Superconductors (module 1)

ch2

superconductivity

phenomenon in which particular materials exhibit zero resistance below a particular temperature called critical temperature. (T_c)

crital temperature (T_c)

particular temperature below which superconductors exhibit superconductivity.

Applications of superconductors

Transmission wires (electricity cables)

MRI Scans (Magnetic Resonance Image)

Transition temperature

temp diff between a particular temp and critcal temp

superconductivity depends on

magnetic field and temperature

critcal field*

Minimum magnetic field required to destroy the superconductive property of a material below critical temperature (T_c).

Tuyns Law

or

Relation between critical field and critical temperature

also derive the relation when T=0K & T=T_c + graph

H_c(T)=H(0)*[1-(T/T_c)²]

H_c(T)- critcal field at temp T K

H(0)- critical field at 0K

T_c-critical temp

T-particular temp T K

Meissner Effect (draw diagram)

phenomenon in which superconductors completely expel magnetic flux lines rom the interior of the material below the critical temperature (Tc) in presence of a magnetic field.

Type 1 and Type 2 superconductors table

BCS Theory (Bardeen, Cooper, Schrieffer)

It was the first successful microscopic theory on superconductors

founded in 1957

explained:

- electron-lattice interactions

-electron-phonon interactions

-cooper pairs

-properties of cooper pairs

results:

proves the existence of energy gaps and flux quantization

Electron-phonon interaction

current passes through superconductor

electron flows towards the positive ion in the metal lattice

coulomb attraction between electron and positive ion

there is a distortion in the lattice, i.e. positive ion gets displaced from its mean position

the smaller the mass of the positive ion core the greater distortion

scattering of electrons creating electrical resistivity

Electron-lattice interaction

after the occurance of electron-phonon interaction

when another electron comes upon the distorted positive ion it also experiences coulombs’s attractive force, interaction between two electrons through lattice

due to this interaction these two electrons develop an apparent force of attraction and move in pairs
at normal temperature the apparent force of attraction between the two electrons is very small so they don’t get paired
below the transition temperature the apparent force of attraction reaches maximum value for any two electrons of equal and opposite spin

this force of attraction > the coulomb’s force of repulsion between teh two electros so they tend to move in pairs

these are called cooper pairs

cooper pairs

electrons pairs formed by the interaction between two electrons of opposite spin and momenta in the phonon field

phonons

quanta of lattice vibrations

bosons

cooper pairs have a net spin of 0 (both e- pairs have opposite spin)

due to the net spin being 0, electron pairs in superconductors are called bosons

(all cooper pairs are bosons but NOT vice versa)

properties of cooper pairs

a dense cloud of cooper pairs form a collective state and drift through cooperatively through the material

superconducting state- ordered state of conduction electrons

motion of all cooper pairs are the same- rest or drifting with identical velocity

density of cooper pairs are very high so  large currents require small velocity
The small velocity and precise ordering of cooper pairs, minimize collision process

collision with the lattice is extremely rare leading to vanishing resistivity

cooper pairs smoothly sail over the lattice point without any exchange of energy resulting in infinite electrical conductivity

Applications of superconductivity

large scale superconducting devices consist of - magnets, motors, generators, cables

magnetohydrodynamic power plant (MHD) -controlled fusion, energy storage

sea and land transportation

superconducting magnet application- maglev train, levitating trains for rapid transit system

low loss transmission lines+transfomers

perform logic and store functions in computers
small size electric generators created using superconducting coils

high capacity+high speed computer chips

cryotron- fast electric switching system operation

SQUID- superconducting magnetic energy storage system