Electron-boson Spectral Function Research Articles

FeTe0.55Se0.45: A multiband superconductor in the clean and dirty limit

The detailed optical properties of the multiband iron-chalcogenide superconductor FeTe$_{0.55}$Se$_{0.45}$ have been reexamined for a large number of temperatures above and below the critical temperature $T_c=14$ K for light polarized in the a-b planes. Instead of the simple Drude model that assumes a single band, above $T_c$ the normal-state optical properties are best described by the two-Drude model that considers two separate electronic subsystems; we observe a weak response ($\omega_{p,D;1}\simeq 3000$ cm$^{-1}$) where the scattering rate has a strong temperature dependence ($1/\tau_{D,1}\simeq 32$ cm$^{-1}$ for $T \gtrsim T_c$), and a strong response ($\omega_{p,D;2}\simeq 14\,500$ cm$^{-1}$) with a large scattering rate ($1/\tau_{D,2}\simeq 1720$ cm$^{-1}$) that is essentially temperature independent. The multiband nature of this material precludes the use of the popular generalized-Drude approach commonly applied to single-band materials, implying that any structure observed in the frequency dependent scattering rate $1/\tau(\omega)$ is spurious and it cannot be used as the foundation for optical inversion techniques to determine an electron-boson spectral function $\alpha^2 F(\omega)$. Below $T_c$ the optical conductivity is best described using two superconducting optical gaps of $2\Delta_1\simeq 45$ and $2\Delta_2 \simeq 90$ cm$^{-1}$ applied to the strong and weak responses, respectively. The scattering rates for these two bands are vastly different at low temperature, placing this material simultaneously in both clean and dirty limit. Interestingly, this material falls on the universal scaling line initially observed for the cuprate superconductors.

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)ω2); 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.

Resistivity in Ba(FeCo)As: Comparison of thin films and single crystals

The temperature dependence of the resistivity of epitaxial Ba(FeCo)As thin films (with nominal doping and ) has been analysed and compared with analogous measurements on single crystals taken from literature. The of thin films looks different from that of single crystals, even when the cobalt content is the same. All curves can be fitted by considering an effective two‐band model (with holes and electrons bands) in which the electrons are more strongly coupled with the bosons (spin fluctuations) than holes, while the effect of impurities is mainly concentrated in the hole band. Within this model the mediating boson has the same characteristic energy in single crystals and thin films, but the shape of the transport spectral function at low energy has to be very different, leading to a “hardening” of the electron–boson spectral function in thin films, associated with the strain induced by the substrate.

Quasiparticle relaxation across the multiple superconducting gaps in the electron-doped BaFe1.85Co0.15As2

We study the quasiparticle relaxation dynamics in the electron-doped superconductor, BaFe1.85Co0.15As2 (BFCA) by using optical spectroscopy in both time and frequency domains. The estimate of the electron−phonon (el–ph) coupling constant from quasiparticle relaxation rate in time domain gives a value of ∼0.16 that is much too small to give a TC of 25 K. We obtain a negative value of the Coulomb pseudopotential that implies that the el−ph interaction alone is not strong enough to induce a superconducting transition in BFCA. More importantly, the electron-boson spectral function determined from optical scattering rate in frequency domain does not resemble the measured phonon density of states and has a dominant peak (at 53 meV) beyond the phonon frequencies. Our results support that the BFCA is a multi-gap s-wave superconductor and that its electron pairing is based on a spin-mediated pairing mechanism.

Electron-boson spectral density function of underdopedBi2Sr2CaCu2O8+δandYBa2Cu3O6.50

We investigate the electron-boson spectral density function, $I^2\chi(\omega,T)$, of CuO$_2$ plane in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) and underdoped YBa$_2$Cu$_3$O$_{6.50}$ (Y-123) using the Eliashberg formalism. We apply a new (in-plane) pseudogap model to extract the electron-boson spectral function. For extracting the spectral function we assume that the spectral density function consists of two components: a sharp mode and the broad Millis-Monien-Pines (MMP) mode. We observe that both the resulting spectral density function and the intensity of the pseudogap show strong temperature dependences: the sharp mode takes most spectral weight of the function and the peak position of the sharp mode shifts to lower frequency and the depth of pseudogap, $1-\tilde{N}(0,T)$, is getting deeper as temperature decreases. We observe also that the total spectral weight of the electron-boson density and the mass enhancement coefficient increase as temperature decreases. We estimate fictitious (maximum) superconducting transition temperatures, $T_c(T)$, from the extracted spectral functions at various temperatures using a generalized McMillan formula. The estimated (maximum) $T_c$ also shows a strong temperature dependence; it is higher than the actual $T_c$ at all measured temperatures and decreases with temperature lowering. Since as lowering temperature the pseudogap is getting stronger and the maximum $T_c$ is getting lower we propose that the pseudogap may suppress the superconductivity in cuprates.

Multigap Superconductivity and Strong Electron-Boson Coupling in Fe-Based Superconductors: A Point-Contact Andreev-Reflection Study ofBa(Fe1−xCox)2As2Single Crystals

Directional point-contact Andreev-reflection measurements in Ba(Fe(1-x)Co(x))2As2 single crystals (T(c) = 24.5 K) indicate the presence of two superconducting gaps with no line nodes on the Fermi surface. The point-contact Andreev-reflection spectra also feature additional structures related to the electron-boson interaction, from which the characteristic boson energy Ω(b)(T) is obtained, very similar to the spin-resonance energy observed in neutron scattering experiments. Both the gaps and the additional structures can be reproduced within a three-band s ± Eliashberg model by using an electron-boson spectral function peaked at Ω(0) = 12 meV ≃ Ω(b)(0).

