A String Approximation for Cooper Pair in High-T$_{\bf c}$ superconductivity
Abstract
It is assumed that in some sense the High-T superconductivity is similar to the quantum chromodynamics (QCD). This means that the phonons in High-T superconductor have the strong interaction between themselves like to gluons in the QCD. At the experimental level this means that in High-T superconductor exists the nonlinear sound waves. It is possible that the existence of the strong phonon-phonon interaction leads to the confinement of phonons into a phonon tube (PT) stretched between two Cooper electrons like a hypothesized flux tube between quark and antiquark in the QCD. The flux tube in the QCD brings to a very strong interaction between quark-antiquark, the similar situation can be in the High-T superconductor: the presence of the PT can essentially increase the binding energy for the Cooper pair. In the first rough approximation the PT can be approximated as a nonrelativistic string with Cooper electrons at the ends. The BCS theory with such potential term is considered. It is shown that Green's function method in the superconductivity theory is a realization of discussed Heisenberg idea proposed by him for the quantization of nonlinear spinor field. A possible experimental testing for the string approximation of the Cooper pair is offered.
Cite
@article{arxiv.cond-mat/0001257,
title = {A String Approximation for Cooper Pair in High-T$_{\bf c}$ superconductivity},
author = {V. Dzhunushaliev},
journal= {arXiv preprint arXiv:cond-mat/0001257},
year = {2009}
}
Comments
Essential changes: (a) the section is added in which it is shown that Green's function method in the superconductivity theory is a realization of discussed Heisenberg quantization method; (b) Veneziano amplitude is discussed as an approximation for the 4-point Green's function in High-T_c; (c) it is shown that Eq.(53) has more natural solution on the layer rather than on 3 dimensional space