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arXiv:cond-mat/0009355

Optical absorption from a non degenerate polaron gas

S. Fratini

Published Sep 22, 2000• 0 citations
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Abstract

We apply the Dynamical Mean Field Theory to calculate the low-density limit of the optical conductivity in the Holstein model. This non perturbative treatment allows to span continuously from the weak-coupling quasi-free electron behaviour to the strong-coupling small polaron picture. New features arise in the intermediate coupling regime: i) a noticeable transfer of spectral weight towards low frequencies occurs at low temperatures, when coherent processes acquire importance; ii) thermally activated Polaron Interband Transitions appear at non zero temperature, whose spectral weight has a non monotonic temperature behaviour. We propose an interpretation of the infrared active vibrations (IRAV) observed in the optical spectra of the underdoped superconducting cuprates in terms of small polarons in the intermediate coupling regime.

DOI
10.48550/arxiv.cond-mat/0009355

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We apply the Dynamical Mean Field Theory to calculate the low-density limit of the optical conductivity in the Holstein model. This non perturbative treatment allows to span continuously from the weak-coupling quasi-free electron behaviour to the strong-coupling small polaron picture. New features arise in the intermediate coupling regime: i) a noticeable transfer of spectral weight towards low frequencies occurs at low temperatures, when coherent processes acquire importance; ii) thermally activated Polaron Interband Transitions appear at non zero temperature, whose spectral weight has a non monotonic temperature behaviour. We propose an interpretation of the infrared active vibrations (IRAV) observed in the optical spectra of the underdoped superconducting cuprates in terms of small polarons in the intermediate coupling regime.
We apply the dynamical mean field theory to calculate the low-density limit of the optical conductivity in the Holstein model. This nonperturbative treatment allows continuous spanning from the weak-coupling quasi-free-electron behavior to the strong-coupling small polaron picture. Different features arise in the intermediate coupling regime: (i) a noticeable transfer of spectral weight toward low frequencies occurs at low temperatures, when coherent processes acquire importance; (ii) thermally activated polaron interband transitions appear at nonzero temperature, whose spectral weight has a nonmonotonic temperature dependence. We propose an interpretation of the infrared active vibrations observed in the optical spectra of underdoped superconducting cuprates in terms of small polarons in the intermediate coupling regime.
We derive an exact solution for the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ of one hole in the Holstein $t\text{\ensuremath{-}}J$ model in the framework of dynamical mean-field theory. We investigate the magnetic and phonon features associated with polaron formation as a function of the exchange coupling JJJ, electron-phonon interaction $\ensuremath{\lambda}$, and temperature. Our solution directly relates the features of the optical conductivity to excitations in the single-particle spectral function, revealing two distinct mechanisms of closing and filling of the optical pseudogap that take place upon varying the microscopic parameters. We show that the optical absorption at the polaron crossover is characterized by a coexistence of a magnon peak at low frequency and a broad polaronic band at higher frequency. An analytical expression for $\ensuremath{\sigma}(\ensuremath{\omega})$ valid in the polaronic regime is presented.
A comprehensive picture of polaron and bipolaron physics is essential to understand the optical absorption spectrum in many materials with electron-phonon interactions. In particular, the finite-temperature properties are of interest since they play an important role in many experiments. Here, we combine the parallel two-site time-dependent variational principle algorithm (p2TDVP) with local basis optimization (LBO) and purification to calculate time-dependent current-current correlation functions. From this information, we extract the optical conductivity for the Holstein polaron and bipolaron with dispersive phonons at finite temperatures. For the polaron in the weak and intermediate electron-phonon coupling regimes, we analyze the influence of phonon dispersion relations on the spectra. For strong electron-phonon coupling, the known result of an asymmetric Gaussian is reproduced for a flat phonon band. For a finite phonon bandwidth, the center of the Gaussian is either shifted to larger or smaller frequencies, depending on the sign of the phonon hopping. We illustrate that this can be well understood by considering the Born-Oppenheimer surfaces. Similar behavior is seen for the bipolaron for strong coupling. For the bipolaron with weak and intermediate coupling strengths and a flat phonon band, we obtain two very different spectra. The latter also has a temperature-dependent resonance at a frequency below the phonon frequency.
A dynamical mean-field theory of the small polaron problem is presented, which becomes exact in the limit of infinite dimensions. The ground-state properties and the one-electron spectral function are obtained for a single electron interacting with Einstein phonons by a mapping of the lattice problem onto a polaronic impurity model. The one-electron propagator of the impurity model is calculated through a continued fraction expansion, at both zero and finite temperature, for any electron-phonon coupling and phonon energy. In contrast to the ground-state properties, such as the effective polaron mass, which show a continuous behavior as the coupling is increased, spectral properties exhibit a sharp qualitative change at low enough phonon frequency: beyond a critical coupling, one energy gap and then more open in the density of states at low energy, while the high-energy part of the spectrum is broad and can be qualitatively explained by a strong coupling adiabatic approximation. As a consequence, narrow and coherent low-energy subbands coexist with an incoherent featureless structure at high energy. The subbands denote the formation of quasiparticle polaron states. Also, divergencies of the self-energy may occur in the gaps. At finite temperature such an effect triggers an important damping and broadening of the polaron subbands. On the other hand, in the large phonon frequency regime such a separation of energy scales does not exist and the spectrum always has a multipeaked structure.