Phonon renormalization from local and transitive electron-lattice couplings in strongly correlated systems

Abstract

Within the time-dependent Gutzwiller approximation applied to one-dimensional Holstein and Su-Schrieffer-Heeger-Hubbard models, we study the influence of electron correlations on the phonon self-energy. For the local Holstein coupling, we find that the phonon-frequency renormalization gets weakened upon increasing the on-site interaction U for all momenta. In contrast, correlations can enhance the phonon-frequency shift for small wave vectors in the Su-Schrieffer-Heeger-Hubbard model. Moreover, the time-dependent Gutzwiller approximation applied to the latter model provides a mechanism which leads to phonon-frequency corrections at intermediate momenta due to the coupling with double-occupancy fluctuations. Both models display a shift of the nesting induced to a q=0 instability when the on-site interaction becomes sufficiently strong and thus establishing phase separation as a generic phenomenon of strongly correlated electron-phonon coupled systems

Charge instabilities and electron-phonon interaction in the Hubbard-Holstein model

“…On the other hand electron-phonon coupling involving modulation of the hopping matrix elements is more involved and will be treated elsewhere. 58 For cuprates, the consequences of an electron-phonon interaction with a peak at small momentum has been discussed in the literature, in connection with similar results derived for the t-J model. 14,39,40 For an order parameter with d x 2 −y 2 symmetry the large momentum suppression of the interaction enhances the pairing since the short momentum-transfer interaction is beneficial for pairing, whereas the large momentum-transfer interaction is detrimental.…”

“…Preliminary results indicate that also for nonlocal interactions there is a transition from CDW to a PS instability close to the Mott regime. 58 Our work has also implications for the discussion of band renormalization or self-energy effects from phonons on quasiparticles in high-T c cuprates. For instance Devereaux et al 74 analyzed the coupling of in-plane Cu-O breathing and out-of-plane ͑B 1g ͒ buckling modes to the electronic states in the copper oxygen planes.…”

“…Of course a complete treatment of electron-phonon interactions should also take into account the acoustic branches which will be considered elsewhere. 58 We treat Eq. ͑2͒ in the extreme adiabatic limit ͑M → ϱ͒, where, using the Born-Oppenheimer principle, we can repre-sent the ground state of the system as ͉ tot ͘ = ͉ e ͉͘ ph ͘.…”

Gutzwiller charge phase diagram of cuprates, including electron–phonon coupling effects

“…It is clear that such instabilites cannot arise for a purely local electron-phonon coupling since local charge fluctuations are significantly suppressed in the presence of correlations. However, the situation is different for the coupling of phonons to transitive fluctuations, [24] which can induce a CDW in a system with sizeable electronic correlations for moderate values of the electron-phonon coupling.…”

Electronic Phase Separation and Electron–Phonon Coupling in Cuprate Superconductors

“…In cuprates, such couplings are believed to be of significance for the so-called breathing and buckling modes which correspond to in-and out-of plane motions of the oxygen atoms and which contribute most to the pairing interaction arising from phonons [58,59]. In contrast to the Holstein-, local-type coupling correlations can enhance the electronphonon vertex for small momentum transfer [60,61] and therefore support the coupling to long wavelength optical phonons in an inhomogeneous electronic environment.…”