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

arXiv:cond-mat/9404019 · Physical review. B, Condensed matter

Electron-phonon interactions in the presence of strong correlations

M. Grilli, Claudio Castellani

Published Dec 15, 1994• 128 citations
arXivHTMLPDF

Abstract

We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view. In particular, we show that the strong interaction is responsible for vertex corrections, which are strongly dependent on the ${\mathit{v}}_{\mathit{F}}$q/\ensuremath{\omega} ratio, where ${\mathit{v}}_{\mathit{F}}$ is the Fermi velocity and q and \ensuremath{\omega} are the transferred momentum and frequency, respectively. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the ${\mathit{v}}_{\mathit{F}}$q/\ensuremath{\omega}\ensuremath{\gg}1 limit. However, such effect is not present when ${\mathit{v}}_{\mathit{F}}$q/\ensuremath{\omega}\ensuremath{\ll}1. Analyzing the stability criterion for the compressibility, which involves the effective interactions in the dynamical limit, we show that a sizable electron-phonon interaction can push the system towards a phase separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model describing the basic structure of a ${\mathrm{CuO}}_{2}$ plane in copper oxides. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.

DOI
10.1103/physrevb.50.16880

Related papers

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

Renormalization of the electron-phonon interaction by strong electronic correlations in high- Tc superconductors

R. Zeyher, Miodrag L. Kulić

The renormalization of the electron-phonon interaction by strong electronic correlations is studied using a one-band Hubbard model with infinite repulsion and nearest (t model) and nearest and second-nearest (tt\ensuremath{'} model) neighbor hopping terms and an on-site electron-phonon coupling. Using Hubbard's X operators and an extension from 2 to N degrees of freedom for the electrons the leading contributions for the electron self-energy and the vertex function in 1/N and the electron-phonon coupling constant are given and numerically evaluated for a square lattice. We find that the momentum dependence of the vertex function depends strongly on doping: For large dopings it is rather weak, with decreasing doping it becomes more and more pronounced leading to a strong reduction of the vertex at larger momentum transfers until, for very small dopings, the vertex essentially consists of a forward scattering peak with a width proportional to the doping. This behavior occurs both in the t and the tt\ensuremath{'} models and also in one dimension where analytic expressions are derived. Correlation effects also change ${\mathrm{\ensuremath{\alpha}}}^{2}$F in general: The full-symmetric component ${\mathrm{\ensuremath{\alpha}}}^{2}$${\mathit{F}}_{1}$ is in the t model somewhat, in the tt\ensuremath{'} model rather strongly suppressed, especially near half-filling; the other symmetry components ${\mathrm{\ensuremath{\alpha}}}^{2}$${\mathit{F}}_{\mathit{i}}$ with i=2,...,5 increase strongly with decreasing doping and are of similar magnitude as ${\mathrm{\ensuremath{\alpha}}}^{2}$${\mathit{F}}_{1}$ near half-filling.Including also direct Coulomb repulsion nontrivial symmetries such as d wave become more stable than the s-wave order parameter below a critical value for the doping even for the considered phonon-mediated superconductivity. Most dramatic, however, is the quenching of the resistivity due to electron-phonon scattering both in the t and the tt\ensuremath{'} models at intermediate and small dopings. This result may explain the absence of phonon features in the experimental transport coefficients of high-${\mathit{T}}_{\mathit{c}}$ compounds. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Feb 1, 1996•147 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

Charge instabilities and electron-phonon interaction in the Hubbard-Holstein model

Andrea Di Ciolo, J. Lorenzana, M. Grilli +1 more

We consider the Hubbard-Holstein model in the adiabatic limit to investigate the effects of electron-electron interactions on the electron-phonon coupling. To this aim we compute at any momentum and filling the static charge susceptibility of the Hubbard model within the Gutzwiller approximation, and we find that electron-electron correlations effectively screen the electron coupling to the lattice. This screening is more effective at large momenta, and as a consequence, the charge-density-wave phase due to the usual Peierls instability of the Fermi-surface momenta is replaced by a phase-separation instability when the correlations are sizable.

arXiv:0806.3385•Physical Review B•Feb 2, 2009•27 citations

Renormalization of the electron-phonon coupling in the one-band Hubbard model

Erik Koch, R. Zeyher

We investigate the effect of electronic correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model. We calculate the static electron-phonon vertex within the linear response of Kotliar-Ruckenstein slave bosons in the paramagnetic saddle-point approximation. Within this approach the on-site Coulomb interaction $U$ strongly suppresses the coupling to Holstein phonons at low temperatures. Moreover, the vertex function does not show particularly strong forward scattering. Going to larger temperatures $kT\ensuremath{\sim}t$ we find that after an initial decrease with $U$, the electron-phonon coupling starts to increase with $U$, confirming a recent result of Cerruti, Cappelluti, and Pietronero. We show that this behavior is related to an unusual reentrant behavior from a phase separated to a paramagnetic state upon decreasing the temperature.

arXiv:cond-mat/0401089•Physical Review B•Sep 21, 2004•29 citations

Renormalization of the electron-phonon interaction in presence of charge fluctuations

R. Citro, S. Cojocaru, M. Marinaro

We investigate the effect of strong electron correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model in the presence of charge fluctuations. Specifically, we analyze the momentum modulation of the electron-phonon vertex induced by the electronic correlations. The role of the on-site Coulomb interaction $U$ is investigated in different regions of the Brillouin zone. The results reveal the presence of a strong forward scattering peak at low temperatures and, after an initial decrease with $U$, we find that the electron-phonon vertex starts to increase above an intermediate value of the Coulomb interaction. We show that this behavior is related to an incipient phase separation that takes place at a critical value of $U$ for fixed doping. A comparison with other approaches is also discussed.

