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/0611067 · Journal of Physics Condensed Matter

Suppression of superconductivity in the Hubbard model by buckling and breathing phonons

Alexandru Macridin, Brian Moritz, Mark Jarrell, Thomas Maier

Published Oct 31, 2012• 9 citations
arXivHTMLPDF

Abstract

We study the effect of buckling and breathing phonons, relevant for cuprate superconductors, on the d-wave superconductivity in the two-dimensional Hubbard model by employing dynamical cluster Monte Carlo calculations. The interplay of electronic correlations and the electron-phonon interaction produces two competing effects: an enhancement of the effective d-wave pairing interaction, which favors d-wave superconductivity, and a strong renormalization of the single-particle propagator, which suppresses superconductivity. In the region of the parameter space relevant for cuprate superconductors, we find that the buckling and the breathing phonons suppress the superconductivity.

DOI
10.1088/0953-8984/24/47/475603

Related papers

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

Carsten Honerkamp A, Henry Fu, D. H. Lee

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 is small. However, in situations where $d$-wave superconductivity and other tendencies, e.g., antiferromagnetism, are closely competing, the combined effect of different phonons may be able to tip the balance towards pairing.

arXiv:cond-mat/0605161•Physical Review B•Jan 4, 2007•57 citations

Enhancing d -wave superconductivity with nearest-neighbor attraction in the extended Hubbard model

Mi Jiang

Motivated by the recent discovery of the anomalously nearest-neighbor attraction arising from the electron-phonon coupling, we quantitatively investigate the enhancing effects of this additional attractive channel on the $d$-wave superconductivity based on dynamic cluster quantum Monte Carlo calculations of a doped two-dimensional extended Hubbard model with nearest-neighbor attraction $\ensuremath{-}V$. Focusing on the range of $0<\ensuremath{-}V/t\ensuremath{\le}2$, our simulations indicate that the dynamics of $d$-wave projected pairing interaction is attractive at all frequencies and increases with $|V|$. Moreover, turning on $\ensuremath{-}V$ attraction enhances the $(\ensuremath{\pi},\ensuremath{\pi})$ spin fluctuations but only enhances (suppresses) the charge fluctuations for small (large) momentum transfer. Thus, at $V/t=\ensuremath{-}1$ relevant to the ``holon folding branch'', the charge fluctuations are insufficient to compete with the $d$-wave pairing interaction strengthened by enhanced spin fluctuations. Our work suggests the underlying rich interplay between the spin and charge fluctuations in giving rise to the superconducting properties.

arXiv:2108.12950•Physical review. B./Physical review. B•Jan 13, 2022•30 citations

Band Renormalization Effect on Interplay between Antiferromagnetism and Superconductivity in Hubbard Model

Kenji Kobayashi, Hisatoshi Yokoyama

To study the relationship between antiferromagnetism (AF) and superconductivity (SC) in cuprate superconductors, we have performed a variational Monte Carlo calculation on the two-dimensional Hubbard model with a diagonal transfer t' [1,2]. The following improvements are introduced into the variational function: (1) Coexistence of AF and d-wave singlet gaps that allows a continuous description of their interplay, (2) band renormalization effect owing to the electron correlation up to the fourth-neighbor hoppings, and (3) refined doublon-holon correlation factors. It is found that the AF and SC orders become coexistent or competitive according to the values of model parameters, U/t, t'/t, and δ (doping rate), and the effective band is strongly renormalized for large U/t and low doping rates, so as to recover the nesting condition favorable to AF.

Asia Pacific Physics Conference (APPC)•Mar 19, 2014•2 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

Effect of long-range hopping on Tc in a two-dimensional Hubbard-Holstein model of the cuprates

Ehsan Khatami, Alexandru Macridin, Mark Jarrell

We study the effect of long-range hoppings on ${T}_{c}$ for the two-dimensional (2D) Hubbard model with and without Holstein phonons using parameters evaluated from band-structure calculations for cuprates. Employing the dynamical cluster approximation (DCA) with a quantum Monte Carlo (QMC) cluster solver for a 4-site cluster, we observe that without phonons, the long-range hoppings, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, generally suppress ${T}_{c}$. We argue that this trend remains valid for larger clusters. In the presence of the Holstein phonons, a finite ${t}^{\ensuremath{'}}$ enhances ${T}_{c}$ in the under-doped region for the hole-doped system, consistent with local-density approximation (LDA) calculations and experiment. This is interpreted through the suppression of antiferromagnetic (AF) correlations and the interplay between polaronic effects and the antiferromagnetism.

arXiv:0806.3996•Physical Review B•Aug 8, 2008•22 citations

New insights into high temperature superconductivity from a computational solution of the two-dimensional Hubbard model

Thomas Maier, James B. White, Mark Jarrell +2 more

The Cray X1 in the Center for Computational Sciences at Oak Ridge National Laboratory as well as algorithmic improvements over the past decade enable significant new science in the simulation of high-temperature cuprate superconductors. We describe the method of dynamic cluster approximation with quantum Monte Carlo, along with its computational requirements. We then show the unique capabilities of the X1 for supporting this method and delivering near optimal performance. This allows us to study systematically the cluster size dependence of the superconductivity in the conventional two-dimensional Hubbard model, which is commonly believed to describe high-temperature superconductors. Due to the non-locality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, converged results are found that display a finite temperature instability to d-wave superconductivity. The results we report here demonstrate for the first time that superconductivity is possible in a system of strongly correlated electrons without the need of a phonon mediated attractive interaction.

