Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Phonon-inducedd-wave pairing in the two-dimensional Hubbard model

Marcin Mierzejewski, J. Zieliński

Published Aug 1, 1995• 13 citations
Publisher

Abstract

We discuss phonon-induced anisotropic superconductivity of strongly correlated quasiparticles within the two-dimensional Hubbard model. The generalized Fr\"olich-like canonical transformation leads to pairing interactions that become repulsive for vanishing concentration of holes but are attractive at low dopings. Our results indicate that the electron-phonon coupling in the presence of strong electron-electron correlations favors the formation of d-wave superconductivity.

DOI
10.1103/physrevb.52.3079

Related papers

Anisotropic superconductivity in the two-dimensional Hubbard model

Marcin Mierzejewski, J. Zieliński

We address the problem of superconductivity in a system where the only many-body interactions are repulsive. The Eliashberg equations have been generalized to account for possible pairing correlations in the two-dimensional Hubbard model. Details of the two-dimensional band structure have been explicitly taken into account when considering the symmetry of the superconducting state. The pairing kernels have been discussed at low doping and at temperatures close to the superconducting transition temperature. We have proved that local Coulomb repulsion leads to attractive pairing correlations in the $d$-wave channel. Extended $s$-wave superconductivity is less likely to occur within this purely electronic model, at least in the physically interesting region of doping.

Physical review. B, Condensed matter•Nov 1, 1997•17 citations

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

Marcin Mierzejewski, J. Zieliński, P. Entel

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.

physica status solidi (b)•Dec 1, 1996•5 citations

d-wave superconductivity in a strongly correlated electron-phonon system

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.

Physical review. B, Condensed matter•Jan 1, 1996•19 citations

Correlation-renormalized electron-phonon interaction in the two-dimensional Hubbard model

Marcin Mierzejewski, J. Zieliński, P. Entel

We have addressed the problem of the influence of Coulomb correlations on the electron-phonon interaction in the two-dimensional Hubbard model. Both the energy and momentum dependence of the renormalization factor have been taken into account. We find that the superconducting properties of the system depend strongly on the phononic momentum and energy transfer values. This dependence is related to the symmetry of the superconducting order parameter. On one hand, the renormalization of the electron-phonon coupling function acts to the detriment of superconductivity in the s-wave channel. On the other hand, an enhancement of pairing correlations for anisotropic extended s-wave and d-wave superconductivity is observed.

Physical review. B, Condensed matter•Oct 1, 1999•7 citations

Relevance of phonon dynamics in strongly correlated systems coupled to phonons: Dynamical mean-field theory analysis

Giorgio Sangiovanni, Massimo Capone, Claudio Castellani

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.

arXiv:cond-mat/0512020•Physical Review B•Apr 21, 2006•43 citations

Strong interaction of correlated electrons with phonons: Exchange of phonon clouds by polarons

V. A. Moskalenko, P. Entel, M. Marinaro +1 more

The interaction of strongly correlated electrons with phonons in the framework of the Hubbard-Holstein model is investigated. The electron-phonon interaction is considered to be strong and is an important parameter of the model, in addition to the Coulomb repulsion of electrons and the band filling. This interaction with nondispersive optical phonons is transformed to the problem of mobile polarons using the canonical transformation of Lang and Firsov. We discuss the case where the on-site Coulomb repulsion is exactly canceled by the phonon-mediated attractive interaction. It is suggested that polarons exchanging phonon clouds can lead to polaron pairing and superconductivity. The fact that the frequency of the collective mode of phonon clouds is larger than the bare frequency then determines the superconducting transition temperature.

arXiv:cond-mat/0208160•Journal of Experimental and Theoretical Physics•Sep 1, 2003•8 citations
We discuss phonon-induced anisotropic superconductivity of strongly correlated quasiparticles within the two-dimensional Hubbard model. The generalized Fr"olich-like canonical transformation leads to pairing interactions that become repulsive for vanishing concentration of holes but are attractive at low dopings. Our results indicate that the electron-phonon coupling in the presence of strong electron-electron correlations favors the formation of d-wave superconductivity.
We address the problem of superconductivity in a system where the only many-body interactions are repulsive. The Eliashberg equations have been generalized to account for possible pairing correlations in the two-dimensional Hubbard model. Details of the two-dimensional band structure have been explicitly taken into account when considering the symmetry of the superconducting state. The pairing kernels have been discussed at low doping and at temperatures close to the superconducting transition temperature. We have proved that local Coulomb repulsion leads to attractive pairing correlations in the ddd-wave channel. Extended sss-wave superconductivity is less likely to occur within this purely electronic model, at least in the physically interesting region of doping.
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 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.
We have addressed the problem of the influence of Coulomb correlations on the electron-phonon interaction in the two-dimensional Hubbard model. Both the energy and momentum dependence of the renormalization factor have been taken into account. We find that the superconducting properties of the system depend strongly on the phononic momentum and energy transfer values. This dependence is related to the symmetry of the superconducting order parameter. On one hand, the renormalization of the electron-phonon coupling function acts to the detriment of superconductivity in the s-wave channel. On the other hand, an enhancement of pairing correlations for anisotropic extended s-wave and d-wave superconductivity is observed.
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 interaction of strongly correlated electrons with phonons in the framework of the Hubbard-Holstein model is investigated. The electron-phonon interaction is considered to be strong and is an important parameter of the model, in addition to the Coulomb repulsion of electrons and the band filling. This interaction with nondispersive optical phonons is transformed to the problem of mobile polarons using the canonical transformation of Lang and Firsov. We discuss the case where the on-site Coulomb repulsion is exactly canceled by the phonon-mediated attractive interaction. It is suggested that polarons exchanging phonon clouds can lead to polaron pairing and superconductivity. The fact that the frequency of the collective mode of phonon clouds is larger than the bare frequency then determines the superconducting transition temperature.