Simulation of a hump structure in the optical scattering rate within a generalized Allen formalism and its application to copper oxide systems

We propose a possible way to simulate a hump structure in the optical scattering rate. The optical scattering rate of correlated charge carriers can be defined within an extended Drude model formalism. When some electron and hole doped copper oxide systems are in the spin density or charge density wave phases they show hump structures in their optical scattering rates. The hump structures have not yet been simulated and understood clearly. We are able to simulate the hump structure by using a peak followed by a dip feature in the normalized density of states within a generalized Allen formalism. We observe that reversing the order of the dip and peak gives completely different features in the optical scattering rate; a peak-dip (dip peak) results in a hump (a valley) in the scattering rate. We also obtain the real part of the optical conductivity and reflectance spectra from the simulated optical scattering rate and compare them with published experimental spectra. From these comparisons we conclude that the peak-dip order can give the hump structure, which is observed experimentally in copper oxide systems. Finally we fit two published optical spectra with our new model and discuss our results and the possible origin of the dip or peak features in the normalized density of states.Comment: 16 pages, 6 figure

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 ($I^2\chi(\omega)$) obtained from optical data using a maximum entropy inversion method. We start with two simple model input $I^2\chi(\omega)$, calculate the optical scattering rates at selected temperatures using the model input spectral density functions and a generalized Allen's formula, then extract back $I^2\chi(\omega)$ 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 $I^2\chi(\omega)$ with the input ones. From this approach we find that the inversion process can recover the input $I^2\chi(\omega)$ almost perfectly when the quality of fits is good enough and also temperature smearing (or thermal broadening) effects appear in the $I^2\chi(\omega)$ 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 $I^2\chi(\omega)$ extracted from the optical data contain intrinsic temperature-dependent evolutions.Comment: 29 pages, 8 figure

Electron-boson spectral density function of correlated multiband systems obtained from optical data: Ba0.6K0.4Fe2As2 and LiFeAs

We introduce an approximate method which can be used to simulate the optical conductivity data of correlated multiband systems for normal and superconducting cases by taking advantage of a reverse process of a usual optical data analysis, which has been used to extract the electron-boson spectral density function from measured optical spectra of single-band systems, like cuprates. We applied this method to optical conductivity data of two multiband pnictide systems (Ba0.6K0.4Fe2As2 and LiFeAs) and obtained the electron-boson spectral density functions. The obtained electron-boson spectral density consists of a sharp mode and a broad background. The obtained spectral density functions of the multiband systems show similar properties as those of cuprates in several aspects. We expect that our method helps to reveal the nature of strong correlations in the multiband pnictide superconductors.Comment: 18 pages, 7 figure

Reverse process of usual optical analysis of boson-exchange superconductors: impurity effects on ss- and dd-wave superconductors

We performed a reverse process of a usual optical data analysis of boson-exchange superconductors. We calculated the optical self-energy from two (MMP and MMP+peak) input model electron-boson spectral density functions using Allen's formula for one normal and two ($s$- and $d$-wave) superconducting cases. We obtained the optical constants including the optical conductivity and the dynamic dielectric function from the optical self-energy using an extended Drude model, and finally calculated reflectance spectrum. Furthermore to investigate impurity effects on optical quantities we added various levels of impurities (from the clean to the dirty limit) in the optical self-energy and performed the same reverse process to obtain the optical conductivity, the dielectric function, and reflectance. We observed that impurities give similar effects on various optical constants of $s$- and $d$-wave superconductors; the more impurities give the more distinct gap feature and the less superfluid density. However, the $s$-wave superconductor gives the superconducting gap feature more clearly than the $d$-wave superconductor because in the $d$-wave superconductors the optical quantities are averaged over the anisotropic Fermi surface. Our results also supply helpful information to see how characteristic features of the electron-boson spectral function and the $s$- and $d$-wave superconducting gaps appear in various optical constants including raw reflectance spectrum. Our study also may help to understand the usual optical analysis process thoroughly. Further systematic study of experimental data collected at various conditions using the optical analysis process will help to reveal the origin of the mediated boson in the boson-exchange superconductors.Comment: 21 pages, 9 figure

High energy fluctuation spectra in cuprates from infrared optical spectroscopy

Coupling of the charge carriers in the high temperature superconducting oxides to bosonic modes has been widely reported using a variety of experimental probes. These include angular resolved photoemission (ARPES), scanning tunnelling spectroscopy (STS), Raman scattering (RS) and infrared optical spectroscopy (IRS). The energy scale investigated has been mostly limited to a relatively small range up to 300 meV or so. Although some ARPES experiments report boson structure up to 800 meV in the dressed electron dispersion curves the data are not analyzed to recover the spectral density of the fluctuation spectrum. We have extended to higher energies up to 2.2 eV the usual maximum entropy technique used to invert optical data so as to obtain an electron-boson spectral density. This has required that we include in our inversions, the calculated (LDA) particle-hole symmetrized energy dependent electronic density of states (DOS). Our analysis reveals that significant spectral weight remains in the fluctuation spectra up to 2.2 eV in the Bi-2212 family and to 1.2 eV in Bi-2201 for all doping levels considered.Comment: 6 pages, 5 figure