Journal of Physics Conference Series•Jan 1, 2005•0 citations
We study the effect of buckling and breathing phonons, relevant for cuprate superconductors, on the d-wave superconductivity in the two-dimensional Hubbard model by employing dynamical cluster Monte Carlo calculations. The interplay of electronic correlations and the electron-phonon interaction produces two competing effects: an enhancement of the effective d-wave pairing interaction, which favors d-wave superconductivity, and a strong renormalization of the single-particle propagator, which suppresses superconductivity. In the region of the parameter space relevant for cuprate superconductors, we find that the buckling and the breathing phonons suppress the superconductivity.
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 UUU, using a functional renormalization group scheme with frequency-dependent interaction vertices. As measured by the pairing scale, the B1g{B}_{1g}B1g​ 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 is small. However, in situations where ddd-wave superconductivity and other tendencies, e.g., antiferromagnetism, are closely competing, the combined effect of different phonons may be able to tip the balance towards pairing.
Motivated by the recent discovery of the anomalously nearest-neighbor attraction arising from the electron-phonon coupling, we quantitatively investigate the enhancing effects of this additional attractive channel on the ddd-wave superconductivity based on dynamic cluster quantum Monte Carlo calculations of a doped two-dimensional extended Hubbard model with nearest-neighbor attraction $\ensuremath{-}V$. Focusing on the range of $0<\ensuremath{-}V/t\ensuremath{\le}2$, our simulations indicate that the dynamics of ddd-wave projected pairing interaction is attractive at all frequencies and increases with ∣V∣|V|∣V∣. Moreover, turning on $\ensuremath{-}V$ attraction enhances the $(\ensuremath{\pi},\ensuremath{\pi})$ spin fluctuations but only enhances (suppresses) the charge fluctuations for small (large) momentum transfer. Thus, at $V/t=\ensuremath{-}1$ relevant to the ``holon folding branch'', the charge fluctuations are insufficient to compete with the ddd-wave pairing interaction strengthened by enhanced spin fluctuations. Our work suggests the underlying rich interplay between the spin and charge fluctuations in giving rise to the superconducting properties.
To study the relationship between antiferromagnetism (AF) and superconductivity (SC) in cuprate superconductors, we have performed a variational Monte Carlo calculation on the two-dimensional Hubbard model with a diagonal transfer t' [1,2]. The following improvements are introduced into the variational function: (1) Coexistence of AF and d-wave singlet gaps that allows a continuous description of their interplay, (2) band renormalization effect owing to the electron correlation up to the fourth-neighbor hoppings, and (3) refined doublon-holon correlation factors. It is found that the AF and SC orders become coexistent or competitive according to the values of model parameters, U/t, t'/t, and δ (doping rate), and the effective band is strongly renormalized for large U/t and low doping rates, so as to recover the nesting condition favorable to AF.
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.
We study the effect of long-range hoppings on Tc{T}_{c}Tc​ for the two-dimensional (2D) Hubbard model with and without Holstein phonons using parameters evaluated from band-structure calculations for cuprates. Employing the dynamical cluster approximation (DCA) with a quantum Monte Carlo (QMC) cluster solver for a 4-site cluster, we observe that without phonons, the long-range hoppings, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, generally suppress Tc{T}_{c}Tc​. We argue that this trend remains valid for larger clusters. In the presence of the Holstein phonons, a finite ${t}^{\ensuremath{'}}$ enhances Tc{T}_{c}Tc​ in the under-doped region for the hole-doped system, consistent with local-density approximation (LDA) calculations and experiment. This is interpreted through the suppression of antiferromagnetic (AF) correlations and the interplay between polaronic effects and the antiferromagnetism.
The Cray X1 in the Center for Computational Sciences at Oak Ridge National Laboratory as well as algorithmic improvements over the past decade enable significant new science in the simulation of high-temperature cuprate superconductors. We describe the method of dynamic cluster approximation with quantum Monte Carlo, along with its computational requirements. We then show the unique capabilities of the X1 for supporting this method and delivering near optimal performance. This allows us to study systematically the cluster size dependence of the superconductivity in the conventional two-dimensional Hubbard model, which is commonly believed to describe high-temperature superconductors. Due to the non-locality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, converged results are found that display a finite temperature instability to d-wave superconductivity. The results we report here demonstrate for the first time that superconductivity is possible in a system of strongly correlated electrons without the need of a phonon mediated attractive interaction.