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arXiv:cond-mat/0204617

Dynamical mean-field theory of electron-phonon interaction in correlated electron materials: general results and application to doped Mott insulators

Andreas Deppeler, Andrew J. Millis

Published Apr 29, 2002• 0 citations
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Abstract

The dynamical mean-field method is used to formulate a computationally tractable theory of electron-phonon interactions in systems with arbitrary local electron-electron interactions in the physically relevant adiabatic limit of phonon frequency small compared to electron bandwidth or interaction scale. As applications, the phonon contribution to the effective mass of a carrier in a lightly doped Mott insulator is determined and the phase separation boundary is discussed.

DOI
10.48550/arxiv.cond-mat/0204617

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The dynamical mean-field method is used to formulate a computationally tractable theory of electron-phonon interactions in systems with arbitrary local electron-electron interactions in the physically relevant adiabatic limit of phonon frequency small compared to electron bandwidth or interaction scale. As applications, the phonon contribution to the effective mass of a carrier in a lightly doped Mott insulator is determined and the phase separation boundary is discussed.
We use the dynamical mean-field theory to develop a systematic and computationally tractable method for studying electron-phonon interactions in systems with arbitrary electronic correlations. The method is formulated as an adiabatic expansion around the limit of static phonons. No specific electronic ground state is assumed. We derive an effective low-frequency phonon action whose coefficients are static local correlation functions of the underlying electron system. We identify the correct expansion parameters. At a critical electron-phonon interaction strength the system undergoes a transition to a polaronic state. We determine the location of this polaronic instability in the presence of electron-electron interactions, doping, and quantum lattice fluctuations and present the formalism needed for study of the electron self-energy and effective mass.
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.
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The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean‐field picture as provided by Hartree‐Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott‐Hubbard metal‐insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean‐field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many‐body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean‐field theory for correlated fermions, the dynamical mean‐field theory (DMFT), (v) derive the DMFT self‐consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.
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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.