WHAT IS SUPERCONDUCTIVITY?? - PDF Free Download

WHAT IS SUPERCONDUCTIVITY?? For some materials, the resistivity vanishes at some low temperature: they become superconducting. Superconductivity is the ability of certain materials to conduct electrical current with no resistance. Thus, superconductors can carry large amounts of current with little or no loss of energy. Type I superconductors: pure metals, have low critical field Type II superconductors: primarily of alloys or intermetallic compounds

BCS theory, 1957 Meissner, 1933 Superconductors History organic, heavy Fermion, Sr 2 RuO 4 T C (K) Sn (Tin) 3.72 Hg (Mercury) 4.15 Pb (Lead) 7.19 NbTi (Niobium Titanium) Nb 3 Sn (Niobium Tin) 10 18.1 Műller, Bednorz 1986 high T c MgB 2 Onnes, 1911 SC Mercury Josephson, 1962

Bardeen Cooper Schreiffer Theory BCS theory requires: (a) low temperatures - to minimise the number of random (thermal) phonons (ie those associated with electron-ion interactions must dominate) (b) a large density of electron states just below E F (the electrons associated with these states are those that are energetically suited to form pairs) (c) strong electron phonon coupling BCS theory is an effective, all encompassing microscopic theory of superconductivity from which all of the experimentally observed results emerge naturally Ginzburg-Landau theory can be derived from BCS theory, and the phenomenological coefficients introduced by Ginzburg and Landau are related to quantities introduced in the microscopic theory

Superconducting Materials 160 HgBa 2 Ca 2 Cu 3 O 9 (under pressure) Superconducting transition temperature (K) 140 120 100 80 60 40 20 Hg Pb HgBa 2 Ca 2 Cu 3 O 9 TlBaCaCuO BiCaSrCuO YBa 2 Cu 3 O 7 (LaBa)CuO Nb Nb NbC NbN 3 Sn Nb 3 Ge V 3 Si Liquid Nitrogen temperature (77K) 1910 1930 1950 1970 1990 Lecture 12

Properties of SC n Zero resistivity n Meissner effect n Energy gap Δ in excitation spectrum n example of SC

Superconductivity Explained BCS Theory Electron lattice interaction Cooper pairs Energy Gap Coherence Flux Quantization Phono ns!

Superconductivity Explained BCS Theory Electron lattice interaction Cooper pairs Energy Gap Coherence Flux Quantization Two coupled electrons with opposite momenta and spins Boson-like Does not scatter - resistanceless Energetically favorable in superconducting state

Superconductivity Explained BCS Theory Electron lattice interaction Cooper pairs Energy Gap Coherence Flux Quantization

Superconductivity Explained BCS Theory Electron lattice interaction Cooper pairs Energy Gap Coherence Flux Quantization Can calculate phase and amplitude at any point on the wave Coherence length One wave equation describes all Cooper pairs:

Superconductivity Explained BCS Theory Electron lattice interaction Cooper pairs Energy Gap Coherence Flux Quantization Magnetic flux around a closed superconducting current loop must be quantized One fluxon

Josephson Tunneling Josephson Junction small gap between two superconductors Cooper pairs can tunnel Critical current supercurrent Phase difference across the junction

Superconducting compounds Perhaps the most widely used class of superconducting compounds are the A 3 B family which crystallise in the A-15 structure. The A-atoms are typically the transition metals V or Nb, whilst the B atoms are nontransition metals such as Sn, Al, Ga, Si, Ge Six A15 compounds have transition temperatures over 17K B A Nb 3 Ge thin films held the record for the highest known T c of 23K for a number of years up to 1986 This was thought to be close to the limit imposed by BCS theory Lecture 12

The Chevrel phase compounds The Chevrel phases were discovered in 1971 They are ternary molybdenum chalcogenides of the type M x Mo 6 X 8 M could be any one of a number of metals at rare earth (4f) elements and X is S, Se or Te The M atoms form a nearly cubic lattice in which the Mo 6 X 8 uinits are inserted These were the first class of superconductors in which magnetic order and superconductivity were found to coexist With M=Gd, Tb, Dy, Er the superconducting transition temperatures are between 1.5 and 2K, while the Neel temperatures are between 0.5 and 1K. Lecture 12

The Chevrel phase compounds Some Chevrel compounds have relatively high transition temperatures, and very high critical fields Compound T c B* SnMo 6 S 8 12K 34T PbMo 6 S 8 15K 60T LaMo 6 S 8 7K PbMo 6 Se 8 3.6K 3.8T Critical current densities as high as 3x10 5 A.cm -2 have been observed at 4.2K Unfortunately the material is extremely brittle and making Lecture wires 12 is problematic

