19 research outputs found
Interaction of strongly correlated electrons and acoustical phonons
We investigate the interaction of correlated electrons with acoustical
phonons using the extended Hubbard-Holstein model in which both, the
electron-phonon interaction and the on-site Coulomb repulsion are considered to
be strong. The Lang-Firsov canonical transformation allows to obtain mobile
polarons for which a new diagram technique and generalized Wick's theorem is
used. This allows to handle the Coulomb repulsion between the electrons emerged
into a sea of phonon fields (\textit{phonon clouds}). The physics of emission
and absorption of the collective phonon-field mode by the polarons is discussed
in detail. Moreover, we have investigated the different behavior of optical and
acoustical phonon clouds when propagating through the lattice. In the
strong-coupling limit of the electron-phonon interaction, and in the normal as
well as in the superconducting phase, chronological thermodynamical averages of
products of acoustical phonon-cloud operators can be expressed by one-cloud
operator averages. While the normal one-cloud propagator has the form of a
Lorentzian, the anomalous one is of Gaussian form and considerably smaller.
Therefore, the anomalous electron Green's functions can be considered to be
more important than corresponding polarons functions, i.e., pairing of
electrons without phonon-clouds is easier to achieve than pairing of polarons
with such clouds.Comment: : 28 pages, 9 figures, revtex4. Invited paper for a special issue of
Low Temperature Physics dedicated to the 20th anniversary of HTS
Strong interaction of correlated electrons with phonons: Exchange of phonon clouds by polarons
We investigate the interaction of strongly correlated electrons with phonons
in the frame of the Hubbard-Holstein model. The electron-phonon interaction is
considered to be strong and is an important parameter of the model besides the
Coulomb repulsion of electrons and band filling. This interaction with the
nondispersive optical phonons has been transformed to the problem of mobile
polarons by using the canonical transformation of Lang and Firsov. We discuss
in particular the case for which the on-site Coulomb repulsion is exactly
cancelled by the phonon-mediated attractive interaction and suggest that
polarons exchanging phonon clouds can lead to polaron pairing and
superconductivity. It is then the frequency of the collective mode of phonon
clouds being larger than the bare frequency, which determines the
superconducting transition temperature.Comment: 23 pages, Submitted to Phys. Rev.