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

TL;DR

This paper investigates how superconductivity affects density correlations via Umklapp processes, revealing spectral weight transfer in plasmonic excitations and a suppression of Umklapp scattering due to electron pairing.

Contribution

It introduces a microscopic model showing how Umklapp processes influence density correlations in superconductors, highlighting a unique suppression mechanism.

Findings

Spectral weight shifts to mid-infrared in plasmonic excitations.

Superconductivity suppresses Umklapp scatterings regardless of gap symmetry.

Predictions for optical conductivity and EELS signatures are provided.

Abstract

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.