Superconductivity

SuperconductivityAn Engineering Physics PresentationShubham Thakur

INTRODUCTIONDiscoverer: Dutch physicist Kamerlingh Onnes, in 1911.He studied the electrical properties of solid 80Hg using liquid 2He.His Observation: At 4.2 Kelvin, resistivity suddenly becomes 0!Current, or super-currents, persist for years independent of supply. This is superconductivity.He received Nobel Prize for physics in 1913.In 1913, 82Pb was found superconducting.In 1941, NbN was found Superconducting.

Resistance Versus TemperatureT (K)R ()

Magnetic Properties

Variation of TC with BC for Lead (Pb)

Meissner EffectWhen T < TC and B < BC, then theres a complete repulsion of magnetic flux lines due to the activation of Cooper pairs.As a result of Newtons third law, the superconductor levitates.Material exhibits perfect diamagnetism.When T > TC and B > BC, then flux starts penetrating completely. Resistivity is restored. Superconductor no longer levitates.Meissner effect is possible is conditions are cryogenically lowered.

Type I & II SuperconductorsType I or Soft SuperconductorsHave unique Critical Magnetic field (BC) value.Type II or Hard SuperconductorsHave two Critical Magnetic field values, BC1 and BC2.

Type I & II SuperconductorsType I or Soft SuperconductorsExhibit complete Meissner Effect behind BC.Only two states- normal and superconductingExamples: Al, Cd, Sn, Zn.Have very small critical temperature values, from 0 to 10 Kelvin.They are Pure elements.Type II or Hard SuperconductorsExhibit complete Meissner effect behind BC1 and incomplete in between BC1 and BC2.Have normal, vortex (mixed) and Superconducting states.Examples: Nb3Sn, Cs2RbC60.Have comparatively large, more than 20 Kelvin, up to 170 Kelvin.Mixtures of different elements.

For B < BC1 total cancellation of magnetic field occurs, material is superconducting.For B > BC2, resistivity is normal due to complete penetration of magnetic flux.For BC2 < B < BC2, partial penetration of flux occurs. The group of flux lines penetrating the material is called flux tubes or vortices. Only that region where penetration occurs, have normal resistivity. Rest of the material remains superconducting.Each flux tube contains one quantized unit of flux called fluxoid.

The Special Case of Type II Superconductors

Vortices

Vortex

BC1 & BC2 of Hard Superconductors

Type I & II SuperconductorsTC and BC Values at 0 K for some Superconductors

London Penetration Depth

Isotope Effect

BCS TheoryDiscoverers: Bardeen, Cooper & Schrieffer.Basis: Electron-phonon interaction, and weakening of like charge repulsion.Causes: Isotope Effect and superconductivity.Particle involved: Cooper pairs, & phonons.Cooper pairs so formed have the tendency to repel the magnetic field.Cooper pairs emerge as the result of formation of phonons.

Cooper PairsAn electron moving through the lattice attracts the positive charges formed due to the magnetic field, resulting increased positive charge density in that lattice region.This region of increased charge density propagates through the material as a vibrational wave in the lattice, called a phonon.Another electron is also attracted and it may get closer to the first electron due to weakened repulsion due to low temperature, forming a Cooper pair.

A Phonon Mediator

A Virtual Phonon Mediator

Cooper PairsCooper pairs have equal but opposite spin angular momentum and linear momentum.Cooper pairs have net 0 spin and 0 linear momentum, thus act as bosons (photon).Thus many cooper pairs can be in same quantum state and thus defy Paulis Exclusion Principle. Because a propagating boson (photon) creates alternating electric and magnetic field, they repel the external magnetic field.And hence can mediate altogether, correlatively in superconducting state.

Superconducting Energy Gap

Magnetic Flux Quantization

Josephson JunctionIn barrier to penetration, an electron tunnels through the barrier (thin insulator). This is called quantum tunneling.Josephson, in 1962 proved that cooper pairs can tunnel from one superconductor to another.This involves no resistance, but a direct current without any potential difference through the junction.This superconductor-insulator- superconductor junction is called Josephson junction.

D.C. Josephson Effect

Electron pairs tunneling through the oxide barrier between the two superconductor junctions

A.C. Josephson Effect

High Temperature SuperconductivityHigh TC values.Are Compounds of many elements.Have perovskite crystal structure.They are reactive and brittle.They usually contain Copper oxides as main constituent.Have 1-2-3 ratio of its constituents (more than three), generally called Ceramics.E.g. YBa2Cu3O7 93 K, La1-xSrxCuO (at x = 0.15) 40 K, BiAl1-yCaSrCoO7-d (d < 0.45 & y < 0.3) 114 K, Tl2Ba2Can-1CunO2n+4 (80, 110 & 125 K for n = 1, 2, & 3), HgBa2Ca2Cu3O1+x with x