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Europhysics Letters (EPL)

Multimode electron-phonon coupling in the two-dimensional t-J–Holstein model

Didier Poilblanc, Tôru Sakai, Douglas J. Scalapino, Werner R. Hanke

Published May 10, 1996• 14 citations
Publisher

Abstract

Polaronic effects are investigated in the two-dimensional t − J model (describing Cu spins and holes of the planes in high- T c cuprates) in the presence of in-plane dynamic oxygen breathing modes. We focus on the effect of dynamic multi-phonon modes. Spin and charge structure factors are computed. We found evidence for self-localization of the holes and increased short-range antiferromagnetic spin-spin correlations between the remaining spins. This effect persists when all the in-plane oxygen vibration degrees of freedom are taken into account. This suggests that dynamic phonons could play a key role in stabilizing inhomogeneous stripe phases or domain wall structures.

DOI
10.1209/epl/i1996-00466-6

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Polaronic effects are investigated in the two-dimensional t − J model (describing Cu spins and holes of the planes in high- T c cuprates) in the presence of in-plane dynamic oxygen breathing modes. We focus on the effect of dynamic multi-phonon modes. Spin and charge structure factors are computed. We found evidence for self-localization of the holes and increased short-range antiferromagnetic spin-spin correlations between the remaining spins. This effect persists when all the in-plane oxygen vibration degrees of freedom are taken into account. This suggests that dynamic phonons could play a key role in stabilizing inhomogeneous stripe phases or domain wall structures.
We investigate the interplay of electron–phonon (EP) coupling and strong electronic correlations in the frame of the two–dimensional (2D) Holstein t–J model (HtJM), focusing on polaronic ordering phenomena for the quarter–filled band case. The use of direct Lanczos diagonalization on finite lattices allows us to include the effects of quantum phonon fluctuations in the calculation of spin/charge structure factors and hole–phonon correlation functions. In the adiabatic strong coupling regime we found evidence for “self-localization ” of polaronic carriers in a (π, π) charge-modulated structure, a type of superlattice solidification reminiscent of those observed in the nickel perovskites La2−xSrxNiO4+y. Electron diffraction measurements on the nickel oxide analogue of the layered high–Tc 214 copper oxide compound, La2−xNixCuO4, reveal a (π, π)–superstructure spot at quarter filling, i.e. for x = 0.5, which has been interpreted as sign of a truly 2D polaron ordered phase [1]. To study charge – and spin–ordering phenomena in such systems, exhibiting besides a substantial EP interaction strong Coulomb correlations, let us consider the planar t-J model with an additional on-site Holstein hole-phonon coupling:
We study the effect of diagonal and off-diagonal electron-phonon coupling in the ground state properties of the $t\text{\ensuremath{-}}J$ model. Adiabatic and quantum phonons are considered using Lanczos techniques. Charge tiles and stripe phases with mobile holes (localized holes) are observed at intermediate (large) values of the diagonal electron-phonon coupling. The stripes are stabilized by half-breathing modes, while the tiles arise due to the development of extended breathing modes. Off-diagonal terms destabilize the charge inhomogeneous structures with mobile holes by renormalizing the diagonal coupling but do not produce new phases. Buckling modes are also studied and they seem to induce a gradual phase separation between hole rich and hole poor regions. The pairing correlations are strongly suppressed when the holes are localized. However, in charge inhomogeneous states with mobile holes no dramatic changes, compared with the uniform state, are observed in the pairing correlations indicating that D-wave pairing and moderate electron-phonon interactions can coexist.
The effects of the electron-phonon interaction on charge and spin dynamics are studied for the one-dimensional two-band Hubbard model by the exact diagonalization method. The parameters of the model are chosen to represent a hole-doped Cu-O system. Local charge fluctuations induced by phonons are expressed in terms of microscopic current and polarization, and it is shown that the dynamic charge transfer is strongly dependent on the phonon wave vector when the system is doped with holes. The dynamic magnetic structure factor is also found to be significantly modified by lattice distortion. In particular the lowest-energy spin excitations are greatly softened, indicating significant spin-phonon coupling. It is shown that the optical response is significantly modified as well due to coupling with the lattice over an energy range far exceeding the phonon energy. These results demonstrate the unconventional nature of the electron-phonon coupling in the strongly correlated electron systems. Its possible implications to the pairing mechanism in the cuprates are discussed.
The effective two-band $t\ensuremath{-}J$ Hamiltonian for holes in Cu-O planes of cuprates is obtained from the three-band Hubbard Hamiltonian. In this model a doped oxygen hole together with two neighboring copper holes is treated as a composite spin-12\frac{1}{2}21​ three-sites particle. The model is studied by exact diagonalization in a Cu16O32{\mathrm{Cu}}_{16}{\mathrm{O}}_{32}Cu16​O32​ square cluster. Both binding energy and hole-hole correlation function indicate that two holes bind together for J/t>0.11J/t>0.11J/t>0.11 and are predominantly located on the next-nearest oxygen sites in the same Cu-O chain. Electron-phonon interaction is studied in the adiabatic phonons approximation. Copper (\ensuremath{\pi},0) ``half-breathing'' mode is shown to couple strongly to doped holes and increase the hole-hole correlation as well as the binding energy. These results are compared with experimental data.