Optical Integral in the Cuprates and the Question of Sum Rule Violation

TL;DR

This paper investigates the optical sum rule in cuprates, showing that the apparent violation in the normal state is mainly due to the finite cut-off in the optical integral, modeled by electron-boson interactions.

Contribution

It demonstrates that the observed sum rule violation in cuprates' normal state arises from finite cut-off effects, not intrinsic electronic changes, using a boson interaction model.

Findings

The temperature dependence is explained by the cut-off dependent term.

The dominant sum rule violation is due to finite optical integral cut-off.

Electron-boson interactions effectively model the cut-off dependent term.

Abstract

Much attention has been given to a possible violation of the optical sum rule in the cuprates, and the connection this might have to kinetic energy lowering. The optical integral is composed of a cut-off independent term (whose temperature dependence is a measure of the sum rule violation), plus a cut-off dependent term that accounts for the extension of the Drude peak beyond the upper bound of the integral. We find that the temperature dependence of the optical integral in the normal state of the cuprates can be accounted for solely by the latter term, implying that the dominant contribution to the observed sum rule `violation' in the normal state is due to the finite cut-off. This cut-off dependent term is well modeled by a theory of electrons interacting with a broad spectrum of bosons.