If there are no long range order in thin films, how one can claim the Cooper pair mechanism exists in amorphous materials?
Though amorphous films are non- crystalline and do not have long range order but they retain short range order up to a few atomic distances. Due to short range order they are found to retain almost all properties of crystalline state in amorphous thin films. Some modifications have, however, been suggested in their electronic structure due to lack of long range order and due to structural defects due to rapid cooling from vapour state to prepare amorphous films.
The epitexial thin films have long range order in two dimensions at least.
Thin films are not two-dimensional in the strict mathematical sense. More accurately, they are quasi-two-dimensional.
It depends on the thickness of the thin films. I understand that with modern tewchnique you can deposit a single layer of atoms of even.
Dear Tapan, thickness is of course important, but one will have to consider the proof of the Mermin-Wagner theorem in order to fully appreciate the role of dimensionality in relation to fluctuations (even a single atom lives in a 3D space). What is relevant is that a given sample can be smaller than the correlation length, so that for such sample it is as though the correlation length were infinitely large. There is also the aspect of the temperature range of interest: Mermin-Wagner does not cover the case of T=0 so that for sufficiently low temperatures the correlation length though finite, it can be considerably large (larger than the sample size).
Thanks dear contributors.
As a proof for Dr. Tapan, attached article can be a reference, describing Curie temperatures for different thicknesses (in atomic distances as Dr. Kumar said). I was wondering what would the colleration length be the if the thickness is about ~100 nm range.
I dont have knowledge about the superconductive mechanism and I will be gratefull if you provide articles for your arguments, so I know where to start.
Kindly regards.
@Benam: I agree with you perfect 2D system does not exist in physical world. Apart from the requirement of perfectly 2D system you add another requirement that T should be finite in order that the Mermin-Wagner theorem be valid. In that case we should be surprised for quasi 2D magnetism or superconductvity. Now I cannot remember whether the Mermin-Wagner theorem is for all type of long range order or just for magnetism, especially ferromagnetism. You may please clarify.
@ Tapan -- Mermin-Wagner does not rule out existence of long-range order at T=0, in any dimension. It is strictly applicable to T>0. There is a whole subject of quantum criticality which is very worthwhile. Subir Sachdev's book Quantum Phase Transitions (Cambridge University Press, 1999) has been entirely devoted to this subject. As for 2D magnetism and superconductivity, they exist because the underlying physical systems are not truly two-dimensional. In fact, the theoretical considerations concerning the high-Tc cuprates are mostly on 2D models and the only reason why they predict superconductivity is because superconductivity in these models are theoretically described in some mean-field sense (they assume a non-vanishing superconducting order parameter and solve some non-linear equation, exactly in the spirit of the Weiß theory of magnetism); including all quantum fluctuations, these models would not predict superconductivity at T>0. This is a tacit assumption that no one talks about in public, however if you quiz speakers at seminars, they will all tell you exactly this (I know this from experience).
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