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 $B_{1g}$ symmetry, 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. 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$_{8+\delta}$ 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) 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 $B_{1g}$ looks more like the optical spectrum. A large peak around $30 - 40\,$meV in $B_{1g}$, much less prominent in $B_{2g}$, is taken as support for the importance of $(\pi,\pi)$ scattering at this frequency.Comment: 7 pages, 3 figure

Signatures of nematic quantum critical fluctuations in the Raman spectra of lightly doped cuprates

We consider the lightly doped cuprates Y$_{0.97}$Ca$_{0.03}$BaCuO$_{6.05}$ and La$_{2-x}$Sr$_x$CuO$_4$ (with $x=0.02$,0.04), where the presence of a fluctuating nematic state has often been proposed as a precursor of the stripe (or, more generically, charge-density wave) phase, which sets in at higher doping. We phenomenologically assume a quantum critical character for the longitudinal and transverse nematic, and for the charge-ordering fluctuations, and investigate the effects of these fluctuations in Raman spectra. We find that the longitudinal nematic fluctuations peaked at zero transferred momentum account well for the anomalous Raman absorption observed in these systems in the $B_{2g}$ channel, while the absence of such effect in the $B_{1g}$ channel may be due to the overall suppression of Raman response at low frequencies, associated with the pseudogap. While in Y$_{0.97}$Ca$_{0.03}$BaCuO$_{6.05}$ the low-frequency lineshape is fully accounted by longitudinal nematic collective modes alone, in La$_{2-x}$Sr$_x$CuO$_4$ also charge-ordering modes with finite characteristic wavevector are needed to reproduce the shoulders observed in the Raman response. This different involvement of the nearly critical modes in the two materials suggests a different evolution of the nematic state at very low doping into the nearly charge-ordered state at higher doping.Comment: 12 pages with 10 figures, to appear in Phys. Rev. B 201

Spectral signatures of critical charge and spin fluctuations in cuprates

We discuss how Raman spectra of high temperature superconducting cuprates are affected by nearly-critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We find that specific fingerprints of nearly-critical collective modes can be observed and that the selectivity of Raman spectroscopy in momentum space may be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-T_c superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover spin modes have larger masses and are more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuating with high frequency.Comment: 6 pages and 3 figures, invited paper to the conference SCES 08, Buzios/Rio, Brazi

Band and momentum dependent electron dynamics in superconducting Ba(Fe1−xCox)2As2{\rm Ba(Fe_{1-x}Co_{x})_2As_2} as seen via electronic Raman scattering

We present details of carrier properties in high quality ${\rm Ba(Fe_{1-x}Co_{x})_2As_2}$ single crystals obtained from electronic Raman scattering. The experiments indicate a strong band and momentum anisotropy of the electron dynamics above and below the superconducting transition highlighting the importance of complex band-dependent interactions. The presence of low energy spectral weight deep in the superconducting state suggests a gap with accidental nodes which may be lifted by doping and/or impurity scattering. When combined with other measurements, our observation of band and momentum dependent carrier dynamics indicate that the iron arsenides may have several competing superconducting ground states.Comment: 5 pages, 4 figure

A balancing act: Evidence for a strong subdominant d-wave pairing channel in Ba0.6K0.4Fe2As2{\rm Ba_{0.6}K_{0.4}Fe_2As_2}

We present an analysis of the Raman spectra of optimally doped ${\rm Ba_{0.6}K_{0.4}Fe_2As_2}$ based on LDA band structure calculations and the subsequent estimation of effective Raman vertices. Experimentally a narrow, emergent mode appears in the $B_{1g}$ ($d_{x^2-y^2}$) Raman spectra only below $T_c$, well into the superconducting state and at an energy below twice the energy gap on the electron Fermi surface sheets. The Raman spectra can be reproduced quantitatively with estimates for the magnitude and momentum space structure of the s$_{+-}$ pairing gap on different Fermi surface sheets, as well as the identification of the emergent sharp feature as a Bardasis-Schrieffer exciton, formed as a Cooper pair bound state in a subdominant $d_{x^2-y^2}$ channel. The binding energy of the exciton relative to the gap edge shows that the coupling strength in this subdominant $d_{x^2-y^2}$ channel is as strong as 60% of that in the dominant $s_{+-}$ channel. This result suggests that $d_{x^2-y^2}$ may be the dominant pairing symmetry in Fe-based sperconductors which lack central hole bands.Comment: 10 pages, 6 Figure

Pinpointing Gap Minima in Ba(Fe0.94_{0.94}Co0.06)2_{0.06})_{2}As2_2 \textit{via} Band Structure Calculations and Electronic Raman Scattering

