Theory of Superconductivity. I. Electron-Lattice Interaction

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Abstract
The electron-lattice interaction responsible for electrical resistivity in perfect metallic crystals is shown to be a form of Jahn-Teller effect. It does not occur in the Born-Oppenheimer (adiabatic) approximation even when the electron-electron interaction is taken fully into account. The matrix elements that describe corrections to the Born-Oppenheimer approximation are derived by a general argument that can be applied to metals with arbitrary electronic energy band structure, and the case of monatomic metals is worked out in detail in the effective mass approximation. Two types of physical phenomena are attributed to these matrix elements. The first is ordinary electrical resistivity due to electron-phonon scattering. The present derivation leads to the same formal structure as the usual theory, but should give quantitatively different results when applied to specific metals. The second type of physical phenomenon is a modification to the stationary states of the electron-lattice system that can significantly alter the total energy spectrum at low energies, and mixes states of electron excitation and lattice excitation. An effect of this kind can account qualitatively for the disappearance of electrical resistivity at finite temperatures in superconductors. Other special properties of superconductors should follow from consideration of the stationary states modified by the Jahn-Teller effect.

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