3.38 Sspd_chapter 1_part 15_quantum fluids_superconductivity &  (Page 4/6)

This complex of effects is called SUPERFLUIDITY and the liquid is in superfluid phase which we referred to as He-II phase. The transition between two phases is called λ transition and this occurs because of the onset of Bose Condensation.

1.15.2. What is BOSE CONDENSATION ?

Let us begin with He-I phase with N atoms in volume V at a temperature T below 4 Kelvin. According to Bose Statistics N is distributed as N ₁ in low states and N ₂ in high states. As the temperature is lowered more and more He-4 is transferred to lower states so that N ₁ + N ₂ = N.

This transfer stops when N reaches N _max corresponding to the lower energy state at a lower temperature because there is an upper limit of the number of quantum states available for the given energy state. The temperature at which this occurs happens to be the degeneracy temperature T ₀ which we referred to in Section (1.13.1). This is the λ phase transition with He-I transforming into He-II.

At a temperature T*<T ₀ , N _max <N because N _max is a function of temperature and it reduces as temperature is decreased. Now Bose distribution cannot accommodate N . So how is the excess atoms accommodated that is excess over N _max . Nature has an ingenious method to circumvent this problem- BOSE CONDENSATION . The excess amount at T* condenses to the ground state. As T* approaches ZERO Kelvin absolute temperature, all the N atoms are condensed to the ground energy state.

This large scale transfer of He-II to energy ground state is what gives rise to super-fluids and its spectacular property of super-fluidity as mentioned in Section ( 1.15.1).

The degeneracy temperature of He-4 is calculated to be 3 K and the onset of super-fluids is 2.17K. This discrepancy occurs because Degeneracy Temperature is calculated for systems with non-interacting particles whereas as He-4 is strongly interacting.

1.15.3. SUPERCONDUCTIVITY.

In 1911 Kamerlingh Onnes discovered that liquid mercury at temperatures below 4.2Kelvin shows zero resistance. This was christened as super conductivity. There is a very narrow temperature range in which the transition takes place. This is defined as Transition Temperature T _C .

In 1986, J.G Bednorz and K. A. Muller, workin.g at IBM Research Laboratories at Zurich, found a new class of materials which are superconducting at a much higher temperature. Yitrium Barium Copper Oxide (YBaCuO) was discovered to behave as superconductor at 77Kelvin (liquid Nitrogen temperature). This started the era of high temperature ceramic superconductors.

Presently super-conductors have been achieved till 125K.

Professor Collins induced a current to flow in superconducting lead ring. This continued to flow for a year. This confirms that indeed resistance is zero in a super conductor.

In 1933, Meissener and Ochsenfeld discovered that a superconductor is a perfect diamagnet. This implies that magnetic flux density B in a superconductor is zero. This has been called Meissener Effect. If a coin size superconductor is placed on one of the magnetic poles then it will be freely suspended in air because of the repulsion force between magnetic pole and the diamagnetic nature of the coin size superconductor. This is known as the magnetic levitation effect.