On the relation between two models for superconductors with a structural distortion

Two three-dimensional models exhibiting coexistence of superconductivity and lattice distortion are discussed. One of the models, studied in detail by Rusinov, Do Chan Kat and Kopayev, takes into account the superconductivity inter- and intra-band pairing phenomenologically. The other has been derived by Mattis and Langer from a Fröhlich-type hamiltonian by eliminating the linear electron-phonon coupling in the presence of a “condensing” phonon mode. Both approaches are shown to agree in the limit ω_D å μ, where ω_D is the cut-off energy and ω is the deviation of the chemical potential from the band centre.