistenceless & perfect diamagnetic.

• When superconductor placed inside a magnetic field in

Tc all magnetic flux is expelled out of it the effect is

called Meissner effect.

• Perfect diamagnetism arises

from some special magnetic

property of Superconductor.

2

• If there is no magnetic field inside the superconductor

relative permeability or diamagnetic constant μr =0.

• Total magnetic induction B is,

• If magnetic induction B=0 then,

0 ( )B H M

00 ( )H M

M H

1 m

M

H

Magnetic Flux Quantisation

• Magnetic flux enclosed in a superconducting ring =integral multiples of fluxon

• Φ = nh/2e = n Φ0 (Φ0 = 2x10-15Wb)

Effect of Pressure

• Pressure ↑, TC ↑

• High TC superconductors – High pressure

Thermal Properties

• Entropy & Specific heat ↓ at TC

• Disappearance of thermo electric effect at TC

• Thermal conductivity ↓ at TC – Type Isuperconductors

Stress

• Stress ↑, dimension ↑, TC ↑, HC affected

Frequency

• Frequency ↑, Zero resistance – modified, TC not affected

Impurities

• Magnetic properties affected

Size

• Size < 10-4cm – superconducting state modified

General Properties

• No change in crystal structure

• No change in elastic & photo-electric properties

• No change in volume at TC in the absence of magnetic field

Isotope Effect

• Maxwell

• TC = Constant / Mα

• TC Mα = Constant (α – Isotope Effect coefficient)

• α = 0.15 – 0.5

• α = 0 (No isotope effect)

• TC√M = constant

Classification & characterization of super

conductor

• Type I or soft super conductor

– Exhibit complete Meissner effect.

– Bellow Hc super conductor above Hc Normal

– Value of Hc is order of 0.1 T.

– Aluminum, lead & Indium are type I super conductor

– Not used as strong electromagnets

3

• Type II or Hard super conductor

– Exhibit complete Meissner effect bellow a certain

critical field Hc1 at this point diamagnetism &

superconductivity ↓. This state is mix state called

vortex state.

– At certain critical field Hc2 superconductivity

disappears.

– Niobium, Aluminum, silicon, ceramic are type II

superconductors.

– Pb is type I superconductor ac Hc =600 gauss at 4º K

when a small impurity of In is added it becomes type

II superconductor with Hc1 =400 gauss & Hc2 =1000

gauss.

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

London equation

• According to London’s theory there are two type of

electrons in SC

– Super electrons

– Normal electrons

At 0º K there are only Super electrons.

With increasing temp. Super electrons ↓ Normal electrons

↑ .

Let nn, un & ns, us are no. density & drift velocity of

normal electrons & super electrons respectively.

Equation of motion of Super electrons under

electric field is

• Now current & drift velocity are related as

sdum eE

dt

2

( )

s s s

s s s

s

s

s

s

s

s s

I n eAu

J n eu

Ju

n e

Jd

n eeE

dt

n e Ed J

dt m

London's first equation

• London's first equation gives absence of

resistance. If E =0 then

• Now from Maxwell's eqns

0sdJ

dt

( )

d BE

dt

B A

d AE

dt

d AE

dt

d AE

dt

2

2

2

2

2

2

( )

( )

s s

s

s

s

s

s

s

s

s

ss

n e Ed J

dt m

d J mE

dt n e

d J m d A

dt n e dt

d m d AJ

dt n e dt

mJ A

n e

n eJ A

m

London's second equation

• Again from ampere Law

Take curl on both sides

0

2

0 ( )

s

s

B J

n eB A

m

2

0

2

22

0

( )

&

( )

s

s

n eB A

m

Now

B B B A B

n eB B B

m

A B

22

0

2

0 2

2

2

2

2

( ) 0

1

1

10

s

s

So B A

n eB B

m

n eAssume

m

B B

or

B B

λ is called London penetration depth

Elements of BCS Theory

• BCS Theory of Superconductivity

• The properties of Type I superconductors were modeled

successfully by the efforts of John Bardeen, Leon Cooper, and

Robert Schrieffer in what is commonly called the BCS theory.

• A key conceptual element in this theory is the pairing of

electrons close to the Fermi level into Cooper pairs through

interaction with the crystal lattice.

• This pairing results form a slight attraction between the

electrons related to lattice vibrations; the coupling to the

lattice is called a phonon interaction.

• Pairs of electrons can behave very differently from single

electrons which are fermions and must obey the Pauli

exclusion principle.

• The pairs of electrons act more like bosons which can

condense into the same energy level.

