Raman scattering through a metal-insulator transition

The exact solution for nonresonant A(1g) and B-1g Raman scattering is presented for the simplest model that has a correlated metal-insulator transition. the Falicov-Kimball model. by employing dynamical mean-field theory. In the general case, the A(1g) response includes nonresonant, resonant, and mixed contributions, and the Big response includes nonresonant and resonant contributions (we prove the Shastry-Shraiman relation for the nonresonant B-1g response), while the B-2g response is purely resonant. Three main features are seen in the nonresonant B-1g channel: (i) the rapid appearance of low-energy spectral weight at the expense of higher-energy weight: (b) the frequency range for this low-energy spectral weight is much larger than the onset temperature, where the response first appears; and (iii) the occurrence of an isosbestic point, which is a characteristic frequency where the Raman response is independent of temperature for low temperatures. Vertex corrections renormalize away all of these anomalous features in the nonresonant A(1g) channel. The calculated results compare favorably to the Raman response of a number of correlated systems on the insulating side of the quantum-critical point (ranging from Kondo insulators to mixed-valence materials to underdoped high-temperature superconductors). We also show why the nonresonant B-1g Raman response is universal on the insulating side of the metal-insulator transition.