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arXiv:cond-mat/0505447 · Physical Review B

Optical absorption and activated transport in polaronic systems

G. Schubert, Gerhard Wellein, Alexander Weiße, Andreas Alvermann, Holger Fehske

Published Sep 27, 2005• 32 citations
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Abstract

We present exact results for the optical response in the one-dimensional Holstein model. In particular, by means of a refined kernel polynomial method, we calculate the ac and dc electrical conductivities at finite temperatures for a wide parameter range of electron-phonon interaction. We analyze the deviations from the results of standard small polaron theory in the intermediate coupling regime and discuss nonadiabaticity effects in detail.

DOI
10.1103/physrevb.72.104304

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We present exact results for the optical response in the one-dimensional Holstein model. In particular, by means of a refined kernel polynomial method, we calculate the ac and dc electrical conductivities at finite temperatures for a wide parameter range of electron-phonon interaction. We analyze the deviations from the results of standard small polaron theory in the intermediate coupling regime and discuss nonadiabaticity effects in detail.
The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalization yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis is put on deviations from weak-coupling, small-polaron or one-electron theories occurring at intermediate coupling and/or finite carrier density. The analytical results are in surprisingly good agreement with exact data, and exhibit the characteristic polaronic excitations observed in experiments on manganites.
Electron-phonon interactions play a key role in many branches of solid-state physics. Here, our focus is on the transport properties of one-dimensional systems, and we apply efficient real-time matrix-product state methods to compute the optical and thermal conductivities of Holstein chains at finite temperatures and filling. We validate our approach by comparison with analytical results applicable to single polarons valid in the small polaron limit. Our work provides a systematic study of contributions to the thermal conductivity at finite frequencies and elucidates differences in the spectrum compared to the optical conductivity, covering both the Luttinger-liquid and charge-density-wave regimes. Finally, we demonstrate that our approach is capable of extracting the DC conductivities as well. Beyond this first application, several future extensions seem feasible, such as the inclusion of dispersive phonons, different types of local electron-phonon coupling, and a systematic study of drag effects in this electron-phonon coupled system.
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.
The Holstein model is a benchmark model of systems with electron-phonon interaction. However, its electrical transport properties are not yet fully understood. In this work, we performed numerically exact calculations of the imaginary-time current-current correlation function of the Holstein Hamiltonian for a broad range of model parameters. These calculations were performed using a path-integral-based quantum Monte Carlo method. We compared these results with the results obtained under the assumption of conventional band transport, small polaron hopping, and polaron band transport. From this comparison, we identified the regions in parameter space where each of these transport regimes is valid. In some cases when an imaginary-time comparison of current-current correlation functions could not give conclusive results, we complemented it with real-time comparisons or a comparison with the literature data on numerically exact dc mobilities. Overall, we found that the parameter space is almost completely covered by the three mentioned transport regimes.
The polaron formation is investigated in the intermediate regime of the Holstein model by using an exact diagonalization technique for the one-dimensional infinite lattice. The numerical results for the electron and phonon propagators are compared to the nonadiabatic weak- and strong-coupling perturbation theories, as well as with the harmonic adiabatic approximation. A qualitative explanation of the crossover regime between the self-trapped and free-particle-like behaviors, not well understood previously, is proposed. It is shown that a fine balance of nonadiabatic and adiabatic contributions determines the motion of small polarons, making them light. A comprehensive analysis of spatially and temporally resolved low-frequency lattice correlations that characterize the translationally invariant polaron states is derived. Various behaviors of the polaronic deformation field, ranging from classical adiabatic for strong couplings to quantum nonadiabatic for weak couplings, are discussed.
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.