Originally posted by Count Iblis II:
Johnny Boy, I'm open to the idea that you can have superconductors for which BCS theory doesn't apply. In fact, We know that for high temperature superconductors BSC theory doesn't apply, so this must be true.
As I wrote earlier here, I'm not an expert in these matters, I read the book by Rickayzen a long time ago. However, if you claim that all of the BCS superconductors are in fact not correctly decribed by BCS theory, you also need to explain why BCS theory does make correct predictions, like e.g. the isotope effect etc.
You are of course correct (to acertain extent); however, such an analysis will be far too long for a BB. So I am not going to concentrate on critisizing BCS; except to note that it is amazing that the BCS theory seems to be consistent and useful when modelling the low temperature metals. I have wondered about this frequently; however there is a LOT about superconduction BCS cannot explain!
Having analysed all the superconductors discovered to date; i.e. low temperature metals, CuO ceramics and semiconductor superconductors; I have found that I can model all of them with the same (one single) mechanism. Thus my model must be better, because BCS cannot model the CuO ceramics.
Going back in the literature, I came to the conclusion that Eugene Wigner has solved superconduction already in the 1930's; without realising it. Wigner looked at the mean-field approach when the metal being modelled is not a "perfect" metal so that the nearly-free electron cannot be used (exactly the metals in which SC manifests). He then found that at a low enough temperature, the electrons will localise to form a crystalline arrangement. The electrons or electron pairs that form can be modelled in terms of Gaussian functions (zero-point vibrational functions). Such an array has become known as a Wigner crystal. In order to form such an array, the electrons must lose energy by de-exciting from one energy level to a lower one. They are then anchored at the site where they form by positive charges. This is why Wigner predicted that the formation of such an array will define a metal-insulator transition.
The point to notice is that such an array forms a dielectric structure. When an external electric field is applied, the now localised electron orbitals become polarised relative to the positive charges that anchor them and cancels the electric applied electric field. Furthermore, they all have the same energy although they are NOT a Bose-Einstein condensate. They are more like marbles on a Chinese Checkers board.
But can these orbitals convey a current? Yes they can if the distances between them becomes small enough. How? they can march coherently from one anchor point to another by "tunnelling". I do not like the term tunnelling here because it implies that electrons move "through" barrier. I believe this is impossible. What really happens is that each orbital borrows the required energy for a time interval, as allowed by Heisenberg's uncertainty principle for energy and time. Thus the kinetic energy when moving from one anchor point to the next is also on loan. For this reason the charge carriers can move at a speed v without gaining kinetic energy.
Now what about the isotope effect? In such a metal the Wigner orbitals are a superpostion of Bloch waves (quasi particles) and the energy levels are not purely electronic but vibronic. Thus when changing the isotope ratio you also change the energy interval between the two vibronic levels over which the electrons have to lose energy in order to form the Wigner orbitals. This is the cause of the isotope effect; not the exchange of virtual phonons (what BS).
In the CuO ceramics the concomitant orbitals form BETWEEN the crystallographic layers. They are in effect covalent bonds forming an array. When their density becomes high enough, superconduction initiates in exactly the same way as in the low temperature metals. In this case the orbitals do not couple as strongly with the phonons in the crystallographic layers; and therefore the isotope effect is minimal.
In highly doped p-time diamond one can also get superconduction at low temperatures. In this case the charge carriers are holes (fermions) tunnelling from one acceptor site to another.
So you do not need a Bose-Einstein condensate. Neither do you need bosons.
ADDITIONAL INFORMATION POSTED BY EDIT:
My model leads to a simple quadratic equation of the speed of the charge carriers that explains ALL superconductors; no perturbation theory, no Feynman diagrams etc. What does Occams Razor tells you?
Furthermore, Bardeen pointed out that Josephson tunnelling is not possible for Cooper pairs. He was right. It is not possible. Josephson tunnelling is a natural consequence of my model. Which model is the best? The one with "epicycles" or the one that does not need ad-hoc corrections like coherence lenghts?
