Electronic Raman scattering in a multiband model for cuprate superconductors

TL;DR

This paper develops a unified response theory for electronic Raman scattering in cuprate superconductors, highlighting the dominance of incoherent processes at low frequencies and the role of antiferromagnetic correlations in spectral features.

Contribution

It introduces a consistent theoretical framework distinguishing direct and indirect scattering channels, applied to a three-band model, explaining experimental Raman spectra in underdoped cuprates.

Findings

Incoherent indirect processes dominate low-frequency Raman spectra.

Long-range screening removes forces in the $A_{1g}$ channel.

Mid-infrared peaks are linked to antiferromagnetic correlations.

Abstract

Charge-charge, current-current and Raman correlation functions are derived in a consistent way using the unified response theory. The theory is based on the improved description of the conduction electron coupling to the external electromagnetic fields, distinguishing further the direct and indirect (assisted) scattering on the quasi-static disorder. The two scattering channels are distinguished in terms of the energy and momentum conservation laws. The theory is illustrated on the Emery three-band model for the normal state of the underdoped high-$T_c$ cuprates which includes the incoherent electron scattering on the disorder associated with the quasi-static fluctuations around the static antiferromagnetic (AF) ordering. It is shown, for the first time consistently, that the incoherent indirect processes dominate the low-frequency part of the Raman spectra, while the long-range screening which is dynamic removes the long-range forces in the $A_{1g}$ channel. In the mid-infrared frequency range the coherent AF processes are dominant. In contrast to the nonresonant $B_{1g}$ response, which is large by itself, the resonant interband transitions enhance both the $A_{1g}$ and $B_{1g}$ Raman spectra to comparable values, in good agreement with experimental observation. It is further argued that the AF correlations give rise to the mid-infrared peak in the $B_{1g}$ Raman spectrum, accompanied by a similar peak in the optical conductivity. The doping behavior of these peaks is shown to be correlated with the linear doping dependence of the Hall number, as observed in all underdoped high-$T_c$ compounds.