Interpretation of temperature dependence of the in-plane electrical resistivity in YBa 2Cu 4O 8: Electron–phonon approach

Abstract

In this paper, we undertake a quantitative analysis of observed temperature-dependent in-plane normal state electrical resistivity of single crystal YBa 2Cu 4O 8. The analysis is within the framework of classical electron–phonon i.e., Bloch-Gruneisen model of resistivity. It is based on the inherent acoustic (low frequency) phonons ( ω ac ) as well as high frequency optical phonons ( ω op ), the contributions to the phonon resistivity were first estimated. The optical phonons of the oxygen breathing mode yields a relatively larger contribution to the resistivity compared to the contribution of acoustic phonons. Estimated contribution to in-plane electrical resistivity by considering both phonons i.e., ω ac and ω op , along with the zero-limited resistivity, when subtracted from single crystal data infers a quadratic temperature dependence over most of the temperature range [80 ⩽ T ⩽ 300]. Quadratic temperature dependence of ρ diff. = [ ρ exp − { ρ 0 + ρ e − ph (= ρ ac + ρ op )}] is understood in terms of electron–electron inelastic scattering. The relevant energy gap expressions within the Nambu-Eliashberg approach are solved imposing experimental constraints on their solution (critical temperature T c ). It is found that the indirect-exchange formalism provides a unique set of electronic parameters [electron–phonon ( λ ph ), electron-charge fluctuations ( λ pl ), electron–electron ( μ) and Coulomb screening parameter ( μ *)] which, in particular, reproduce the reported value of T c .