Electron-phonon interaction in Fermi systems

The momentum distribution function of a one-dimensional interacting many electron-phonon system is calculated analytically within the framework of the Luttinger model. We have shown that, even a small electron-electron interaction destroys the fermi surface and in the presence of the electron-phonon interaction the residual fermi surface vanishes completely and the function becomes a continuous function of the wave vector as we increase the coupling strength. It shows that in one dimension, the Fermi liquid theory breaks down completely, if we include the electron-phonon interactions along with the electron-electron interaction.The momentum distribution function of a one-dimensional interacting many electron-phonon system is calculated analytically within the framework of the Luttinger model. We have shown that, even a small electron-electron interaction destroys the fermi surface and in the presence of the electron-phonon interaction the residual fermi surface vanishes completely and the function becomes a continuous function of the wave vector as we increase the coupling strength. It shows that in one dimension, the Fermi liquid theory breaks down completely, if we include the electron-phonon interactions along with the electron-electron interaction.

AIP conference proceedingsJan 1, 20130 citations

Electron-phonon interaction in strongly correlated systems

V. A. Moskalenko

Theoretical and Mathematical PhysicsJun 1, 199711 citations

Presence versus absence of two-dimensional Fermi surface anomalies

Donovan L. Buterakos, DinhDuy Vu, Jiabin Yu +1 more

We theoretically consider Fermi surface anomalies manifesting in the temperature-dependent quasiparticle properties of two-dimensional (2D) interacting electron systems, comparing and contrasting with the corresponding three-dimensional (3D) Fermi liquid situation. In particular, employing microscopic many-body perturbative techniques, we obtain analytically the leading-order and the next-to-leading-order interaction corrections to the renormalized effective mass for three distinct physical interaction models: electron-phonon, electron-paramagnon, and electron-electron Coulomb coupling. We find that the 2D renormalized effective mass does not develop any Fermi surface anomaly due to electron-phonon interaction, manifesting $\mathcal{O}({T}^{2})$ temperature correction and thus remaining consistent with the Sommerfeld expansion of the noninteracting Fermi function, in contrast to the corresponding 3D situation where the temperature correction to the renormalized effective mass has the anomalous ${T}^{2}logT$ behavior. In contrast, both electron-paramagnon and electron-electron interactions lead to the anomalous $\mathcal{O}(T)$ corrections to the 2D effective mass renormalization in contrast to ${T}^{2}logT$ behavior in the corresponding 3D interacting systems. We provide detailed analytical results, and comment on the conditions under which a ${T}^{2}logT$ term could possibly arise in the 2D quasiparticle effective mass from electron-phonon interactions. We also compare results for the temperature-dependent specific heat in the interacting 2D and 3D Fermi systems, using the close connection between the effective mass and specific heat.We theoretically consider Fermi surface anomalies manifesting in the temperature-dependent quasiparticle properties of two-dimensional (2D) interacting electron systems, comparing and contrasting with the corresponding three-dimensional (3D) Fermi liquid situation. In particular, employing microscopic many-body perturbative techniques, we obtain analytically the leading-order and the next-to-leading-order interaction corrections to the renormalized effective mass for three distinct physical interaction models: electron-phonon, electron-paramagnon, and electron-electron Coulomb coupling. We find that the 2D renormalized effective mass does not develop any Fermi surface anomaly due to electron-phonon interaction, manifesting $\mathcal{O}({T}^{2})$ temperature correction and thus remaining consistent with the Sommerfeld expansion of the noninteracting Fermi function, in contrast to the corresponding 3D situation where the temperature correction to the renormalized effective mass has the anomalous ${T}^{2}logT$ behavior. In contrast, both electron-paramagnon and electron-electron interactions lead to the anomalous $\mathcal{O}(T)$ corrections to the 2D effective mass renormalization in contrast to ${T}^{2}logT$ behavior in the corresponding 3D interacting systems. We provide detailed analytical results, and comment on the conditions under which a ${T}^{2}logT$ term could possibly arise in the 2D quasiparticle effective mass from electron-phonon interactions. We also compare results for the temperature-dependent specific heat in the interacting 2D and 3D Fermi systems, using the close connection between the effective mass and specific heat.

arXiv:2101.07815Physical review. B./Physical review. BMay 28, 20214 citations

Electron-phonon interaction in the Hubbard model

Anh Tuan Hoang, Toan Thang Nguyen, Ngoc Thuan Nguyen

Unknown eBooksJun 1, 19940 citations

Electron-phonon interactions in the presence of strong correlations

M. Grilli, Claudio Castellani

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.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.

arXiv:cond-mat/9404019Physical review. B, Condensed matterDec 15, 1994128 citations

\mathcal{O}({T}^{2})

temperature correction and thus remaining consistent with the Sommerfeld expansion of the noninteracting Fermi function, in contrast to the corresponding 3D situation where the temperature correction to the renormalized effective mass has the anomalous

{T}^{2}logT

behavior. In contrast, both electron-paramagnon and electron-electron interactions lead to the anomalous

\mathcal{O}(T)

corrections to the 2D effective mass renormalization in contrast to

{T}^{2}logT

behavior in the corresponding 3D interacting systems. We provide detailed analytical results, and comment on the conditions under which a

{T}^{2}logT

term could possibly arise in the 2D quasiparticle effective mass from electron-phonon interactions. We also compare results for the temperature-dependent specific heat in the interacting 2D and 3D Fermi systems, using the close connection between the effective mass and specific heat.

{\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.