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” T C -- these materials called superconductors -- critical temperature T C 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 “high T C 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 T C up to 125K. advantage of high T C 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).

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??

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)