# Phonons and d -wave pairing in the two-dimensional Hubbard model

@article{Honerkamp2007PhononsAD, title={Phonons and d -wave pairing in the two-dimensional Hubbard model}, author={Carsten Honerkamp and Henry C. Fu and Dunghai Lee}, journal={Physical Review B}, year={2007}, volume={75}, pages={014503} }

We analyze the influence of phonons on the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-pairing instability in the Hubbard model on the two-dimensional square lattice at weak to moderate interaction $U$, using a functional renormalization group scheme with frequency-dependent interaction vertices. As measured by the pairing scale, the ${B}_{1g}$ buckling mode enhances the pairing, while other phonon modes decrease the pairing. When various phonon modes are included together, the net effect on the scale… Expand

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#### References

SHOWING 1-10 OF 36 REFERENCES

Electron-phonon vertex in the two-dimensional one-band Hubbard model

- Physics
- 2003

Using quantum Monte Carlo techniques, we study the effects of electronic correlations on the effective electron-phonon (el-ph) coupling in a two-dimensional one-band Hubbard model. We consider a… Expand

Deformation of the Fermi surface in the extended Hubbard model

- Physics
- 2001

The deformation of the Fermi surface induced by Coulomb interactions is investigated in the $t\ensuremath{-}{t}^{\ensuremath{'}}$-Hubbard model. The interplay of the local U and extended V… Expand

Electron-phonon interactions in the presence of strong correlations.

- Physics, Medicine
- Physical review. B, Condensed matter
- 1994

Analyzing the stability criterion for the compressibility, which involves the effective interactions in the dynamical limit, it is shown that a sizable electron-phonon interaction can push the system towards a phase separation instability. Expand

Phonon-mediated tuning of instabilities in the Hubbard model at half-filling

- Physics
- 2006

We obtain the phase diagram of the half-filled two-dimensional Hubbard model on a square lattice in the presence of Einstein phonons. We find that the interplay between the instantaneous… Expand

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

- Physics, Medicine
- Physical review. B, Condensed matter
- 1996

The renormalization of the electron-phonon interaction by strong electronic correlations is studied using a one-band Hubbard model with infinite repulsion and nearest ({ital t} model) and nearest and… Expand

Renormalization Group Approach to Strong-Coupled Superconductors

- Physics
- 2005

We develop an asymptotically exact renormalization-group approach that treats electron-electron and electron-phonon interactions on an equal footing. The approach allows an unbiased study of the… Expand

Influence of electron-phonon interaction on spin-fluctuation-induced superconductivity

- Physics
- 1999

We investigate the interplay of the electron-phonon and the spin fluctuation interaction for the superconducting state of YBa$_2$Cu$_3$O$_{7}$. The spin fluctuations are described within the nearly… Expand

dx2-y2 symmetry and the pairing mechanism.

- Physics, Medicine
- Physical review. B, Condensed matter
- 1996

Three different types of electron-phonon interactions affect the d_{x^2-y^2} pairing found within an RPA treatment of the 2D Hubbard model, implying that interactions which become more positive as the momentum transfer increases favor d_x-y-y pairing in a nearly half-filled band. Expand

Eliashberg equations of electrons on a square lattice: Interplay of strong electron-phonon interactions and electron correlations

- Physics
- 1998

We discuss vertex corrections to the Eliashberg equations of correlated electrons due to strong electron-phonon interactions. Local electron correlations have been taken into account in the… Expand

Electron-doping versus hole-doping in the 2D t-t' Hubbard model

- Physics
- 2001

Abstract:We compare the one-loop renormalization group flow to strong coupling of the electronic interactions in the two-dimensional t-t'-Hubbard model with t' = - 0.3t for band fillings smaller and… Expand