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.

We describe the results of electronic Raman-scattering experiments in differently doped single crystals of YBa 2 Cu 3 O 6ϩx and Bi 2 Sr 2 (Ca x Y 1Ϫx )Cu 2 O 8 . The data in antiferromagnetic insulating samples suggest that at least the low-energy parts of the spectra of metallic samples originate predominantly from excitations of free carriers. We therefore propose an analysis of the data in terms of a memory function approach which has been introduced earlier for the current response. Dynamical scattering rates ⌫()ϭ1/() and mass-enhancement factors 1ϩ()ϭm*()/m of the carriers are obtained. It is found that a strong polarization dependence of the carrier lifetime develops towards low doping. In B 2g (xy) symmetry selecting predominantly electrons with momenta along the diagonals of the CuO 2 planes the Raman data compare well with the results obtained from dc and dynamical transport. In B 1g (x 2 Ϫy 2 ) symmetry projecting out momenta along the Cu-O bonds the dc scattering rates of underdoped materials become temperature independent and considerably larger than in B 2g symmetry. This increasing anisotropy is accompanied by a loss of spectral weight in B 2g symmetry in the range between the superconducting transition at T c and a characteristic temperature T* of the order of room temperature which compares well with the pseudogap temperature found in other experiments. The energy range affected by the pseudogap is doping and temperature independent. The integrated spectral loss is approximately 25% in underdoped samples and becomes much weaker towards higher carrier concentration. In underdoped samples, superconductivity-related features in the spectra can be observed only in B 2g symmetry. The peak frequencies scale with T c . We do not find a direct relation between the pseudogap and the superconducting gap.

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Raman spectra of YBa 2 Cu 3 O 72x and Bi 2 Sr 2 ͑Ca 0.62 Y 0.38 ͒Cu 2 O 81d with T c Х 0.65T max c in the underdoped regime of the phase diagram are studied as a function of temperature and polarization. At B 2g ͑xy͒ symmetry a reduction of spectral weight by 10% for frequencies less than 700 cm 21 or 15k B T c is found below approximately 200 K. Below T c , a superconducting gap opens up which closely resembles that observed at higher doping levels. It is compatible with d x 2 2y 2 pairing and its amplitude 2D 0 can be estimated to be 8k B T c . [S0031-9007(97)