Intrinsic temperature-dependent evolutions in the electron-boson spectral density obtained from optical data

We investigate temperature smearing effects on the electron-boson spectral density function (I(2)χ(ω)) obtained from optical data using a maximum entropy inversion method. We start with two simple model input I(2)χ(ω), calculate the optical scattering rates at selected temperatures using the model input spectral density functions and a generalized Allen’s formula, then extract back I(2)χ(ω) at each temperature from the calculated optical scattering rate using the maximum entropy method (MEM) which has been used for analysis of optical data of high-temperature superconductors including cuprates, and finally compare the resulting I(2)χ(ω) with the input ones. From this approach we find that the inversion process can recover the input I(2)χ(ω) almost perfectly when the quality of fits is good enough and also temperature smearing (or thermal broadening) effects appear in the I(2)χ(ω) when the quality of fits is not good enough. We found that the coupling constant and the logarithmically averaged frequency are robust to the temperature smearing effects and/or the quality of fits. We use these robust properties of the two quantities as criterions to check whether experimental data have intrinsic temperature-dependent evolutions or not. We carefully apply the MEM to two material systems (one optimally doped and the other underdoped cuprates) and conclude that the I(2)χ(ω) extracted from the optical data contain intrinsic temperature-dependent evolutions.