Theory of Superconductivity

A quantum-mechanical model has been developed exhibiting the characteristic properties of superconductors. Localized "atomic" wave functions are used to construct many-electron wave functions obeying the exclusion principle and corresponding to definite electronic localization ($\phi$ functions). The crystal translations will take these over into a set of, say $\omega$, equivalent $\phi$-functions. Quantum resonance of these provides a zero-order wave function with the correct symmetry properties. ($\Psi$-functions.) The $\phi$-functions of small $\omega$ have a high translational symmetry and are referred to as "electron-lattices." The model has super-conducting properties if its lowest state is described by a $\psi$-function obtained through the resonance of at least three resonating electron lattices, and if this state is somewhat depressed below the continuum of high $\omega$-states. The latter can also be described in the standard band formalism. In the absence of external fields the lowest state is without a current. If the transition from $\phi$- to $\psi$-functions is carried out in the presence of a magnetic field, one automatically obtains a current "induced" by the field, and connected with it by the well-known London relation. The present method is not adequate to prove that the conditions stated are actually satisfied in superconductors. Nevertheless, qualitative quantum-chemical arguments make it appear plausible that these conditions are satisifed in the regions of the periodic table where the actual superconductors are located. Conversely, if the theory is accepted, a rather detailed insight is gained into the quantum-chemical properties of superconductors. The recent experimental and theoretical work on the isotope effect is being discussed.