This ppt gives the explanation of Bardeen Cooper and Schrieffer (BCS) theory

1. A lecture by Dr. K. Ramya
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SuperConductivity

2. Bardeen Cooper Schrieffer proposed a
microscopic theory : BCS theory
Electron- Phonon-Electron interaction
(Phonons act as mediators)
 Normal Conductors :
 Electrons are moving at random; Electrons
approach vibrating atoms- repulsive force
predominates the attractive force- they get
scattered – resistance will start increasing
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Scattering of electrons in a
normal conductor
Formation of Superconducting
paired electrons in a
superconductor
References: Applied Physics : Thyagarajan

4.  Super Conductors:
Decrease in energy : Scattering of electrons by
lattice vibrations decreases: resistance decreases :
stable state: electrons get paired up: Cooper pairs
Explanation of the Cooper Pairs:
 Electrons moving in the solid interact with the lattice
vibrations : electrostatic forces between them
 Oscillator distortion due to phonons : electron phonon
interaction : scattering of electrons
 Number of Phonons increases with temperature
 Electron with wave vector K1 : lattice ion : suffers
coulomb interaction: Momentum decreases by K1-q
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5.  Another electron with wave vector K2 : enter the
volume : electron interacts with distorted lattice :
gains momentum : K2+q: electron energy is
lowered
 Lowering of energy : attractive forces between the
electrons.
 Virtual process : Energy is not conserved
 Electron with wave vector K1 emits phonon q that
is absorbed by the second electron with wave
vector K2: two electrons are scattered with wave
vectors K1-q and K2+q
 Attractive interaction: pair of electrons : cooper
pairs (K , K )
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Electron-Phonon Interaction

7. Electrons in the superconductors form
cooper pairs
A cooper pair is a system of two electrons
having equal and opposite momenta and
spin
Lower temperature : the interaction
between cooper pairs and positive ion core
vanishes : Resistivity becomes zero.
Hence conductor becomes
superconductor.
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8. 1. Electrical Generators : Smaller size, less
weight, Consume low energy.
Superconducting coil is rotated in a strong
magnetic field : energy power saving systems
2. Low loss transmission lines and
transformers: Superconducting wires : electrical
cables : transmission losses are low: winding of
a transformer: electrical losses are low.
3. Magnetic Levitation: Diamagnetic property :
High speed transportation
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10. 4. Fast electrical Switching : Application of
Magnetic field greater than HC: superconducting
state to normal state: removal of field reverses the
process: switching element
5. Logic and Storage functions in computers:
Memory elements in computers: logic and
storage functions in computers
6. Superconducting Quantum Interference
Devices (SQUIDS):
Two Josephson junctions mounted on a
superconducting ring: Sensitive magnetometer :
study tiny magnetic signals from brain to heart
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12. 7. Superconducting Magnets : these magnets :
coils of wires made of superconductors : current
once entered : persistent current : used in
electrical machines, transformers and MRI
instruments
8. Superconducting Susceptometer : Consists of
superconducting magnets and SQUIDS. Used to
detect the iron content in human body.
9. Magnetoencephalography : Damaged portions
of the brain can be located (by using SQUID
magnetometers) around the patient’s head:
received small signals are fed to a computer for
analysis.
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