Sum rule analysis of Umklapp processes and Coulomb energy: application to cuprate superconductivity

TL;DR

This paper rederives the third moment sum rule for density correlations considering Umklapp processes, providing bounds on Coulomb energy relevant for understanding superconductivity in cuprates.

Contribution

It introduces a revised sum rule incorporating Umklapp processes and applies it to analyze Coulomb energy changes in cuprates during superconducting transition.

Findings

Umklapp processes significantly affect density fluctuation spectra.

Bounds on Coulomb energy can be derived from sum rules and spectroscopy.

Application to cuprates aids understanding of superconducting mechanisms.

Abstract

The third moment frequency sum rule for the density-density correlation function is rederived in the presence of Umklapp processes. Upper and lower bounds on the electron-electron Coulomb energy are derived in two-dimensional and three-dimensional media, and the Umklapp processes are shown to be crucial in determining the spectrum of the density fluctuations (especially for the two-dimensional systems). This and other standard sum rules can be used in conjunction with experimental spectroscopies (electron-energy loss spectroscopy, optical ellipsometry, etc.) to analyse changes of the electron-electron Coulomb energy at the superconducting transition in cuprates.