First-Order Type Effects in YBa2_2Cu3_3O6+x_{6+x} at the Onset of Superconductivity

We present results of Raman scattering experiments on tetragonal ${\rm (Y_{1-y}Ca_{y})Ba_{2}Cu_{3}O_{6+x}}$ for doping levels $p(x,y)$ between 0 and 0.07 holes/CuO$_2$. Below the onset of superconductivity at $p_{\rm sc1} \approx 0.06$, we find evidence of a diagonal superstructure. At $p_{\rm sc1}$, lattice and electron dynamics change discontinuously with the charge and spin properties being renormalized at all energy scales. The results indicate that charge ordering is intimately related to the transition at $p_{\rm sc1}$ and that the maximal transition temperature to superconductivity at optimal doping $T_{c}^{\rm max}$ depends on the type of ordering at $p>p_{\rm sc1}$.Comment: 4 pages, 4 figure

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

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

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

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

Structural Change in (Economic) Time Series

Methods for detecting structural changes, or change points, in time series data are widely used in many fields of science and engineering. This chapter sketches some basic methods for the analysis of structural changes in time series data. The exposition is confined to retrospective methods for univariate time series. Several recent methods for dating structural changes are compared using a time series of oil prices spanning more than 60 years. The methods broadly agree for the first part of the series up to the mid-1980s, for which changes are associated with major historical events, but provide somewhat different solutions thereafter, reflecting a gradual increase in oil prices that is not well described by a step function. As a further illustration, 1990s data on the volatility of the Hang Seng stock market index are reanalyzed.Comment: 12 pages, 6 figure

High-field muSR studies of superconducting and magnetic correlations in cuprates above Tc

The advent of high transverse-field muon spin rotation (TF-muSR) has led to recent muSR investigations of the magnetic-field response of cuprates above the superconducting transition temperature T_c. Here the results of such experiments on hole-doped cuprates are reviewed. Although these investigations are currently ongoing, it is clear that the effects of high field on the internal magnetic field distribution of these materials is dependent upon a competition between superconductivity and magnetism. In La_{2-x}Sr_xCuO_4 the response to the external field above Tc is dominated by heterogeneous spin magnetism. However, the magnetism that dominates the observed inhomogeneous line broadening below x ~ 0.19 is overwhelmed by the emergence of a completely different kind of magnetism in the heavily overdoped regime. The origin of the magnetism above x ~ 0.19 is currently unknown, but its presence hints at a competition between superconductivity and magnetism that is reminiscent of the underdoped regime. In contrast, the width of the internal field distribution of underdoped YBa_2Cu_3O_y above Tc is observed to track Tc and the density of superconducting carriers. This observation suggests that the magnetic response above Tc is not dominated by electronic moments, but rather inhomogeneous fluctuating superconductivity.Comment: 28 pages, 11 figures, 104 reference

A study of the superconducting gap in RNi2_2B2_2C (R = Y, Lu) single crystals by inelastic light scattering

Superconductivity-induced changes in the electronic Raman scattering response were observed for the RNi$_2$B$_2$C (R = Y, Lu) system in different scattering geometries. In the superconducting state, 2$\Delta$-like peaks were observed in A$_{1g}$, B$_{1g}$, and B$_{2g}$ spectra from single crystals. The peaks in A$_{1g}$ and B$_{2g}$ symmetries are significantly sharper and stronger than the peak in B$_{1g}$ symmetry. The temperature dependence of the frequencies of the 2$\Delta$-like peaks shows typical BCS-type behavior, but the apparent values of the $2\Delta$ gap are strongly anisotropic for both systems. In addition, for both YNi$_2$B$_2$C and LuNi$_2$B$_2$C systems, there exists reproducible scattering strength below the $2\Delta$ gap which is roughly linear to the frequency in B$_{1g}$ and B$_{2g}$ symmetries. This discovery of scattering below the gap in non-magnetic borocarbide superconductors, which are thought to be conventional BCS-type superconductors, is a challenge for current understanding of superconductivity in this system.Comment: Added text, changed a figure, and added references. Will appear in Phys. Rev.

Inelastic Light Scattering From Correlated Electrons

Inelastic light scattering is an intensively used tool in the study of electronic properties of solids. Triggered by the discovery of high temperature superconductivity in the cuprates and by new developments in instrumentation, light scattering both in the visible (Raman effect) and the X-ray part of the electromagnetic spectrum has become a method complementary to optical (infrared) spectroscopy while providing additional and relevant information. The main purpose of the review is to position Raman scattering with regard to single-particle methods like angle-resolved photoemission spectroscopy (ARPES), and other transport and thermodynamic measurements in correlated materials. Particular focus will be placed on photon polarizations and the role of symmetry to elucidate the dynamics of electrons in different regions of the Brillouin zone. This advantage over conventional transport (usually measuring averaged properties) indeed provides new insights into anisotropic and complex many-body behavior of electrons in various systems. We review recent developments in the theory of electronic Raman scattering in correlated systems and experimental results in paradigmatic materials such as the A15 superconductors, magnetic and paramagnetic insulators, compounds with competing orders, as well as the cuprates with high superconducting transition temperatures. We present an overview of the manifestations of complexity in the Raman response due to the impact of correlations and developing competing orders. In a variety of materials we discuss which observations may be understood and summarize important open questions that pave the way to a detailed understanding of correlated electron systems.Comment: 62 pages, 48 figures, to appear in Rev. Mod. Phys. High-resolution pdf file available at http://onceler.uwaterloo.ca/~tpd/RMP.pd

Stripe order and quasiparticle Nernst effect in cuprate superconductors

After a brief review of current ideas on stripe order in cuprate high-temperature superconductors, we discuss the quasiparticle Nernst effect in the cuprates, with focus on its evolution in non-superconducting stripe and related nematic states. In general, we find the Nernst signal to be strongly enhanced by nearby van-Hove singularities and Lifshitz transitions in the band structure, implying that phases with translation symmetry breaking often lead to a large quasiparticle Nernst effect due to the presence of multiple small Fermi pockets. Open orbits may contribute to the Nernst signal as well, but do so in a strongly anisotropic fashion. We discuss our results in the light of recent proposals for a specific Lifshitz transition in underdoped YBCO and make predictions for the doping dependence of the Nernst signal.Comment: 10 pages, 4 figs, article prepared for a special issue of New J Phy