The nickel borocarbides The rare earth nickel borocarbides, discovered in 1994 have relatively high transition temperatures but also order magnetically at temperatures comparable to T T N (K) T c (K) (g-1) 2 c J(J+1) Y 0 15 0 Yb 0 0 (HF?) Lu 0 16 0 Tm 1.5 10.8 1.17 Er 6.5 10.5 2.55 Ho 6 8.5 4.5 Dy 10 6.2 7.08 Tb 15 0 10.5 Gd 19.5 0 15.5 Y, Lu, Tm, Er, Ho, Dy (Tb, Gd, Nd, Pr, Ce, Yb) Ni B C

The nickel borocarbides

Organic Superconductors The Bechgaard salts are nearly one dimensional conductors with very low carrier densities The electronic properties are extremely anisotropic Most of the class of compounds (TTMTSF) 2 -X, where X is an anion are only superconducting under pressure CH 3 Se Se CH 3 CH 3 Se Se CH 3 TMTSF tetramethyltetraselenafulvane X p c /kbar T c ClO 4 0 1.2K PF 6 9 1.2K ReO 4 9.5 1.4K

Organic superconductors under pressure The systems are particularly interesting from a fundamental perspective Is the superconductivity conventional?

The Bucky balls Buckminsterfullerene contains 60 carbon atoms at the apices of a triacontaduohedron 7.1Å in diameter C60 itself is not a superconductor, but it can be doped with alkali metals (which form an fcc lattice with a lattice parameter of 10Å) giving A3C60 Compound K3C60 K2 RbC60 Rb2KC60 Rb3C60 Cs3C60 Tc 19K 22K 25K 29K 47K

MEISSNER EFFECT When you place a superconductor in a magnetic field, the field is expelled below T C. B B T >T c T < T c Magnet Superconductor Currents i appear, to cancel B. i x B on the superconductor produces repulsion.

Conductors in a Magnetic Field Normal metal Perfect (metallic) conductor Superconductor Apply field Apply field Cool Apply field Cool Field off

Magnetic Penetration Depth - λ Screening not immediate; characteristic decay length 2 λ = m µ n e 0 s 2 B 2 1 = 2 λ B Typical λ ~ 50 nm m,e fixed λ uniquely specifies the superconducting electron density n s B( z) = B(z) B e 0 z / λ SC Sometimes called the superfluid density B 0 λ z

H(x) ξ Type I λ ψ(x) λ >> ξ κ λ ξ H(x) λ Type II ξ ψ(x) λ >> ξ g net (x) g magnetic (x) g sc (x) κ > 1 2 g net (x) g magnetic (x) g sc (x) κ > 1 2 elemental superconductors predicted in 1950s by Abrikosov ξ (nm) λ (nm) T c (K) H c2 (T) Al 1600 50 1.2.01 Pb 83 39 7.2.08 Sn 230 51 3.7.03 ξ (nm) λ (nm) T c (K) H c2 (T) Nb 3 Sn 11 200 18 25 YBCO 1.5 200 92 150 MgB 2 5 185 37 14

Type II Superconductors Normal state cores Superconducting region H http://www.nd.edu/~vortex/research.html

APPLICATIONS: Superconducting Magnetic Levitation The track are walls with a continuous series of vertical coils of wire mounted inside. The wire in these coils is not a superconductor. As the train passes each coil, the motion of the superconducting magnet on the train induces a current in these coils, making them electromagnets. The electromagnets on the train and outside produce forces that levitate the train and keep it centered above the track. In addition, a wave of electric current sweeps down these outside coils and propels the train forward. The Yamanashi MLX01MagLev Train

APPLICATIONS: Superconducting Magnetic Levitation On 2 December 2003, a threecar train reached a maximum speed of 581 km/h (361 mph) (world record in a manned vehicle) http://www.youtube.com/watch?v=ghtawqxvsuk

APPLICATIONS: Superconducting Magnetic Levitation The L0 Series Shinkansen train is planned to run at 500 km/h (310 mph). The train is planned to run at 500 km/h (310 mph), but not until 2027. http://www.youtube.com/watch?v=sjoddoiukja

APPLICATIONS: Medical MRI (Magnetic Resonance Imaging) scans produce detailed images of soft tissues. The superconducting magnet coils produce a large and uniform magnetic field inside the patient's body.

How it works Phase change due to external magnetic field Current flow Voltage change Due to B field Due to junctions Must be quantized

Superconducting Wind Generation Conventional Gearbox 5 MW ~ 410 tons Conventional Gearless 6 MW ~ 500 tons HTS Gearless 8 MW ~ 480 tons Wind turbine output limited by weight supported on the tower Superconducting generators: half the size and weight Generator Gearbox Shaft Matthews, Physics Today 62(4), 25 (April 2009) à double the output for same land area

APPLICATIONS: Power The cable configuration features a conductor made from HTS wires wound around a flexible hollow core. Liquid nitrogen flows through the core, cooling the HTS wire to the zero resistance state. The conductor is surrounded by conventional dielectric insulation. The efficiency of this design reduces losses. Superconducting Transmission Cable From American Superconductor

APPLICATIONS: Power