Exchange Enhancement of the Electron-Phonon Pair Interaction

TL;DR

This paper investigates how exchange interactions enhance electron-phonon coupling, leading to increased critical temperatures in high-$T_c$ superconductors by phonon softening effects.

Contribution

It introduces a calculation of exchange interaction effects on phonon frequencies and electron-phonon vertices, revealing a significant enhancement of superconducting pairing.

Findings

Strong enhancement of electron-electron attraction via phonons

Critical temperature increase primarily due to phonon softening

Self-consistent solutions show increased $T_c$ with exchange effects

Abstract

The critical temperature of high-$T_c$ superconductors is determined, at least in part, by the electron-phonon coupling. We include the effect of an exchange interaction between the electrons and calculate the renormalization of the bare phonon frequencies and the electron-phonon verticies in a random phase approximation and obtain a strongly enhanced attractive phonon-induced electron-electron interaction. Using Fast Fourier Transform techniques, the weak-coupling selfconsistency equation for the order parameter is solved in the 2D first Brillouin zone for the Emery tight-binding band with different band fillings. The enhancement of $T_c$ arises primarily from the softening of the phonon frequencies rather than the vertex renormalization.