Clean-dirty compares the coherence length xi_0 (of a clean system) with the mean free path l. If l >> xi_0, the superconductor is in clean limit, if l

@Jens Hänisch 

Dear Sir,

Thank you so much, I am very happy to have gotten your answer. I have understood it well. I will try to understand more by going through the reference you have given.

Sincerely,

Dinesh

@Behnam Farid 

Dear Sir,

Thank you so much. I will go through the paper and try to understand more.

Sincerely,

Dinesh

Just to add to the above discussions, the notion of phenomenological coherence length gets intimately connected to Cooper's pairing idea involving two fermions. The coherence length gives the size of a "super-electron" which is the most important carrier in all the phenomenological theories including that of Gorter-Casimir as well.

There is one more and an important aspect to Clean and dirty Superconductors, that is the critical current density Jc in Type II superconductors. Type II superconductors are known to have two characteristic critical magnetic field Bc1 and Bc2 and Bc2 happens to be very high up to 100 T and more. These superconductors are therefore most useful materials for the production of high magnetic field (record field to-date is 35 T at NHFML USA). Between these two lower and upper critical fields (Bc1 and Bc2) the superconductor undergoes a Mixed State in which the material is threaded by flux line each carrying a unit of flux quanta. If the material is a clean type II superconductor the critical current drops sharply the moment a small magnetic field is applied as the flux line starts moving under the influence of Lorentz force and a voltage appears and the material turns normal. So a clean superconductor cannot carry a useful current even though it stays superconducting until high Bc2 and is of no use for practical applications like magnets. However if you introduce suitable impurities or imperfections in the superconductor and make it Dirty it carries large current in presence of high magnetic field thus becoming most useful material for high field production. These materials have been used in LHC and are being built for ITER Tokamak. These impurities blocks the flux lines movement in the mixed state of the superconductor, that is, the flux lines are pinned down to the crystal lattice overcoming the Lorentz force. They will move now only at very high value of the critical current. This is called flux pining. 

For clarity you may read sections 3.3 &3.4 page 53-55 of the book (if available in your institute) titled "Superconductivity-Basics and Applications to Magnets" by RG Sharma, Published as Vol. 214 of the Springer Series in Materials Science, 2015, ISBN: 9783319137124

RG Sharma

Dirty nonmagnetic gapless superconductors suppress superconductivity.

I mean, the scattering by nonmagnetic impurities suppresses the superconductivity in gapless superconductors dopped with non-magnetic impurities.

And at very low temperatures, the behaviour of the kinetic coefficients - KC corresponds sometimes to the so-called unitary limit Prof. Dinesh Kumar, instead of the Born behaviour.

Transport kinetic coefficients (thermal conductivity for example) have a residual value at T = O K, a that is called the unitary limit or behaviour, On the other hand, the Born limit says that the KC tend to zero as T ---> 0 K.

See the references therein in the following papers:

Article Electronic heat transport for a multiband superconducting ga...

Article A nonlinear minimization calculation of the renormalized fre...