3.38 Sspd_chapter 1_part 15_quantum fluids_superconductivity &  (Page 5/6)

At low temperatures, ordered behavior appears spontaneously in a macroscopic system. Because of this ordered behavior, the given system exhibits super fluidity and super conductivity. Enormous number of particles behave coherently to give rise to frictionless flow of liquids (super fluidity) and frictionless flow of electrons(super conductivity).

A kind of phase transition occurs just as there is phase transition from gas to liquid to solid or the onset of ferromagnetism in iron when it cools below the Curie temperature. In the same way lowering of temperature causes electron pairing into cooper pairs. These cooper pairs suppress the fermionic properties to produce super conducting state. This is spontaneous self organization.

1.15.3.1. PHYSICS OF SUPERCONDUCTIVITY.

A metal at room temperature has a metallic bonding. As we discussed in Section (1.12) the metallic atoms release their outer orbital electrons at room temperature. These semi-free electrons (semi-free because they are free to move around the whole lattice but confined within the boundaries of the crystal because of the surface barrier potential φ _SB = W _F (Work Function of the metal)/q ) belong to the whole metallic lattice and not just to their parent atoms. This conducting electron gas hold the regular crystalline array of positively charged ionic cores together as a metallic solid.. In alloys these ionic cores are held irregularly. This electron gas follows Fermi- Dirac Statistics as shown in Figure (1.83).

At zero Kelvin all the quantum states are filled up to Fermi Energy level (E _F ) with a pair of opposite spin electrons in each quantum state. Above E _F all the states are empty. But as the temperature is raised the distribution becomes skewed and the upper electrons within kT energy segment start jumping to higher energy states. This is the reason why the actual specific heat of the electron gas is kT/E _F of the classically expected value.

By taking the effective mass of the conducting electrons into account we can describe these electrons by de Broglie matter waves traveling in free space. The effective mass which may range from 0.1m _e to 10m _e accounts for the deformation caused in the de Broglie free wave. But the crystal defects, foreign impurities and the thermal vibration of the ideal regular array of ionic cores are there to scatter the matter wave. These factors limit the mean free path to several inter atomic spacings. This is the reason for the limited mobility , limited conductivity and finite resistance. But if the thermal vibrations are frozen out by cryogenic cooling to 4K (liquid He-4 temperature) , impurities are absent and the crystal is defect-free then the mean free path is of the order of centimeter and mobility is drastically improved and resistance fall to a residual value. This ideal gas model is correct by and large and is able to explain the general features of the behavior of metal.

But there is a class of metals and ceramic conductors which experience a definite phase transition at a critical temperature or transition temperature T _C just as we saw λ- phase transition in He-4. In He-4 below T ₀ ( the degeneracy temperature) the bosonic Helium-4 atoms start condensing to energy ground state and manifest the behavior of a super-fluid.