Raman scattering through a metal-insulator transition - art. no. 125110

The exact solution for nonresonant A(1g) and B-1g Raman scattering is prese nted for the simplest model that has a correlated metal-insulator transitio n. the Falicov-Kimball model. by employing dynamical mean-field theory. In the general case, the A(1g) response includes nonresonant, resonant, and mi xed contributions, and the Big response includes nonresonant and resonant c ontributions (we prove the Shastry-Shraiman relation for the nonresonant B- 1g response), while the B-2g response is purely resonant. Three main featur es are seen in the nonresonant B-1g channel: (i) the rapid appearance of lo w-energy spectral weight at the expense of higher-energy weight: (b) the fr equency range for this low-energy spectral weight is much larger than the o nset temperature, where the response first appears; and (iii) the occurrenc e of an isosbestic point, which is a characteristic frequency where the Ram an response is independent of temperature for low temperatures. Vertex corr ections renormalize away all of these anomalous features in the nonresonant A(1g) channel. The calculated results compare favorably to the Raman respo nse of a number of correlated systems on the insulating side of the quantum -critical point (ranging from Kondo insulators to mixed-valence materials t o underdoped high-temperature superconductors). We also show why the nonres onant B-1g Raman response is "universal" on the insulating side of the meta l-insulator transition.