Theory of Superconductivity

Abstract

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 ($\ensuremath{\varphi}$ functions). The crystal translations will take these over into a set of, say $\ensuremath{\omega}$, equivalent $\ensuremath{\varphi}$-functions. Quantum resonance of these provides a zero-order wave function with the correct symmetry properties. ($\ensuremath{\Psi}$-functions.) The $\ensuremath{\varphi}$-functions of small $\ensuremath{\omega}$ 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 $\ensuremath{\psi}$-function obtained through the resonance of at least three resonating electron lattices, and if this state is somewhat depressed below the continuum of high $\ensuremath{\omega}$-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 $\ensuremath{\varphi}$- to $\ensuremath{\psi}$-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.