3.38 Sspd_chapter 1_part 15_quantum fluids_superconductivity &  (Page 3/6)

Excepting element He, all elements and compounds freeze at degeneracy temperature T ₀ . Helium remains liquid all the way to 0 Kelvin so it is an appropriate candidate for the study of super-fluids. This good fortune is due to low atomic mass and weak inter-atomic forces. Weak inter-atomic force is due to the completion of octave in the outer filled orbit. It does not freeze under its own vapor pressure but it does solidify if the external pressure is increased to 30 atmospheric pressures. Also luckily we have two stable isotopes 4He and 3He providing bosonic system and fermionic systems respectively. 4He has 2 p’s, 2 n’s and 2’s and therefore it forms a bosonic system. 3He has 2p’s, 1n and 2’s ( produced in beta decay of tritium from nuclear reactors) and therefore it forms a fermionic system. These two liquid systems at temperatures below degeneracy temperature provide an ideal laboratory material for the study of quantum statistics ( Fermi-Dirac/Bose-Einstein).

The electrons in solid metal or liquid metal are degenerate systems since, as we saw in Section 1.3.1., the degeneracy temperature is of the order of 10,000Kelvin.

The electrons in White Dwarf and neutrons in Neutron Stars are degenerate systems. Because of very high density in these compact stars, the degeneracy temperature is very high of the order of 10 ¹⁰ K. Nevertheless they form quantum liquids.

In Table (1.32) tabulates the quantum liquids, their degeneracy temperatures and the onset temperature of superfluidity/superconductivity.

The charged systems containing conducting electrons exhibit superconductivity and neutral atomic systems exhibit super-fluidity at temperatures much below degeneracy temperatures.

Table 1.32. Laboratory Quantum Liquids. ( Table 9.1. Low Temperature Physics, super conductivity and super fluidity. By Anthony Leggett, ‘The New Physics’ edited by Paul Davies, Cambridge University Press, 1992.)

1.15.1. LIQUID HELIUM-4 AS A SUPERFLUID.

Helium ² He ₄ has two protons, 2 neutrons and 2 orbital electrons. Since all the particles are in pairs hence total spin angular momentum is zero as well as electrons orbital angular momentum is zero. Therefore two Helium atoms are indistinguishable. In this sense Helium atom is a boson.

Above 4 Kelvin, Helium is in gaseous state. At 4 K it liquefies. This liquid does not have any special property. It exhibits the same properties as any other viscous liquids. This is called He-I phase.

As we cool it below T _λ = 2.17 K there is a phase transition to He-II and in He-II phase it exhibits abnormal and spectacular behavior such as :

1. it flows through tiny capillaries without experiencing any friction;
2. it climbs in the form of film over the edge of vessels containing it. This phenomena is referred to as ‘film creep’;
3. spouts in a spectacular way when heated under certain conditions;
4. if contained in a rotating container, the content in He-II phase never rotates along with the container;