A detailed knowledge of the gap structure for the Fe-pnictide superconductors is still rather rudimentary, with several conflicting reports of either nodes, deep gap minima, or fully isotropic gaps on the Fermi surface sheets, both in the $k_{x}-k_{y}$ plane and along the c-axis. In this paper we present considerations for electronic Raman scattering which can help clarify the gap structure and topology using different light scattering geometries. Using density functional calculations for the Raman vertices, it is shown that the location of the gap minima may occur on loops stretching over a portion of the c-axis in Ba(Fe$_{0.94}$Co$_{0.06})_{2}$As$_2$.Comment: 4+ pages, three figure

Electron interactions and charge ordering in La2−x_{2-x}Srx_xCuO4_4

We present results of inelastic light scattering experiments on single-crystalline La$_{2-x}$Sr$_{x}$CuO$_4$ in the doping range $0.00 \le x=p \le 0.30$ and Tl$_2$Ba$_2$CuO$_{6+\delta}$ at $p=0.20$ and $p=0.24$. The main emphasis is placed on the response of electronic excitations in the antiferromagnetic phase, in the pseudogap range, in the superconducting state, and in the essentially normal metallic state at $x \ge 0.26$, where no superconductivity could be observed. In most of the cases we compare B$_{1g}$ and B$_{2g}$ spectra which project out electronic properties close to $(\pi,0)$ and $(\pi/2, \pi/2)$, respectively. In the channel of electron-hole excitations we find universal behavior in B$_{2g}$ symmetry as long as the material exhibits superconductivity at low temperature. In contrast, there is a strong doping dependence in B$_{1g}$ symmetry: (i) In the doping range $0.20 \le p \le 0.25$ we observe rapid changes of shape and temperature dependence of the spectra. (ii) In La$_{2-x}$Sr$_{x}$CuO$_4$ new structures appear for $x < 0.13$ which are superposed on the electron-hole continuum. The temperature dependence as well as model calculations support an interpretation in terms of charge-ordering fluctuations. For $x \le 0.05$ the response from fluctuations disappears at B$_{1g}$ and appears at B$_{2g}$ symmetry in full agreement with the orientation change of stripes found by neutron scattering. While, with a grain of salt, the particle-hole continuum is universal for all cuprates the response from fluctuating charge order in the range $0.05 \le p < 0.16$ is so far found only in La$_{2-x}$Sr$_{x}$CuO$_4$. We conclude that La$_{2-x}$Sr$_{x}$CuO$_4$ is close to static charge order and, for this reason, may have a suppressed $T_c$.Comment: 17 pages, 15 figure

Raman-Scattering Detection of Nearly Degenerate ss-Wave and dd-Wave Pairing Channels in Iron-Based Ba0.6_{0.6}K0.4_{0.4}Fe2_2As2_2 and Rb0.8_{0.8}Fe1.6_{1.6}Se2_2 Superconductors

We show that electronic Raman scattering affords a window into the essential properties of the pairing potential $V_{\mathbf{k},\mathbf{k^{\prime}}}$ of iron-based superconductors. In Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ we observe band dependent energy gaps along with excitonic Bardasis-Schrieffer modes characterizing, respectively, the dominant and subdominant pairing channel. The $d_{x^2-y^2}$ symmetry of all excitons allows us to identify the subdominant channel to originate from the interaction between the electron bands. Consequently, the dominant channel driving superconductivity results from the interaction between the electron and hole bands and has the full lattice symmetry. The results in Rb$_{0.8}$Fe$_{1.6}$Se$_2$ along with earlier ones in Ba(Fe$_{0.939}$Co$_{0.061}$)$_2$As$_2$ highlight the influence of the Fermi surface topology on the pairing interactions.Comment: 5 pages, 4 figure

Bosons in high temperature superconductors: an experimental survey

We review a number of experimental techniques that are beginning to reveal fine details of the bosonic spectrum \alpha^2F(\Omega) that dominates the interaction between the quasiparticles in high temperature superconductors. Angle-resolved photo emission (ARPES) shows kinks in electronic dispersion curves at characteristic energies that agree with similar structures in the optical conductivity and tunnelling spectra. Each technique has its advantages. ARPES is momentum resolved and offers independent measurements of the real and imaginary part of the contribution of the bosons to the self energy of the quasiparticles. The optical conductivity can be used on a larger variety of materials and with the use of maximum entropy techniques reveals rich details of the spectra including their evolution with temperature and doping. Scanning tunnelling spectroscopy offers spacial resolution on the unit cell level. We find that together the various spectroscopies, including recent Raman results, are pointing to a unified picture of a broad spectrum of bosonic excitations at high temperature which evolves, as the temperature is lowered into a peak in the 30 to 60 meV region and a featureless high frequency background in most of the materials studied. This behaviour is consistent with the spectrum of spin fluctuations as measured by magnetic neutron scattering. However, there is evidence for a phonon contribution to the bosonic spectrum as well.Comment: 71 pages, 52 figure