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arXiv:cond-mat/0607623 · Physical Review Letters

Synergistic Polaron Formation in the Hubbard-Holstein Model at Small Doping

Alexandru Macridin, Brian Moritz, M. Jarrell, Thomas Maier

Published Aug 2, 2006• 49 citations
arXivHTMLPDF

Abstract

We study the effect of dynamical Holstein phonons on the physics of the Hubbard model at small doping using the dynamical cluster approximation on a 2x2 cluster. Nonlocal antiferromagnetic correlations are found to significantly enhance the electron-phonon coupling, resulting in polaron formation for moderate coupling strengths. At finite doping, the electron-phonon coupling is found to strongly enhance the nonlocal spin correlations, indicating a synergistic interplay between the electron-phonon coupling and antiferromagnetic correlations. Although it enhances the pairing interaction, the electron-phonon coupling is found to decrease the superconducting transition temperature, due to the reduction in the quasiparticle fraction.

DOI
10.1103/physrevlett.97.056402

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We study the effect of dynamical Holstein phonons on the physics of the Hubbard model at small doping using the dynamical cluster approximation on a 2x2 cluster. Nonlocal antiferromagnetic correlations are found to significantly enhance the electron-phonon coupling, resulting in polaron formation for moderate coupling strengths. At finite doping, the electron-phonon coupling is found to strongly enhance the nonlocal spin correlations, indicating a synergistic interplay between the electron-phonon coupling and antiferromagnetic correlations. Although it enhances the pairing interaction, the electron-phonon coupling is found to decrease the superconducting transition temperature, due to the reduction in the quasiparticle fraction.
The isotope effect (IE) in the two-dimensional Hubbard model with Holstein phonons is studied using the dynamical cluster approximation with quantum Monte Carlo. At small electron-phonon (EP) coupling the IE is negligible. For larger EP coupling there is a large and positive IE on the superconducting temperature that decreases with increasing doping. A significant IE also appears in the low-energy density of states, kinetic energy, and charge excitation spectrum. A negligible IE is found in the pseudogap and antiferromagnetic (AF) properties at small doping, whereas the AF susceptibility at intermediate doping increases with decreasing phonon frequency ${\ensuremath{\omega}}_{0}$. This IE stems from increased polaronic effects with decreasing ${\ensuremath{\omega}}_{0}$. A larger IE at smaller doping occurs due to stronger polaronic effects determined by the interplay of the EP interaction with stronger AF correlations. The IE of the Hubbard-Holstein model exhibits many similarities with the IE measured in cuprate superconductors.
We study effects of the Coulomb repulsion on the electron-phonon interaction (EPI) in the Holstein-Hubbard model, using the antiferromagnetic (AF) dynamical mean-field approximation. AF correlations strongly enhance EPI effects on the electron Green's function with respect to the paramagnetic correlated system, but the net effect of the Coulomb interaction is a moderate suppression of the EPI. Doping leads to additional suppression. In contrast, the Coulomb interaction strongly suppresses EPI effects on phonons, but the suppression weakens with doping.
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.
In this work we investigate doping and temperature dependences of electronic structure of system with strong electronic correlations and strong electron-phonon interaction modeling cuprates in the frameworks of the three-band p-d-Holstein model by a polaronic version of the generalized tight binding (GTB) method. Within this approach the electronic structure is formed by polaronic quasiparticles constructed as excitations between initial and final polaronic multielectron states. Doping and temperature effects are taken into account by occupation numbers of local excited polaronic states and variations in the magnitude of spin-spin correlation functions. Both effects are manifested in the reconstruction of band structure, Fermi contours, density of states and redistribution of the spectral weight over the Hubbard polaron subbands. Doping leads to transformation of Fermi contour from small hole pockets around k=(pi/2,pi/2) with inhomogeneous spectral weight distribution at small hole concentration to large contour around k=(pi,pi) in the overdoped compound as a result of two quantum phase transitions. In the system with phonon subsystem and EPI doping results in the top of the valence band splitting off and new polaron subbands appearance. Temperature increasing in the system with doped holes and moderate EPI leads to formation of the flatband around k=(pi,pi) and transfer of the spectral weight to the splitted off top of the valence band.
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 Holstein Hubbard and Holstein t-J models are studied for a wide range of phonon frequencies, electron-electron, and electron-phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron-phonon coupling, in particular in the adiabatic regime. Using parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.