Polaron theory of mid-infrared conductivity a numerical cluster solution

Abstract

Mid-infrared spectra are obtained with numerical calculations of the optical conductivity σ(ω) of a finite-size Holstein model. The results show that the analytic formula of Reik for the optical conductivity is valid only in a strong electron-phonon coupling regime. σ(ω) shows a number of peaks corresponding to the bound states of polarons with a different number of phonons. Calculation of σ(ω) has also been done in the adiabatic limit in the one-dimensional case. It is found that for intermediate coupling the peak in σ(ω) is strongly asymmetric. The optical conductivity of the two-site model in the presence of two electrons is studied. Numerical results show a shift of the peak in σ(ω) to the low-energy region with an increasing Hubbard U for the strong electron-phonon interaction (E p>U) whereas the peak moves to the high-energy region for U>E p high-energy region starts to develop in the large U limit in the presence of phonons. The significance of these calculations for the experimental observations of the mid-infrared spectra of high- T c cuprates is discussed.