Energy scale of the electron-boson spectral function and superconductivity inNpPd5Al2

The energy scale ${\ensuremath{\Omega}}_{0}$ of the electron-boson spectral function in the heavy-fermion, $d$-wave superconductor ${\text{NpPd}}_{5}{\text{Al}}_{2}$ is predicted on the basis of Eliashberg theory calculations. Assuming a spectral function shape typical for antiferromagnetic spin fluctuations, and imposing constraints provided by the experimental values for the critical temperature and the low-temperature energy gap, one obtains values of ${\ensuremath{\Omega}}_{0}$ of about 2--2.5 meV, slightly dependent from the strength of the Coulomb pseudopotential. These values are in excellent agreement with the characteristic magnetic fluctuations energy estimated from NMR measurements of the nuclear-spin-lattice relaxation time at the Al site. The calculated temperature dependence of the upper critical field, the local spin susceptibility, and the nuclear-spin-lattice relaxation rate is also in good agreement with available experimental data, showing that a coherent description of the superconducting state can be obtained assuming that the electron pairing in ${\text{NpPd}}_{5}{\text{Al}}_{2}$ is mediated by antiferromagnetic fluctuations. We finally report predictions for the London penetration depth, the energy dependence of the tunneling differential conductance at different temperatures, and the temperature dependence of the energy gap.

Doping-dependent optical properties of Bi2201

An experimental study of the in-plane optical conductivity of (Pbx, Bi2−x)(LaySr2−y)CuO6+δ (Bi2201) is presented for a broad doping and temperature range. The in-plane conductivity is analyzed within a strong coupling formalism. We address the interrelationship between the optical conductivity (σ(ω)), the single particle self-energy and the electron–boson spectral function. We find that the frequency and temperature dependence can be well described within this formalism. We present a universal description of optical, angle resolved photoemission spectroscopy (ARPES) and tunneling spectra. The full frequency and temperature dependence of the optical spectra and single particle self-energy is shown to result from an electron–boson spectral function, which shows a strong doping dependence and weak temperature dependence.

Bosonic Spectral Density of Epitaxial Thin-FilmLa1.83Sr0.17CuO4Superconductors from Infrared Conductivity Measurements

We use optical spectroscopy to investigate the excitations responsible for the structure in the optical self-energy of thin epitaxial films of La(1.83)Sr(0.17)CuO(4). Using Eliashberg's formalism to invert the optical spectra we extract the electron-boson spectral function and find that at low temperature it has a two component structure closely matching the spin excitation spectrum recently measured by magnetic neutron scattering. We contrast the temperature evolution of the spectral density and the two-peak behavior in La(2-Sr(x)CuO(4) with another high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta). The bosonic spectral functions of the two materials account for the low T(c) of LSCO as compared to Bi-2212.

Effect of a magnetic field on the electron-boson spectral function of cuprate superconductors

We have performed magneto-optical measurements on a series of $\mathrm{high}\text{\ensuremath{-}}{T}_{c}$ superconductors with magnetic field up to $18\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. Similar to previous reports in smaller fields, the results reveal that the optical constants, both in the normal and superconducting state, of several families of $\mathrm{high}\text{\ensuremath{-}}{T}_{c}$ cuprates are completely insensitive to the application of external magnetic field. These magneto-optical results seem to indicate that either the bosonic mode responsible for pairing is not magnetic in origin, or the charge carriers are not very strongly coupled to it. We discuss the results within the existing theoretical models.

Effects of energy dependence in the quasiparticle density of states on far-infrared absorption in the pseudogap state

We derive a relationship between the optical conductivity scattering rate 1/\tau(\omega) and the electron-boson spectral function \alpha^2F(\Omega) valid for the case when the electronic density of states, N(\epsilon), cannot be taken as constant in the vicinity of the Fermi level. This relationship turned out to be useful for analyzing the experimental data in the pseudogap state of cuprate superconductors.

Extracting the electron-boson spectral functionα2F(ω)from infrared and photoemission data using inverse theory

We present a new method of extracting electron-boson spectral function $\alpha^2$F($\omega$) from infrared and photoemission data. This procedure is based on inverse theory and will be shown to be superior to previous techniques. Numerical implementation of the algorithm is presented in detail and then used to accurately determine the doping and temperature dependence of the spectral function in several families of high-T$_c$ superconductors. Principal limitations of extracting $\alpha^2$F($\omega$) from experimental data will be pointed out. We directly compare the IR and ARPES $\alpha^2$F($\omega$) and discuss the resonance structure in the spectra in terms of existing theoretical models.

Optical studies of charge dynamics in optimally dopedBi2Sr2CaCu2O8+δ

Systematic temperature-dependent optical studies of optimally doped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (OP Bi2212) single crystals have been carried out. An electron-boson spectral function peaked at 43 meV is derived in the normal state at 100 K, indicating that the most significant spectral feature in OP Bi2212 is a resonance at 43 meV. The optical data below ${T}_{c}$ show that this boson is directly involved in the pair formation in OP Bi2212. Origins of the 43 meV mode are discussed.