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

Antiferromagnetism and superconductivity are both fundamental and common states of matter. In many strongly correlated systems, including the high Tc cuprates, the heavy fermion compounds and the organic superconductors, they occur next to each other in the phase diagram and influence each other's physical properties. The SO(5) theory unifies these two basic states of matter by a symmetry principle and describes their rich phenomenology through a single low energy effective model. In this paper, we review the framework of the SO(5) theory, and its detailed comparison with numerical and experimental results.

/pdf/so-5-theory-of-antiferromagnetism-and-superconductivity-3qzte27w8u.pdf

SO(5) theory of antiferromagnetism and superconductivity

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

We review a number of experimental techniques that are beginning to reveal fine details of the bosonic spectrum α2F(Ω) that dominates the interaction between the quasiparticles in high-temperature superconductors. Angle-resolved photoemission spectroscopy (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 spatial 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 temperatures which evolves, as the temperature is lowered, into a peak in the 30–60 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.

https://iopscience.iop.org/article/10.1088/0034-4885/74/6/066501/pdf

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.

Bosons in high temperature superconductors: an experimental survey

The Raman electronic continuum is calculated in an antiferromagnetic spin-fluctuation model of the superconducting state. The dependence of the Raman cross section on temperature and on band structure is investigated. A tight-binding model with, up to second nearest neighbors is used and in one case with effective mass anisotropy. The gap is determined from numerical solution of the BCS equations using fast Fourier transforms, with pairing through the phenomenological spin susceptibility of Millis, Monien, and Pines.

Raman electronic continuum in a spin-fluctuation model for superconductivity

In a two-dimensional band-structure model, the effect of doping on the Raman electronic background of a superconductor with {ital d}{sub {ital x}{sup 2}{minus}{ital y}{sup 2}} gap symmetry is studied. Emphasis is placed near optimum doping and on the role of the van Hove singularity. The relationship between peaks in the Raman spectrum for three often discussed photon geometries and the gap is studied. No simple relationship exists, although the {ital B}{sub 1{ital g}} mode can show many of the features of the quasiparticle density of states. {copyright} {ital 1996 The American Physical Society.}

Doping and van hove singularity dependence of raman background in dx2-y2 superconductors

We use the nearly antiferromagnetic Fermi liquid model to illustrate the effect of strongly anisotropic inelastic scattering on the electron Raman response. Both normal and superconducting states are considered, accounting fully for the momentum and frequency dependence of the resulting self-energy. Special attention is paid to the low frequency of the response and an ω to ω3 crossover in B
1g
. By analogy to the infrared conductivity case, effective Raman scattering times are extracted, and their temperature and frequency dependences are studied and are compared with equivalent optical quantities. Impurities, within a unitary scattering approximation, are introduced and found to also have a strong characteristic signature on the Raman response.

Inelastic scattering in normal and superconducting Raman response

There should be no Josephson current between a CuO2 plane with a gap of d-wave symmetry and a conventional s-wave superconductor. Nevertheless such a current is observed to exist between YBCO and Pb although with a reduced magnitude. Penetration depth measurements have revealed a large anisotropy between a- and b-directions presumably due to the existence of the CuO chains. Using a simple anisotropic tight binding model in qualitative agreement with the measured penetration depths and a standard model for the spin susceptibility we obtain, on solution of the BCS gap equations, a gap function with a mainly d-wave symmetry but with a minor extended s-wave component. The resultant Josephson current for YBCO-Pb junctions is in good agreement with experiment.

Josephson current in an anisotropic d-wave model

A theory is given for the structure present in the normal state optical conductivity that reflects the underlying spin fluctuations for a system in which the charge carriers interact through the antiferromagnetic spin susceptibility. Such an interaction involves strong momentum anisotropies and energy dependence that modulates the frequency dependence of the conductivity.

D. Branch

Papers

Raman electronic continuum in a spin-fluctuation model for superconductivity

Doping and van hove singularity dependence of raman background in dx2-y2 superconductors

Inelastic scattering in normal and superconducting Raman response

Josephson current in an anisotropic d-wave model

Spin fluctuations in the normal state optical conductivity