SUPERCONDUCTORS

1. SUPERCONDUCTORS • mobile electrons in conducting material move through lattice of atoms or ions that vibrate (thermal motion) • when conductor is cooled down less vibration  “easier” for electrons to get through  resistivity of conductors decreases (i.e. they become better conductors) when they are cooled down • in some materials, resistivity goes to zero below a certain “critical temperature” TC -- these materials called superconductors -- critical temperature TC different for different materials; • no electrical resistance  electric current, once started, flows forever! • superconductivity first observed by Heike Kamerlingh Onnes (1911) in Hg (mercury) at temperatures below 4.12 K. • many other superconductors with critical temperatures below about 20K found by 1970 -- “high TC superconductors”: (Karl Alex Müller and Johannes Georg Bednorz, 1986) • certain ceramic oxides show superconductivity at much higher temperatures; since then many new superconductors discovered, with TC up to 125K. • advantage of high TC superconductors: • can cool with (common and cheap) liquid nitrogen rather than with (rare and expensive) liquid helium; • much easier to reach and maintain LN temperatures (77 K) than liquid Helium temperatures (few K).

2. PROPERTIES OF SUPERCONDUCTORS: • electrical resistivity is zero (currents flowing in superconductors without attenuation for more than a year) • there can be no magnetic field inside a superconductor (superconductors ”expell” magnetic field -- “Meissner effect”) • transition to superconductivity is a phase transition (without latent heat). • about 25 elements and many hundreds of alloys and compounds have been found to be superconducting (examples: In, Sn, V, Mo, Nb-Zr, Nb-Ge, Nb-Ti alloys, ) • applications of superconductors: e.g. superconducting magnets: • magnetic fields stronger, the bigger the current - “conventional” magnets need lots of power and lots of water for cooling of the coils; • s.c. magnets use much less power (no power needed to keep current flowing, power only needed for cooling) • most common coil material is NbTi alloy; liquid He for cooling • e.g. particle accelerator “Tevatron” at Fermi National Accelerator Laboratory (“Fermilab”) uses 990 superconducting magnets in a ring with circumference of 6 km, magnetic field is 4.5 Tesla. • magnetic resonance imaging (MRI): create images of human body to detect tumors, etc.; need uniform magnetic field over area big enough to cover person; can be done with conventional magnets, but s.c. magnets better suited - hundreds in use • magnetic levitation - high speed trains??

3. explanation of superconductivity: • due to interaction of the electrons with the lattice (ions) of the material, there is a small net effective attraction between the electrons; (presence of one electron leads to lattice distortion, second electron attracted by displaced ions) • this leads to formation of “bound pairs” of electrons (called Cooper pairs); (energy of pairing very weak - thermal agitation can throw them apart, but if temperature low enough, they stay paired) • electrons making up Cooper pair have momentum and spin opposite to each other; net spin = 0  behave like ”bosons”. • unlike electrons, bosons like to be in the same state; when there are many of them in a given state, others also go to the same state • nearly all of the pairs locked down in a new collective ground state; this ground state is separated from excited states by an energy gap; • consequence is that all pairs of electrons move together (collectively) in the same state; electron cannot be scattered out of the regular flow because of the tendency of Bose particles to go in the same state  no resistance • (explanation given by John Bardeen, Leon N. Cooper, J. Robert Schrieffer, 1957)