Microscopic theory of Raman spectra of superconducting heavy fermion system

Abstract

A microscopic theory of the Raman spectra of superconducting heavy fermion systems (HFSs) is reported here. The periodic Anderson model is used to describe the HF behaviour to which a BCS-type Cooper pairing mechanism is added to describe superconductivity. The electron–phonon interaction is introduced through the hybridization between the conduction electrons and f-electrons as well as the on-site f-electrons. The phonon Green's function for the system is evaluated by the equation of motion technique of Zubarev. The phonon spectral density is calculated at zero temperature and in the long wavelength limit. Four Raman active phonon modes with reduced frequencies ω=(ω/ω 0) around ω=0.03 , 0.073, 2.25 and 2.32 are seen in the superconducting state in addition to the original phonon. The influence of the model parameters, like electron–phonon coupling strength ( g), position of the f-level ( d), hybridization strength ( v), Coulomb correlation ( u), superconducting gap ( z) and bare phonon frequency ( p), on the Raman peaks, is discussed.