Bismuth cubic superconductors: polaronic and superconducting properties of the Rice-Sneddon model

The Rice-Sneddon model of cubic bismuth superconductors is studied by combined analytical, variational, and numerical methods. A new representation is introduced for the phononic degrees of freedom, which makes phonon wavefunctions at different sites to be orthogonal. Due to that, then, the generalized Lang-Firsov transformation with two variational parameters may be exactly performed. One parameter is the classical displacement, whereas the second one is the squeezing variable. The transformed, effective electronic Hamiltonian has the form of the extended Hubbard model with longer-range electron-electron interactions and negative value of the Hubbard interaction, U. This effective Hamiltonian is further studied by means of numerical and analytical methods. First, using the Lanczos diagonalization scheme, the polaronic properties of the derived model have been studied. Second, the superconducting transition temperature T-c has been evaluated in the Hartree-Fock approximation. From the calculated values of T-c it is argued that the bare, electronic interaction U should be close to + 0.36 eV. (C) 2000 Elsevier Science B.V. All rights reserved.