String approximation for the Cooper Pair in high-Tc superconductivity

Abstract

It is assumed that in some sense high-Tc superconductivity is similar to quantum chromodynamics (QCD). This means that the phonons in high-Tc superconductors have a strong interaction between themselves, like they do to gluons in the QCD. At the experimental level this means that in high-Tc superconductors nonlinear sound waves exist. It is possible that the existence of the strong phonon-phonon interaction can lead 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 leads to a very strong interaction between quark and antiquark, a similar situation can exist in the high-Tc 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 a potential term is considered. It is shown that the Green’s-function method in the superconductivity theory is a realization of the idea Heisenberg proposed for the quantization of a nonlinear spinor field. A possible experimental testing for the string approximation of the Cooper pair is offered.

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