Originally posted by J. Arthur God:
If you are looking at conduction in low dimensional (e.g. 2D or quasi-2D) systems, a lot of work has already been done on this. In particular, much work has been done on charge density waves where the electron periodicity is incommensurate with the nuclear lattice. This leads to a type of conduction very similar to superconductivity (at least in theory).
Back to your proposals. You are stating that a Wigner Crystal--a 2D or 1D lattice of electrons-- is responsible for all superconductivity?
You realize that a Wigner crystal can be observed with neutron diffraction. e.g.
"Wigner-crystal and bi-stripe models for the magnetic and crystallographic superstructures of La0.333Ca0.667MnO3 "
PHYSICAL REVIEW B 59 (22): 14440-14450 JUN 1 1999
I don't see any report of Wigner crystals being observed by neutrons in superconductors.
I am not stating that Wigner crystals are responsible for all superconduction; but only surmise that this is the case for the low-temperature metals. As far as my knowledge goes, in order to observe a Wigner crystal it has to form an insulating array; i.e. as Wigner surmised, the formation of a Wigner crystal should cause a metal-insulator transition. What he missed, and what I am lifting out in my model, is that the electrons (or electron pairs) forming such a crystal can initiate superconduction as soon as the distance between them (and this can be in a single direction) becomes small enough for coherent tunnelling to occur. This tunnelling is limited by Heisenberg's Uncertainty Relationshipin energy and time.
What you require for superconduction to occur is an array of dielectric centres; i.e. centres which can be polarised when an external electric field is applied. If this is not possible, you cannot have a zero electric field between two contacts as is observed. In the case of a Wigner crystal, the electron-orbitals have to be bound by positive charges in order to form stationary centres. They can thus be polarised. In the case of the CuO ceramics, the dielectric arrays are bi-electron orbitals that form between the crystallographic layers. It is for this reason that the metals have a strong isotope effect while the ceramics have a small or negligible isotope effect. The electron-orbitals foming a Wigner crystal are pseudo-"particles", the energy of which is affected by vibronic states in the material. In the case of the CuO ceramics, the electron-orbitals between the layers are similar to covalent bonds. They do not couple strongly with the phonons within the layers.
I am enjoying this discussion. Thanks for your input.
