Abstract

The observed characteristics of mid infrared (MIR) spectra in doped semiconductors are discussed. These characteristics were explained by Reik and coworkers on the basis of hopping motion of small polarons from a localized site to a neighbouring localized site. The success and limitations of this model are pointed out. Emin, on the other hand, showed the importance of large polarons for the conductivity. The recently observed features of MIR spectra in high-Tc cuprates are then summarized. The low-frequency peak in many cuprates with frequency 0.1−0.2 eV has been ascribed by many investigators to polaronic origin. We have undertaken in the present work numerical studies of polaronic conductivity in the two-site and four-site cluster model by diagonalization of the dynamical matrix. Broadening of the phonon spectra due to damping has been taken into account by considering a small but finite phonon lifetime. For intermediate and strong coupling, a number of peaks in the optical conductivity appear due to bound states with different numbers of phonons. We have also studied the importance of Hubbard U by calculating the optical conductivity as a function of U with two electrons in a two-site model. The experimental results of MIR spectra for the cuprates can be better understood on the basis of the present calculations.

Introduction

It was Landau who first introduced the idea of polarons for explaining the F centres in NaCl as due to self-trapping of electrons [1]. Polarons are the quasiparticles formed by the accompanying self-consistent polarization field and are generated due to the dynamical electron–phonon interaction. As a consequence there is extra scattering of the charge carriers, phonon energies are renormalized and the charge carriers are heavy [2].