Extended Drude model analysis of superconducting optical spectra of correlated electron systems

Correlation information in strongly correlated electron systems can be obtained using an extended Drude model. An interesting method related to the extended Drude model analysis of superconducting optical data was proposed recently, and it has attracted attention from researchers. This method aims to extract the optical self-energy of quasiparticles (or residual unpaired electrons) from measured optical data in the superconducting state. However, this residual optical self-energy is a partial optical self-energy. The interpretation and significance of this partial optical self-energy is unclear. We investigate this method using a reverse process with simple electron-boson spectral density functions. With our obtained results, we conclude that the residual (or partial) optical self-energy is difficult to interpret because it contains unphysical features, in particular, a negative optical effective mass. The present study clarifies the extended Drude analysis method for superconducting optical data.Comment: 20 pages, 3 figure

Near-infrared studies of glucose and sucrose in aqueous solutions: water displacement effect and red shift in water absorption from water-solute interaction

We use near infrared spectroscopy to obtain concentration dependent glucose absorption spectra in their aqueous solutions in the near-infrared range (3800 - 7500 cm^{-1}). We introduce a new method to obtain reliable glucose absorption bands from aqueous glucose solutions without measuring the water displacement coefficients of glucose separately. Additionally, we are able to extract the water displacement coefficients of glucose, and this may give a new general method using spectroscopy techniques applicable to other water soluble materials. We also observe red shifts in the absorption bands of water in the hydration shell around solute molecules, which comes from contribution of the interacting water molecules around the glucose molecules in solutions. The intensity of the red shift get larger as the concentration increases, which indicates that as the concentration increases more water molecules are involved in the interaction. However, the red shift in frequency does not seem to depend significantly on the concentration up to our highest concentration. We also performed the same measurements and analysis with sucrose instead of glucose as solute and compare.Comment: 25 papges, 9 figure

Determination of boson spectrum from optical data in pseudogap phase of underdoped cuprates

Information on the nature of the dominant inelastic processes operative in correlated metallic systems can be obtained from an analysis of their AC optical response. An electron-boson spectral density can usefully be extracted. This density is closely related to the optical scattering rate. However, in the underdoped region of the high Tc cuprate phase diagram a new energy scale (the pseudogap) emerges, which alters the optical scattering and needs to be taken into account in any fit to data. This can influence the shape and strength of the recovered boson spectral function. Including a pseudogap in an extended maximum entropy inversion for optimally doped Bi-2212 is more consistent with existing data than when it is left out as done previously.Comment: 18 pages, 5 figure

Evolution of electron-boson spectral density in the underdoped region of Bi_2Sr_{2-x}La_xCuO_6

We use a maximum entropy technique to obtain the electron-boson spectral density from optical scattering rate data across the underdoped region of the Bi_2Sr_{2-x}La_xCuO_6 (Bi-2201) phase diagram. Our method involves a generalization of previous work which explicitly include finite temperature and the opening of a pseudogap which modifies the electronic structure. We find that the mass enhancement factor \lambda associated with the electron-boson spectral density increases monotonically with reduced doping and closer proximity to the Mott antiferromagnetic insulating state. This observation is consistent with increased coupling to the spin fluctuations. At the same time the system has reduced metallicity because of increased pseudogap effects which we model with a reduced effective density of states around the Fermi energy with the range of the modifications in energy set by the pseudogap scale.Comment: 14 pages, 5 figure

Analysis of optical data using extended Drude model and generalized Allen's formulas

Extended Drude model formalism has been successfully utilized for analyzing optical spectra of strongly correlated electron systems including heavy-fermion systems and high-$T_c$ superconducting iron pnictides and cuprates. Furthermore, generalized Allen's formulas has been developed and applied to extract the electron-boson spectral density function from measured optical data of high temperature superconductors including cuprates in various material phases. Here we used a reverse process to obtain various optical quantities starting from two typical electron-boson spectral density model functions for three intriguing (normal, pseudogap, and $d$-wave superconducting) material phases in cuprates. We also assigned the calculated optical results to designated regions in the phase diagram of hole-doped cuprates and compared them with the corresponding measured optical spectra of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212). This comparison suggested that this way of optical data analysis can be a convincing method to study correlated electrons in the copper oxide superconductors and other superconducting systems as well.Comment: 19 pages, 8 figure