• The electron pairs have a slightly lower energy and leave

an energy gap above them on the order of 0.001eV which

inhibits the kind of collision interactions which lead to

ordinary resistivity.

• For temperatures such that the thermal energy is less than

the band gap, the material exhibits zero resistivity.

• Bardeen, Cooper, and Schrieffer received the Nobel

Prize in 1972 for the development of the theory of

superconductivity.

• Cooper Pairs

• The transition of a metal from the normal to the

superconducting state has the nature of a condensation of

the electrons into a state which leaves a band gap above

them.

• This kind of condensation is seen with super fluid helium,

but helium is made up of bosons -- multiple electrons can't

collect into a single state because of the Pauli exclusion

principle.

• Froehlich was first to suggest that the electrons act as pairs

coupled by lattice vibrations in the material.

• This coupling is viewed as an exchange of phonons,

phonons being the quanta of lattice vibration energy.

• Experimental corroboration of an interaction with the

lattice was provided by the isotope effect on the

superconducting transition temperature.

• The boson-like behavior of such electron pairs was

further investigated by Cooper and they are called

"Cooper pairs".

• The condensation of Cooper pairs is the foundation of

the BCS theory of superconductivity.

4

• In the normal state of a metal, electrons move

independently, whereas in the BCS state, they are bound

into "Cooper pairs" by the attractive interaction. The

BCS formalism is based on the "reduced" potential for

the electrons attraction.

• You have to provide energy equal to the 'energy gap' to

break a pair, to break one pair you have to change

energies of all other pairs.

• This is unlike the normal metal, in which the state of an

electron can be changed by adding a arbitrary small

amount of energy.

• The energy gap is highest at low temperatures but does

not exist at temperatures higher than the transition

temperature.

• The BCS theory gives an expression of how the gap grows

with the strength of attractive interaction and density of

states.

• The BCS theory gives the expression of the energy gap

that depends on the Temperature T and the Critical

Temperature Tc and is independent of the material:

APPLICATIONSOF

SUPER CONDUCTORS

1. Engineering

• Transmission of power

• Switching devices

• Sensitive electrical instruments

• Memory (or) storage element in computers.

• Manufacture of electrical generators and transformers

2. Medical

•Nuclear Magnetic Resonance (NMR)

•Diagnosis of brain tumor

•Magneto – hydrodynamic power generation

JOSEPHSON

DEVICES

by Brian Josephson

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 tunnelling occurs when a particle moves through a space in a manner forbidden by classical physics, due to the potential barrier involved

5

Components of current

• In relation to the BCS theory (Bardeen Cooper

Schrieffer) mentioned earlier, pairs of electrons move

through this barrier continuing the superconducting

current. This is known as the dc current.

• Current component persists only till the external

voltage application. This is ac current.

Josephson junctions

• A type of electronic circuit

capable of switching at very

high speeds when operated at

temperatures approaching

absolute zero.

• Named for the British

physicist who designed it,

• a Josephson junction exploits

the phenomenon of

superconductivity.

6

Construction• A Josephson junction is made

up of two superconductors, separated by a nonsuperconducting layer so thin that electrons can cross through the insulating barrier.

• The flow of current between the superconductors in the absence of an applied voltage is called a Josephson current,

• the movement of electrons across the barrier is known as Josephson tunneling.

• Two or more junctions joined by superconducting paths form what is called a Josephson interferometer.

7

Construction :

Consists of

superconducting

ring having

magnetic fields of

quantum

values(1,2,3..)

Placed in between

the two Josephson

junctions

8

Explanation :

• When the magnetic field is applied perpendicular to

the ring current is induced at the two junctions

• Induced current flows around the ring thereby

magnetic flux in the ring has quantum value of field

applied

• Therefore used to detect the variation of very minute

magnetic signals

Uses of Josephson devices

• Magnetic Sensors

• Gradiometers

• Oscilloscopes

• Decoders

• Analogue to Digital converters

• Oscillators

• Microwave amplifiers

• Sensors for biomedical, scientific and defencepurposes

• Digital circuit development for Integrated circuits

• Microprocessors

• Random Access Memories (RAMs)

SQUIDS

(Super conducting Quantum Interference Devices)

9

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.

Types

Two main types of SQUID:

1) RF SQUIDs have only one Josephson

junction

2)DC SQUIDs have two or more junctions.

Thereby,

• more difficult and expensive to produce.

• much more sensitive.

Fabrication • Lead or pure niobium The lead is usually in the form

of an alloy with 10% gold or indium, as pure lead is unstable when its temperature is repeatedly changed.

• The base electrode of the SQUID is made of a very thin niobium layer

• The tunnel barrier is oxidized onto this niobium surface.

