Exchange boson dynamics in cuprates: optical conductivity of HgBa_2CuO_4+delta

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 have 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 Bi₂Sr₂CaCu₂ [Formula: see text] (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.

Tracing the Electronic Pairing Glue in Unconventional Superconductors via Inelastic Scanning Tunneling Spectroscopy

Scanning tunneling microscopy has been shown to be a powerful experimental probe to detect electronic excitations and further allows us to deduce fingerprints of bosonic collective modes in superconductors. Here, we demonstrate that the inclusion of inelastic tunnel events is crucial for the interpretation of tunneling spectra of unconventional superconductors and allows us to directly probe electronic and bosonic excitations via scanning tunneling microscopy. We apply the formalism to the iron based superconductor LiFeAs. With the inclusion of inelastic contributions, we find strong evidence for a nonconventional pairing mechanism, likely via magnetic excitations.

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.

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

We performed a reverse process of the 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 the 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. From these optical constants obtained from the reverse process we extracted the impurity-dependent superfluid densities for two superconducting cases using two independent methods (the Ferrel-Glover-Tinkham sum rule and the extrapolation to zero frequency of -ϵ1(ω)ω(2)); we found that a certain level of impurities is necessary to get a good agreement on results obtained by the two methods. We observed that impurities give similar effects on various optical constants of s- and d-wave superconductors; the greater the impurities the more distinct the gap feature and the lower the 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 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 may help with a thorough understanding of the usual optical analysis process. 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.

Electron-boson spectral density of LiFeAs obtained from optical data

We analyze existing optical data in the superconducting state of LiFeAs at T = 4 K, to recover its electron-boson spectral density. A maximum entropy technique is employed to extract the spectral density I(2)χ(ω) from the optical scattering rate. Care is taken to properly account for elastic impurity scattering which can importantly affect the optics in an s-wave superconductor, but does not eliminate the boson structure. We find a robust peak in I(2)χ(ω) centered about Ω(R) ≅ 8.0 meV or 5.3 k(B)Tc (with Tc = 17.6 K). Its position in energy agrees well with a similar structure seen in scanning tunneling spectroscopy (STS). There is also a peak in the inelastic neutron scattering (INS) data at this same energy. This peak is found to persist in the normal state at T = 23 K. There is evidence that the superconducting gap is anisotropic as was also found in low temperature angular resolved photoemission (ARPES) data.

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 spin density or charge density wave phases they show hump structures in their optical scattering rates. The hump structures have not yet been simulated or clearly understood. 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 parts 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 that 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.

Evolution of electron-boson spectral density in the underdoped region of Bi2Sr(2-x)La(x)CuO6

We use a maximum entropy technique to obtain the electron-boson spectral density from optical scattering rate data across the underdoped region of the Bi2Sr(2-x)La(x)CuO6 (Bi-2201) phase diagram. Our method involves a generalization of previous work which explicitly includes finite temperature and the opening of a pseudogap which modifies the electronic structure. We find that the mass enhancement factor λ 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.

An electron-boson glue function derived from electronic Raman scattering

Raman scattering cross sections depend on photon polarization. In the cuprates, nodal and antinodal directions are weighted more strongly in B(2g) and B(1g) symmetries, respectively. On the other hand, in angle-resolved photoemission spectroscopy (ARPES), electronic properties are measured along well-defined directions in momentum space rather than their weighted averages being taken. In contrast, the optical conductivity involves a momentum average over the entire Brillouin zone. Newly measured Raman response data on high-quality Bi(2)Sr(2)CaCu(2)O(8 + δ) single crystals up to high energies have been inverted using a modified maximum entropy inversion technique to extract from B(1g) and B(2g) Raman data corresponding electron-boson spectral densities (glue), and these are compared to the results obtained with known ARPES and optical inversions. We find that the B(2g) spectrum agrees qualitatively with nodal direction ARPES while the B(1g) results look more like the optical spectrum. A large peak around 30-40 meV in B(1g) and a much less prominent one in B(2g) are taken as support for the importance of (π, π) scattering at this frequency.

A perspective on the Fe-based superconductors

FeSe is employed as reference material to elucidate the observed high T(c) superconducting behaviour of the related layered iron pnictides. The structural and ensuing semimetallic band structural forms are here rather unusual, with the resulting ground state details extremely sensitive to the precise shape of the Fe-X coordination unit. The superconductivity is presented as coming from a combination of resonant valence bond and excitonic insulator physics, and incorporating boson-fermion degeneracy. Although sourced in a very different fashion, the latter leads to some similarities with the high temperature superconducting (HTSC) cuprates. The excitonic insulator behaviour sees spin density wave, charge density wave/periodic structural distortion, and superconductive instabilities all vie for ground state status. The conflict leads to a very sensitive and complex set of properties, frequently mirroring HTSC cuprate behaviour. The delicate balance between ground states is made particularly difficult to unravel by the micro-inhomogeneity of structural form which it can engender. It is pointed out that several other notable superconductors, layered in form, semimetallic with indirect overlap and possessing homopolar bonding, would look to fall into the same general category, β-ZrNCl and MgB(2) and the high pressure forms of several elements, like sulfur, phosphorus, lithium and calcium, being cases in point.

On properly integrating the electronic Raman and optical infra-red spectra of high temperature superconducting cuprate materials

New electronic Raman and infra-red spectroscopy results from optimally and overdoped high temperature superconducting cuprate systems are interpreted in terms of the negative- U, boson-fermion crossover model. A distinction is made between those features which follow the condensate gap, 2Δ(p), and those that are set by the local pair binding energy, [Formula: see text]. The critical role of the doping level p(c) = 0.185 is highlighted in conjunction with the question of developing quasiparticle incoherence, making connection here with recent transport and related results. [Formula: see text] IR results for magnetic fields parallel and perpendicular to  c prove particularly illuminating. The general scheme developed continues to embrace all experimental data very satisfactorily.