Dynamics of impurity modes and electron–phonon interaction in Heavy Fermion (HF) systems

A theoretical explanation is provided to understand the effect of small concentration of impurities characterized by change in mass and nearest neighbor force constants on the phonon spectrum as well as on the electron–phonon interaction in some Heavy Fermion (HF) systems in the normal state within theoretical framework of the Periodic Anderson Model (PAM). Three different mechanisms of the electron–phonon interactions, namely, the usual interaction between the phonons with the electrons in the f-bands, electrons arising from that of hybridization term of PAM and the local electron–phonon coupling at the impurity sites are considered. Coherent Potential Approximation (CPA) is used to evaluate the configuration averaged self–energy and the total Green function. For simplicity of calculation the CPA self–energy is evaluated in Average t -matrix Approximation (ATA). The analytical analysis is carried out for finite T in the long wavelength limit. The influence of impurity mass parameter λ and other system parameters such as d, the position of f-level, the effective coupling strength g on the calculated re-normalized phonon frequency and the excitation spectrum through the spectral function is studied. The numerical analysis of the results does show the influence of impurities as evident from different plots in this paper.