Influence of electron-phonon interaction on effective mass in some heavy Fermion (HF) systems

It is a fact that for ordinary metals, the electron-phonon interaction increases the quasi-particle mass, which is in contrast to the finding by Fulde et al. that, for some heavy Fermion (HF) systems, it decreases. Some experiments on HF systems suggest that there exists a strong coupling of the elastic degrees of freedom with these at the electronic and magnetic ones. To understand the effect of electron phonon interaction on effective mass, the electron phonon coupling mechanism in the framework of the periodic Anderson model is considered, and a simple expression is derived. This involves various model parameters namely, the position of the 4f level; the effective coupling strength, g, temperature, b; and the electron phonon coupling strength, r. The influence of these parameters on the value of effective mass is studied, and interesting results were found. For simplicity, the numerical calculation is performed in the long wavelength limit.