• The top electrode is a layer of lead alloy deposited on top of the other two, forming a sandwich arrangement.

• To achieve the necessary superconducting characteristics, the entire device is then cooled to within a few degrees of absolute zero with liquid helium

Uses

• Storage device for magnetic flux

• Study of earthquakes

• Removing paramagnetic impurities

• Detection of magnetic signals from brain, heart etc.

Cryotron

The cryotron is a switch that operates using superconductivity. The cryotron works on the principle that magnetic fields destroy superconductivity. The cryotron is a piece of tantalum wrapped with a coil of niobium placed in a liquid helium bath. When the current flows through the tantalum wire it is superconducting, but when a current flows through the niobium a magnetic field is produced. This destroys the superconductivity which makes the current slow down or stop.

Magnetic Levitated Train

Principle: Electro-magnetic induction

Introduction:

Magnetic levitation transport, or maglev, is a form of

transportation that suspends, guides and propels

vehicles via electromagnetic force. This method can be

faster than wheeled mass transit systems, potentially

reaching velocities comparable to turboprop and jet

aircraft (500 to 580 km/h).

• Superconductors may be considered perfect diamagnets

(μr = 0), completely expelling magnetic fields due to the

Meissner effect.

• The levitation of the magnet is stabilized due to flux

pinning within the superconductor.

• This principle is exploited by EDS (Electrodynamic

suspension) magnetic levitation trains.

•In trains where the weight of the large electromagnet is a

major design issue (a very strong magnetic field is required

to levitate a massive train) superconductors are used for the

electromagnet, since they can produce a stronger magnetic

field for the same weight.

Why superconductor ?

How to use a Super conductor

• Electrodynamics suspension

• In Electrodynamic suspension (EDS), both the rail and the train

exert a magnetic field, and the train is levitated by the repulsive

force between these magnetic fields.

• The magnetic field in the train is produced by either

electromagnets or by an array of permanent magnets.

• The repulsive force in the track is created by an induced

magnetic field in wires or other conducting strips in the track.

• At slow speeds, the current induced in these coils and the

resultant magnetic flux is not large enough to support the weight

of the train.

• For this reason the train must have wheels or some other form of

landing gear to support the train until it reaches a speed that can

sustain levitation.

• Propulsion coils on the guide way are used to exert a

force on the magnets in the train and make the train

move forwards.

• The propulsion coils that exert a force on the train are

effectively a linear motor: An alternating current

flowing through the coils generates a continuously

varying magnetic field that moves forward along the

track.

• The frequency of the alternating current is

synchronized to match the speed of the train.

• The offset between the field exerted by magnets on the

train and the applied field create a force moving the

train forward.

10

Advantages

No need of initial energy in case of magnets for low speeds

One liter of Liquid nitrogen costs less than one liter of mineral

water

Onboard magnets and large margin between rail and train

enable highest recorded train speeds (581 km/h) and heavy load

capacity. Successful operations using high temperature

superconductors in its onboard magnets, cooled with inexpensive

liquid nitrogen

Magnetic fields inside and outside the vehicle are insignificant;

proven, commercially available technology that can attain very

high speeds (500 km/h); no wheels or secondary propulsion

system needed

Free of friction as it is “Levitating”

Engineering physics By Dr. M N Avadhnulu, S Chand publication

Engineering physics by G Vijayakumari

http://www.cengage.com/resource_uploads/static_resources/0534493394/4891/SerwayCh12-

Superconductivity.pdf

https://www.repository.cam.ac.uk/bitstream/handle/1810/34597/Chapter%201.pdf?sequence=5

http://chabanoiscedric.tripod.com/NSCHSS.PDF

http://www.physics.usyd.edu.au/~khachan/PTF/Superconductivity.pdf

Image references links

1. http://s6.postimg.org/brbxzhti5/New_Picture_8.png

2. http://s6.postimg.org/mlte1fcm5/New_Picture_9.png

3. http://s6.postimg.org/xvm3wdhnh/New_Picture_10.png

4. http://s6.postimg.org/6rj35ad99/New_Picture_11.png

5. http://s6.postimg.org/cjelyoxp9/New_Picture_12.png

6. http://s6.postimg.org/ilm8p6m59/New_Picture_13.png

7. http://s6.postimg.org/dkeunteot/New_Picture_14.png

8. http://s6.postimg.org/sy8jb9fod/New_Picture_15.png

9. http://s6.postimg.org/qkqlk9199/New_Picture_16.png

10. http://s6.postimg.org/uftzmtkf1/New_Picture_17.png