Bosonization of coupled electron-phonon systems

U. Trapper, Holger Fehske, Martin Deeg +1 more

Marcin Mierzejewski, J. Zieliński, P. Entel

The problem of phonon-mediated and phonon-free contributions to d-wave superconductivity in the two-dimensional Hubbard model has been addressed. Strong local correlations (U\ensuremath{\rightarrow}\ensuremath{\infty} limit) have been incorporated in the slave boson formulation. In order to consider electron-boson and electron-phonon coupling on equal footing, fluctuations of the auxiliary boson fields over their mean-field value have been introduced. The magnitude of effective pairing interactions derived with the help of a canonical transformation indicates that within the weak-coupling theory, phonon-mediated pairing plays a marginal role and can be dominated by a phonon-free pairing mechanism. On the other hand, in the strong-coupling limit (Eliashberg formulation), electron-phonon and electron-phonon-boson interactions can significantly enhance the superconducting transition temperature. It is also shown that Coulomb correlations together with the electron-phonon interaction can effectively stabilize a d-wave superconducting state. \textcopyright{} 1996 The American Physical Society.

M. Schneider, E. Sigmund

Christoph Brockt, Eric Jeckelmann

We investigate the scattering of an electron by phonons in a small structure between two one-dimensional tight-binding leads. This model mimics the quantum electron transport through atomic wires or molecular junctions coupled to metallic leads. The electron-phonon-coupled structure is represented by the Holstein model. We observe permanent energy transfer from the electron to the phonon system (dissipation), transient self-trapping of the electron in the electron-phonon-coupled structure (due to polaron formation and multiple reflections at the structure edges), and transmission resonances that depend strongly on the strength of the electron-phonon coupling and the adiabaticity ratio. A recently developed TEBD algorithm, optimized for bosonic degrees of freedom, is used to simulate the quantum dynamics of a wave packet launched against the electron-phonon-coupled structure. Exact results are calculated for a single electron-phonon site using scattering theory and analytical approximations are obtained for limiting cases.

Eric Jeckelmann, Chunli Zhang, Steven R. White

A. S. Alexandrov, Nevill Mott

In the adiabatic Migdal description of coupled electrons and phonons the instability appears at the bare coupling constant A ~ 1/2: the phonon frequency renormalised by the interaction u ~ u>\/l — 2A (Chapter 3). In a more general sense this is a boson vacuum instability driven by the strong interaction of fermionic and bosonic fields.