Physical Review B•Sep 12, 2005•8 citations
We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view. In particular, we show that the strong interaction is responsible for vertex corrections, which are strongly dependent on the vF{\mathit{v}}_{\mathit{F}}vF​q/\ensuremath{\omega} ratio, where vF{\mathit{v}}_{\mathit{F}}vF​ is the Fermi velocity and q and \ensuremath{\omega} are the transferred momentum and frequency, respectively. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the vF{\mathit{v}}_{\mathit{F}}vF​q/\ensuremath{\omega}\ensuremath{\gg}1 limit. However, such effect is not present when vF{\mathit{v}}_{\mathit{F}}vF​q/\ensuremath{\omega}\ensuremath{\ll}1. Analyzing the stability criterion for the compressibility, which involves the effective interactions in the dynamical limit, we show that a sizable electron-phonon interaction can push the system towards a phase separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model describing the basic structure of a CuO2{\mathrm{CuO}}_{2}CuO2​ plane in copper oxides. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.
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 renormalization of the electron-phonon interaction by strong electronic correlations is studied using a one-band Hubbard model with infinite repulsion and nearest (t model) and nearest and second-nearest (tt\ensuremath{'} model) neighbor hopping terms and an on-site electron-phonon coupling. Using Hubbard's X operators and an extension from 2 to N degrees of freedom for the electrons the leading contributions for the electron self-energy and the vertex function in 1/N and the electron-phonon coupling constant are given and numerically evaluated for a square lattice. We find that the momentum dependence of the vertex function depends strongly on doping: For large dopings it is rather weak, with decreasing doping it becomes more and more pronounced leading to a strong reduction of the vertex at larger momentum transfers until, for very small dopings, the vertex essentially consists of a forward scattering peak with a width proportional to the doping. This behavior occurs both in the t and the tt\ensuremath{'} models and also in one dimension where analytic expressions are derived. Correlation effects also change ${\mathrm{\ensuremath{\alpha}}}^{2}$F in general: The full-symmetric component ${\mathrm{\ensuremath{\alpha}}}^{2}$F1{\mathit{F}}_{1}F1​ is in the t model somewhat, in the tt\ensuremath{'} model rather strongly suppressed, especially near half-filling; the other symmetry components ${\mathrm{\ensuremath{\alpha}}}^{2}$Fi{\mathit{F}}_{\mathit{i}}Fi​ with i=2,...,5 increase strongly with decreasing doping and are of similar magnitude as ${\mathrm{\ensuremath{\alpha}}}^{2}$F1{\mathit{F}}_{1}F1​ near half-filling.Including also direct Coulomb repulsion nontrivial symmetries such as d wave become more stable than the s-wave order parameter below a critical value for the doping even for the considered phonon-mediated superconductivity. Most dramatic, however, is the quenching of the resistivity due to electron-phonon scattering both in the t and the tt\ensuremath{'} models at intermediate and small dopings. This result may explain the absence of phonon features in the experimental transport coefficients of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ compounds. \textcopyright{} 1996 The American Physical Society.
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 consider the Hubbard-Holstein model in the adiabatic limit to investigate the effects of electron-electron interactions on the electron-phonon coupling. To this aim we compute at any momentum and filling the static charge susceptibility of the Hubbard model within the Gutzwiller approximation, and we find that electron-electron correlations effectively screen the electron coupling to the lattice. This screening is more effective at large momenta, and as a consequence, the charge-density-wave phase due to the usual Peierls instability of the Fermi-surface momenta is replaced by a phase-separation instability when the correlations are sizable.
We investigate the effect of electronic correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model. We calculate the static electron-phonon vertex within the linear response of Kotliar-Ruckenstein slave bosons in the paramagnetic saddle-point approximation. Within this approach the on-site Coulomb interaction UUU strongly suppresses the coupling to Holstein phonons at low temperatures. Moreover, the vertex function does not show particularly strong forward scattering. Going to larger temperatures $kT\ensuremath{\sim}t$ we find that after an initial decrease with UUU, the electron-phonon coupling starts to increase with UUU, confirming a recent result of Cerruti, Cappelluti, and Pietronero. We show that this behavior is related to an unusual reentrant behavior from a phase separated to a paramagnetic state upon decreasing the temperature.
We investigate the effect of strong electron correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model in the presence of charge fluctuations. Specifically, we analyze the momentum modulation of the electron-phonon vertex induced by the electronic correlations. The role of the on-site Coulomb interaction UUU is investigated in different regions of the Brillouin zone. The results reveal the presence of a strong forward scattering peak at low temperatures and, after an initial decrease with UUU, we find that the electron-phonon vertex starts to increase above an intermediate value of the Coulomb interaction. We show that this behavior is related to an incipient phase separation that takes place at a critical value of UUU for fixed doping. A comparison with other approaches is also discussed.