Effects of a low-energy local mode on the Eliashberg function.

Abstract

Anharmonic contributions to the Eliashberg function due to a low-energy local boson mode of finite width are considered for a harmonic metal. Excitation of the multiple-frequency modes leads to redistribution of spectral weight in the generalized Eliashberg function from the low- to the high-energy region, which reduces the electron-boson coupling. This is seen in the calculated temperature dependence of the interaction constants ${\ensuremath{\lambda}}_{\mathit{n}}$ entering the Eliashberg equations. The rapid decrease with temperature of ${\ensuremath{\lambda}}_{\mathit{n}>0}$ can be used to derive a simple analytical expression, which reproduces almost exactly the temperature dependence, ${\ensuremath{\lambda}}_{\mathit{n}>0}$(T), calculated from the exact expression. Normal-state properties of alkaline-doped ${\mathrm{C}}_{60}$ are investigated within the two-peak model (${\mathrm{\ensuremath{\omega}}}_{0}$\ensuremath{\sim}50 K and ${\mathrm{\ensuremath{\omega}}}_{1}$\ensuremath{\sim}900 K) for the possibility to extract information about the local modes themselves and their coupling to the conduction electrons. The electronic specific heat shows peculiarities only in the case of an extremely strong coupling. Due to the low-energy peak the temperature dependence of the electrical resistivity deviates more and more from the linear law with increasing adiabaticity parameter A=(m/M)(${\mathrm{\ensuremath{\epsilon}}}_{\mathit{F}}$/\ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{0}$). This leads, however, to a negative-curvature dependence. The experimental curve for ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$ has a positive curvature and can be fitted only in the case of a very strong coupling of electrons to the high-energy mode. The thermal electronic conductivity displays a minimum at T\ensuremath{\sim}\ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{0}$/${\mathit{k}}_{\mathit{B}}$. The curvature as a function of temperature is determined by the magnitude of A.