Optical Absorption of Polarons in the Feynman-Hellwarth-Iddings-Platzman Approximation

Abstract

The optical absorption of polarons at rest at zero temperature is calculated starting from the Feynman-Hellwarth-Iddings-Platzman (FHIP) theory of the impedance. The results are compared with the results of theories whose physical interpretation is clearer [weak-coupling theory of Gurevich, Lang, and Firsov (GLF) and product-ansatz strong-coupling theory of Kartheuser, Evrard, and Devreese (KED)] in order to obtain a better understanding of the FHIP approximation. We are particularly interested in the possible role of lattice relaxation [leading to relaxed excited states (RES)] in the optical absorption process. If the FHIP perturbation method were used to expand the conductivity (this would be the normal procedure), essentially Franck-Condon transitions would be found in the spectrum, and lattice relaxation would be absent. In this case the results do not fit with the product ansatz and provide merely the asymptotic limit $\alpha \to 0$, where $\alpha$ is the electron-phonon coupling constant. If, however, the impedance function rather than the conductivity is expanded (as preferred by FHIP for intuitive reasons, without further justification) more reliable results for the optical absorption appear. For $\alpha >5\mathrm{}$, intense absorption peaks now occur, which presumably correspond to transitions to RES, and the results are in qualitative agreement with the predictions of the product-ansatz treatment in this coupling region. Also in the limit $\alpha \to 0$ the correct behavior is found. For $3\lesssim \alpha \lesssim 5$, the interpretation of the results is somewhat delicate but the possibility that RES contribute to the oscillator strength as soon as $\alpha >3\mathrm{}$ should be considered. The results so obtained for the optical absorption seem reliable at all $\alpha$. This provides an indirect justification for the expansion of $Z\left(\Omega \right)$ rather than $\frac{1}{Z\left(\Omega \right)}$ in FHIP theory and a confirmation of the qualitative strong-coupling predictions of KED. The present study indicates that optical absorption peaks due to free polarons should be observable experimentally in crystals for which $\alpha >1\mathrm{}$.