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)