Sum-rules for Raman scattering off strongly correlated electron systems

Abstract

We investigate sum-rules applying to the Raman intensity in a strongly correlated system close to the Mott transition. Quite generally, it can be shown that, provided the frequency integration is performed up to a cutoff smaller than the upper Hubbard band, a sum-rule applies to the non-resonant Raman signal of a doped Mott insulator, resulting in an integrated intensity which is proportional to the doping level. We provide a detailed derivation of this sum-rule for the t-J model, for which the frequency cutoff can be taken to infinity and an unrestricted sum-rule applies. A quantitative analysis of the sum-rule is also presented for the d-wave superconducting phase of the t-J model, using slave boson methods. The case of the Hubbard model is studied in the framework of dynamical mean-field theory, with special attention to the cutoff dependence of the restricted sum-rule, and also to the intermediate coupling regime. The sum-rule investigated here is shown to be consistent with recent experimental data on cuprate superconductors, reporting measurements of Raman scattering intensities on an absolute scale.

11 pages, 8 figures

References in corpus (9)

• Inelastic Light Scattering From Correlated Electrons
• Two Energy Scales and two Quasiparticle Dynamics in the Superconducting State of Underdoped Cuprates
• Carrier relaxation, pseudogap, and superconducting gap in high-Tc cuprates: A Raman scattering study
• Optical conductivity and the correlation strength of high temperature copper-oxide superconductors
• Kinetic energy change with doping upon superfluid condensation in high temperature superconductors
• Cluster Dynamical Mean Field Theories
• Quasiparticle Formation and Optical Sum Rule Violation in Cuprate Superconductors
• Evolution of the gaps through the cuprate phase-diagram
• Optical sum rules that relate to the potential energy of strongly correlated systems

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