Electron Orbital Angular Momentum and Spin- Orbit Coupling in Superconductivity

Received DOI: 2 Superconductivity arises when solids have conducting bands (singly occupied wave functions) that do not have electron-nuclear scattering (Fermi contact) and the temperature is low enough to eliminate partial wave scattering of electrons. This means that the conducting bands do not include s basis functions (atomic quantum numbers l ,m = 0), and the temperature is low enough so that electron scattering in conduction bands with l > 0 is negligible. In most cases, the transition to superconductivity involves a breakdown in the Born-Oppenheimer approximation that separates degenerate electronic states as distinct electron-phonon states. In the case of molecular wires, and related materials, based on-electron conjugation the transition to superconductivity may not be a first order phase transition but rather a weak continuous phase transition that has an asymptotic change in slope of resistivity v. temperature as the superconducting state is approached. The theory presented here is not in conflict in any substantive way with the standard model for superconductivity, BCS theory. Azimuthal quantum numbers (l) do not appear in BCS theory. The formulations of the two theories are distinct, so if the theories are to be combined it will be essential to reformulate (the quantum mechanical basis of) one or the other. The lack of superconductivity in Cu, Ag, and Au, all of which are excellent conductors, is due to their lowest energy conduction band being a s basis-set band, which will always have Fermi contact electron scattering resistivity. The confirmation of this band for copper can be seen in the zero slope of resistivity v. temperature at the lowest temperatures for the purest samples of this metal. Without a transition that removes Fermi contact, s basis set bands cannot be superconducting at any temperature because of Fermi contact induced resistivity. In this model of superconductivity the energy gap that is known to appear in superconducting states is caused by spin-orbit coupling and the magnetic field associated with the superconducting state. The magnetic field dependence of the energy gap in this model should be linear. In the BCS model the energy gap in superconductivity is not dependent on the magnetic field. 3 Energy gap measurements at varying magnetic fields should shed light on the validity of either or both theories. Bosonic conductors, such as aromatic hydrocarbons, are not capable to directly becoming superconductors. This is because in the absence of a magnetic field the ground state of …