Sum rule analysis of umklapp processes and Coulomb energy: Application to cuprate superconductivity
Misha Turlakov, Anthony J. Leggett
DOI 10.1103/PhysRevB.67.094517 · Physical Review B
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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 analyze changes of the electron-electron Coulomb energy at the superconducting transition in cuprates.
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