SUPERCONDUCTORS
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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).
PROPERTIES OF SUPERCONDUCTORS:
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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:
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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:
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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)