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arXiv:2503.12113 · Physical Review Letters

Effective Enhancement of the Electron-Phonon Coupling Driven by Nonperturbative Electronic Density Fluctuations

Emin Moghadas, M. Reitner, Tim Oliver Wehling, Giorgio Sangiovanni, Sergio Ciuchi, A. Toschi

Published Feb 19, 2026• 7 citations
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Abstract

We present a dynamical mean-field study of nonperturbative electronic mechanisms, which may lead to significant enhancements of the electron-phonon coupling in correlated electron systems. Analyzing the effects of electronic correlations on the lowest-order electron-phonon processes, we show that in the proximity of the Mott metal-to-insulator transition of the doped square lattice Hubbard model, where the isothermal charge response becomes particularly large at small momenta, the coupling of electrons to the lattice is strongly increased. This, in turn, induces significant corrections to both the electronic self-energy and phonon-mediated pairing interaction, indicating the possible onset of a strong interplay between lattice and electronic degrees of freedom even for small values of the bare electron-phonon coupling.

DOI
10.1103/ld8v-qpf8

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We present a dynamical mean-field study of nonperturbative electronic mechanisms, which may lead to significant enhancements of the electron-phonon coupling in correlated electron systems. Analyzing the effects of electronic correlations on the lowest-order electron-phonon processes, we show that in the proximity of the Mott metal-to-insulator transition of the doped square lattice Hubbard model, where the isothermal charge response becomes particularly large at small momenta, the coupling of electrons to the lattice is strongly increased. This, in turn, induces significant corrections to both the electronic self-energy and phonon-mediated pairing interaction, indicating the possible onset of a strong interplay between lattice and electronic degrees of freedom even for small values of the bare electron-phonon coupling.
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In phonon mediated conventional sss-wave superconductors, higher-frequency phonon (or smaller atomic mass) leads to a higher superconducting transition temperature, known as the isotope effect. However, in correlated systems, various competing electronic order (such as spin-density-wave, charge-density-wave, and unconventional superconductivity) arises and the effect of electron-phonon coupling on these orders is a long-standing problem. Using the functional renormalization group, here we investigated the interplay between the electron correlation and electron-phonon coupling in the Hubbard-Holstein model on a square lattice. At half-filling, we found spin-density-wave and charge-density-wave phases and the transition between them, while no superconducting phase arises. Upon finite doping, ddd-wave/sss-wave superconductivity emerges in proximity to the spin-density-wave/charge-density-wave phase. Surprisingly, lower-frequency Holstein phonons are either less destructive or even beneficial to the various phases, resulting in a negative isotope effect. For the superconducting phases, such an effect is apparently beyond the Bardeen-Cooper-Schrieffer theory.
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We study the isotope effects arising from the coupling of correlated electrons with dispersionless phonons by considering the Hubbard-Holstein model at half-filling within the dynamical mean-field theory. In particular we calculate the isotope effects on the quasiparticle spectral weight ZZZ, the renormalized phonon frequency, and the static charge and spin susceptibilities. In the weakly correlated regime $U∕t\ensuremath{\lesssim}1.5$, where UUU is the Hubbard repulsion and ttt is the bare electron half-bandwidth, the physical properties are qualitatively similar to those characterizing the Holstein model in the absence of Coulomb repulsion, where the bipolaronic binding takes place at large electron-phonon coupling and it is reflected in divergent isotope responses. On the contrary in the strongly correlated regime $U∕t\ensuremath{\gtrsim}1.5$, where the bipolaronic metal-insulator transition becomes of first order, the isotope effects are bounded, suggesting that the first-order transition is likely driven by an electronic mechanism, rather then by a lattice instability. These results point out how the isotope responses are extremely sensitive to phase boundaries and they may be used to characterize the competition between the electron-phonon coupling and the Hubbard repulsion.
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.
The role of the electron-phonon interaction in the Holstein-Hubbard model is investigated in the metallic phase close to the Mott transition and in the insulating Mott phase. The model is studied by means of a variational slave boson technique. At half-filling, mean-field static quantities are in good agreement with the results obtained by numerical techniques. By taking into account Gaussian fluctuations, an analytic expression of the spectral density is derived in the Mott insulating phase showing that an increase of the electron-phonon coupling leads to a sensitive reduction of the Mott gap through a reduced effective repulsion. The relation of the results with recent experimental observations in strongly correlated systems is discussed.