Quasi-particle Dynamics of a Strongly Correlated Polaron Metal

We develop a simple diagrammatic low-energy boson exchange strong-coupling model for an antiferromagnetically correlated polaronic metal. The model is based on a simplified, local anharmonic oscillator representation of the highly anharmonic Born-Oppenheimer lattice potential which typically arises in a finite density po-laron system, as a result of polaronic self-localization. This Born-Oppenheimer potential exhibits a large manifold of nearly degenrate local potential minima, and hence a new class of low-energy excitations, associated with tunneling processes between the multiple Born-Oppenheimer wells. In the present paper, we employ a simple Migdal-type single-exchange diagrammatic approximation in order to study the what happens when conduction electrons are coupled to these anharmonic tunneling excitations via conventional electron-phonon interactions. Important low-temperature features of such a model are (i) a large polaronic mass enhancement Z and a strongly narrowed, low-energy, near-Fermi-level van Hove resonance peak in the interacting density of states at temperatures T well below the lattice tunneling energy scale Ω t ; (ii) a rapid thermal suppression of Z and of the van Hove resonance which occurs when the temperature T becomes comparable to the lattice tunneling excitation energy scale Ω t ; (iii) a broad incoherent background in the single-particle spectra |G ′′ (k, ω)| near the Fermi energy; (iv) strongly flattened quasi-particle bands over wide regions of the Brillouin zone near the van Hove points; and (v) strong isotopic mass dependence of the elec-– 1 – tronic mass enhancement Z at temperatures T well below Ω t which, along with Z, becomes rapidly suppressed for T comparable to Ω t. Surprisingly, in spite of the large low-T mass enhancment, the anharmonic lattice fluctuations in the high temperature regime T > ∼ Ω t , give rise only to a moderate, essentially T-independent quasi-particle damping. This damping does not suppress coherent quasi-particle propagation in a wide, physically relevant parameter regime. We thus argue that, in a " weakly bound " finite-density polaron system, a novel polaron scenario may be realized where only the lattice motion, but not the quasi-particle propagation become incoherent in the high-T regime. This scenario is in contrast to the conventional small-polaron strong-coupling picture, where the quasi-particle transport inevitably becomes incoherent at temperatures exceeding the polaron tunneling energy scale. We also discuss possible implications of the anharmonic tunneling model for the cuprate superconductors. The predicted isotopic mass dependence of the low-T (T < Ω t) electron quasi-particle mass enhancement provides a unique …