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physica status solidi (b)

D‐Wave Superconductivity Induced Renormalization of Phonons in Strongly Interacting Fermion Systems

Marcin Mierzejewski, J. Zieliński, P. Entel

Published Dec 1, 1996• 5 citations
Publisher

Abstract

Abstract We have calculated changes in the phonon self‐energy originating from d‐wave superconductivity in the two‐dimensional Hubbard model (U → ∞ limit). Strong local correlations have been incorporated within the mean‐field approximation for auxiliary boson fields. Due to the presence of correlated quasiparticles at the Fermi surface, changes in phonon‐energy shifts and linewidths strongly depend on the concentration of holes. In particular, pronounced effects have been derived for low frequency q = 0 phonons at low doping, where superconductivity starts to set in.

DOI
10.1002/pssb.2221980226

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Physical review. B, Condensed matter•Aug 1, 1995•25 citations
Abstract We have calculated changes in the phonon self‐energy originating from d‐wave superconductivity in the two‐dimensional Hubbard model (U → ∞ limit). Strong local correlations have been incorporated within the mean‐field approximation for auxiliary boson fields. Due to the presence of correlated quasiparticles at the Fermi surface, changes in phonon‐energy shifts and linewidths strongly depend on the concentration of holes. In particular, pronounced effects have been derived for low frequency q = 0 phonons at low doping, where superconductivity starts to set in.
The properties of the electron-phonon interaction in the presence of a sizable electronic repulsion at finite doping are studied by investigating the metallic phase of the Hubbard-Holstein model with dynamical mean-field theory. Analyzing the quasiparticle weight at finite doping, we find that a large Coulomb repulsion reduces the effect of electron-phonon coupling at low energy, while this reduction is not present at high energy. The renormalization of the electron-phonon coupling induced by the Hubbard repulsion depends in a surprisingly strong and nontrivial way on the phonon frequency. Our results suggest that phonon might affect differently high-energy and low-energy properties and this, together with the effect of phonon dynamics, should be carefully taken into account when the effects of the electron-phonon interaction in a strongly correlated system, like the superconducting cuprates, are discussed.
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.
Within the time-dependent Gutzwiller approximation applied to one-dimensional Holstein and Su-Schrieffer-Heeger-Hubbard models, we study the influence of electron correlations on the phonon self-energy. For the local Holstein coupling, we find that the phonon-frequency renormalization gets weakened upon increasing the on-site interaction UUU for all momenta. In contrast, correlations can enhance the phonon-frequency shift for small wave vectors in the Su-Schrieffer-Heeger-Hubbard model. Moreover, the time-dependent Gutzwiller approximation applied to the latter model provides a mechanism which leads to phonon-frequency corrections at intermediate momenta due to the coupling with double-occupancy fluctuations. Both models display a shift of the nesting induced to a q=0q=0q=0 instability when the on-site interaction becomes sufficiently strong and thus establishing phase separation as a generic phenomenon of strongly correlated electron-phonon coupled systems.
We show that a strongly renormalized band of polaronic quasiparticle excitations is induced at the Fermi level of an interacting many-electron system on increasing the coupling of the electrons to local phonons. We give results for the local density of states at zero temperature both for the electrons and phonons. The polaronic quasiparticles satisfy Luttinger's theorem for all regimes considered, and their dispersion shows a kink similar to that observed experimentally in copper oxides. Our calculations are based on the dynamical mean field theory and the numerical renormalization group for the hole-doped Holstein-Hubbard model and large on-site repulsion.
The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) is momentum dependent. Using Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.