Theory of superconductivity. II. Properties of the modified electron-lattice states of low energy

Abstract

In addition to causing electron-phonon scattering, the electron-lattice interaction, considered in a previous paper, also modifies the structure of the stationary states, which become mixtures of the states considered in the adiabatic or Born-Oppenheimer approximation. The modified phonon and electron energies and electric current density are calculated. When a criterion depending on band structure is satisfied, the modified electronic configuration of lowest energy can be qualitatively different from the Fermi distribution of a normal metal, due to an effective interaction between electrons and holes of the same spin on each energy shell that arises from the electron-lattice interaction. Below a critical temperature there are two independent states of stationary free energy. The upper state has normal conductivity and heat capacity. The lower state has associated with it an electric current density that appears to have no dissipative resistance and that exhibits a Meissner effect with a resonance phenomenon at certain frequencies in an oscillatory field. In zero field the phase transition between these states is of second order, with a discontinuity in heat capacity at the transition temperature. An energy gap can occur, but it is not required in deriving the properties of the electric current density and of the phase transition between the two states. Various quantities calculated from the present theory for a simple model (effective mass, spherical Fermi surface, single conduction band) are in reasonable agreement with experimental values. Energies are generally an order of magnitude smaller than in the earlier theory of Fröhlich. © 1962 The American Physical Society.