Electron-phonon vertex and its influence on the superconductivity of two-dimensional metals on a piezoelectric substrate

TL;DR

This paper analyzes how electron-phonon interactions, specifically via piezoelectric substrate phonons, influence superconductivity in 2D metals, showing that phonon-mediated attraction cannot surpass Coulomb repulsion at long wavelengths.

Contribution

It provides a theoretical analysis demonstrating the limitations of phonon-mediated pairing in 2D metals on piezoelectric substrates, highlighting fundamental energy constraints.

Findings

Phonon-mediated attraction cannot overcome Coulomb repulsion at long wavelengths.

Energy inequalities restrict the effectiveness of phonons in inducing pairing.

Implications for superconductivity in 2D materials on piezoelectric substrates.

Abstract

We investigate the interaction between the electrons of a two-dimensional metal and the acoustic phonons of an underlying piezoelectric substrate. Fundamental inequalities can be obtained from general energy arguments. As a result, phonon mediated attraction can be proven to never overcome electron Coulomb repulsion, at least for long phonon wavelengths. We study the influence of these phonons on the possible pairing instabilities of a two-dimensional electron gas such as graphene.