A comparative study of finite frequency scattering rate from Allen, Mitrović–Fiorucci, Shulga–Dolgov–Maksimov, Sharapov–Carbotte and memory function formalisms

Abstract

We report a comparative study of scattering rates which are calculated using different formalisms such as [P. B. Allen, Phys. Rev. B 3, 305 (1971); S. V. Shulga, D. V. Dolgov and E. G. Maksimov, Physica C 178, 266 (1991); B. Mitrović and M. A. Fiorucci, Phys. Rev. B 31, 2694 (1985); S. G. Sharapov and J. P. Carbotte, Phys. Rev. B 72, 134506 (2005)] and memory function formalism (MemF) [H. Mori, Prog. Theor. Phys. 33, 423 (1965)]. An advantage of this study is that it sheds light on the physical assumptions used in these formalisms. In this context, we consider a case of electron–phonon interaction and discuss frequency- and temperature-dependent behavior of scattering rates. Further, a comparative study of scattering rate proceeds for distinct phonon density of states (PDOS) and electron density of states (EDOS). From the detailed analysis, we observe that the MemF is the most general one and others are based on restrictive assumptions as discussed in this work.