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Superconductivity-Induced Changes in Density-Density Correlation Function Enabled by Umklapp Processes

Motivated by the mid-infrared scenario for high-temperature superconductivity proposed by Leggett, the effects of Umklapp processes on the density-density correlation function in the presence of long-range Coulomb interaction have been investigated on a microscopic model. We show that because Umklapp processes enable scatterings that conserve total momentum only up to $n\vec{K}$, where $n$ is an integer and $\vec{K}$ is the reciprocal wave vector, significant amounts of spectral weight in the plasmonic excitations at long wavelength are transferred into lower frequency around mid-infrared regime. We further find that regardless of the gap symmetry, superconductivity generally suppresses the Umklapp scatterings due to the formation of the electron pairing. This suppression is unique for the superconductivity due to the interplay between electron pairing and the odd parity of the matrix elements associated with Umklapp channels, which usually does not occur in other known competing orders. Specific predictions for the experimental signatures in optical conductivity and electron energy loss spectroscopy (EELS) will be discussed.