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

The Rice-Sneddon model of cubic bismuth superconductors is studied by combi ned analytical, variational, and numerical methods. A new representation is introduced for the phononic degrees of freedom, which makes phonon wavefun ctions at different sites to be orthogonal. Due to that, then, the generali zed Lang-Firsov transformation with two variational parameters may be exact ly performed. One parameter is the classical displacement, whereas the seco nd one is the squeezing variable. The transformed, effective electronic Ham iltonian has the form of the extended Hubbard model with longer-range elect ron-electron interactions and negative value of the Hubbard interaction, U. This effective Hamiltonian is further studied by means of numerical and an alytical methods. First, using the Lanczos diagonalization scheme, the pola ronic properties of the derived model have been studied. Second, the superc onducting transition temperature T-c has been evaluated in the Hartree-Fock approximation. From the calculated values of T-c it is argued that the bar e, electronic interaction U should be close to + 0.36 eV. (C) 2000 Elsevier Science B.V. All rights reserved.