Superconductors & Critical Temperatures
As the temperature of the conductor increase the vibration of the ions also decreases. Hence the electrical resistance of a metallic conductor should decrease to a low but non-zero value as the temperature deceases toward absolute zero. However below certain temperatures some material resistances disappear completely at sufficiently low temperatures.
The temperature at which a superconductor material loses all its electrical resistance is called its critical temperature, Tc .
Superconductivity is the phenomenon exhibited by certain conductors where they have no resistance to current.
The BSC Theory of Superconductivity Bardeen, Cooper, Schrieffer
BCS Theory suggests that superconductors have zero electrical resistance below their critical temperatures because at such temperatures the electrons pass unimpeded through the crystal lattice and therefore lose no energy. The theory states that the supercurrent in a superconductor is carried by many millions of bound electron pairs, called Cooper pairs.
These pairs form when one electron passing between adjacent positive ions in the lattice attracts the ions, causing them to move slightly inwards and to create a region of increased positive charge density. Due to the elastic properties of the lattice, this region of increased positive charge density propagates through the lattice as a wave. A second electron passing through the lattice is attracted into this moving region of increased positive charge density and is effectively swept along by the lattice wave created by the first electron. Thus, by pairing off two by two, the electrons pass more smoothly through the lattice.
Cooper pairs continually form, break and re-form. Since random lattice vibrations break up Cooper pairs, the temperature needs to be low enough to keep such vibrations to a minimum.
*edited underline*
Below is an illustration of cooper pairs:
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