Sum-rules for Raman scattering off strongly correlated electron systems

TL;DR

This paper derives and analyzes sum-rules for the Raman scattering intensity in strongly correlated electron systems near the Mott transition, linking the integrated intensity to doping and model parameters, and compares with experimental data.

Contribution

It provides a detailed derivation of sum-rules for Raman scattering in the t-J and Hubbard models, including cutoff dependence and experimental validation.

Findings

Sum-rule relates Raman intensity to doping level in doped Mott insulators.

In the t-J model, the sum-rule holds with an infinite frequency cutoff.

Experimental data on cuprates align with the theoretical sum-rule predictions.

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.