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 in both the visible (Raman effect) and 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, 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) provides new insights into anisotropic and complex many-body behavior of electrons in various systems. 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 are reviewed. An overview of the manifestations of complexity in the Raman response due to the impact of correlations and developing competing orders is presented. In a variety of materials, observations which may be understood and a summary of important open questions that pave the way to a detailed understanding of correlated electron systems, are discussed.

/pdf/inelastic-light-scattering-from-correlated-electrons-3u08u0719o.pdf

Inelastic light scattering from correlated electrons

A consistent explanation of the unusual combination of anisotropies of the Knight shifts and relaxation rates of Cu(1) and Cu(2) nuclei in YBa2Cu3O7 is given. The key features are an anisotropic on-site hyperfine coupling to local Cu2+ electronic spins and an isotropic transferred hyperfine coupling to the neighboring Cu2+-spins. We use a quantum chemical model of the Cu-O hybridization to estimate the strength of these hyperfine interactions. Good agreement is found between our estimated parameters and experiment.

Analysis of magnetic resonance experiments in YBa2Cu3O7

We present a phenomenological description of the high-frequency vortex dynamics in and discuss the main parameters related to vortex motion, namely the viscous drag coefficient , the pinning constant (Labusch parameter) and the depinning frequency . We demonstrate experimental results on the angular and temperature dependence of , and in and compare these results with existing models. We show how studies of the vortex viscosity may yield information on the superclean limit. This limit corresponds to the formation of the discrete excitation spectrum in the vortex core due to quantum confinement and small coherence length. From the low-temperature viscosity data we conclude that the superclean limit in is reached for magnetic field perpendicular to the c-axis.

https://iopscience.iop.org/article/10.1088/0953-2048/9/1/001/pdf

High-frequency vortex dynamics in

Raman and IR-measurements on the high- T c material series La 2 CuO 4 and YBa 2 Cu 3 O 7 are reviewed. This summary focuses on lattice vibrations in these superconducting systems, on impurity phases, the influence of oxygen stoichiometry and element substitution. The determination of the superconducting gap, the phonon renormalization in the superconducting state, and the isotope effect with its implications on the theory of superconductivity in these materials are discussed. In addition, the measured lattice vibrations are compared with the results of lattice dynamics calculations.

Lattice vibrations in high-Tc superconductors: Optical spectroscopy and lattice dynamics☆

Interplay of electron–phonon interaction and strong correlations: the possible way to high-temperature superconductivity

The authors report single-crystal Cu NMR data for YBa/sub 2/Cu/sub 3/O/sub 7-//sub delta/ (T/sub c/ = 90 K). The shift tensor K/sub ..cap alpha..//sub ..cap alpha../ (..cap alpha.. = a,b,c), the electric-field-gradient tensor ..nu../sub ..cap alpha..//sub ..cap alpha../, and the spin-lattice-relaxation-rate tensor are reported for Cu atoms in the planes and chains. The authors show that a model in which both chain and plane Cu are approximated as Cu/sup 2+/ ions with a net spin accounts for the field-gradient tensor and the shift tensor at both chain and plane sites, and for the relaxation rate at the plane sites.

Static and dynamic Cu NMR tensors of YBa2Cu3O7- delta.

The authors report the transverse NMR relaxation of chain [Cu(1)] and plane [Cu(2)] nuclei in a single crystal of $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ (${T}_{c}=90$ K) in the normal state They demonstrate the existence of a strong indirect spin-spin coupling between Cu(2) nuclei, and show that it can be explained using a model in which the Cu(2) atoms possess electronic magnetic moments which are exchange coupled to one another In such a model, the strength of the coupling implies an effective electronic exchange coupling ${J}_{\mathrm{eff}}\ensuremath{\approx}1100$ ${\mathrm{cm}}^{\ensuremath{-}1}$

NMR measurement of the exchange coupling between Cu(2) atoms in Y Ba 2 Cu 3 O 7 − δ ( T c = 90 K)

We report a Raman scattering investigation of superconducting gap anisotropy in single-crystal $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$. Gap anisotropy is investigated by studying the peak in the low-temperature Raman continuum in various symmetries. Roughly a 35% difference in the energy of this peak is observed between different symmetries, suggesting the presence of substantial gap anisotropy. Anisotropy is further evidenced by the damping behavior of the 340-${\mathrm{cm}}^{\ensuremath{-}1}$ Raman-active phonon below ${T}_{c}$, which displays increased attenuation due to phonon-induced pair breaking. The temperature dependence of this attenuation is consistent with a $T=0$ pair-breaking peak which is much larger than the 340-${\mathrm{cm}}^{\ensuremath{-}1}$ phonon in certain regions of the Fermi surface.

Gap anisotropy and phonon self-energy effects in single-crystal YBa2Cu3O7- delta.

Using torque magnetometry, we have obtained a lower bound of \ensuremath{\sim}${10}^{5}$ for the anisotropy of the superconducting effective mass in a single crystal of ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{\mathit{x}}$. This is the largest such anisotropy yet reported for a high-${\mathit{T}}_{\mathit{c}}$ material.

Superconducting effective-mass anisotropy in Tl2Ba2CaCu2Ox.

The results of polarized light-scattering studies of single-crystal YBa2Cu3O7-δ are presented. In the normal state, strong electronic scattering is observed both directly and through interference effects with certain phonons. Below Tc this electronic scattering undergoes a redistribution that is due to gap formation. The redistribution of the continuum below Tc has a strong symmetry dependence, suggesting possible gap anisotropy in YBa2Cu3O7-δ. Phonon self-energy effects are also shown to be consistent with gap anisotropy. Finally, studies of untwinned single crystals illustrate striking optical anisotropy of the Raman spectra in the a–b plane.

E. D. Bukowski

Papers

Static and dynamic Cu NMR tensors of YBa2Cu3O7- delta.

NMR measurement of the exchange coupling between Cu(2) atoms in Y Ba 2 Cu 3 O 7 − δ ( T c = 90 K)

Gap anisotropy and phonon self-energy effects in single-crystal YBa2Cu3O7- delta.

Superconducting effective-mass anisotropy in Tl2Ba2CaCu2Ox.

Raman-scattering studies of coupled modes and superconducting gap excitations in single-crystal YBa2Cu3O7-δ