# Extending the theory of phonon-mediated superconductivity in quasi-2D

## TL;DR

This paper extends the Migdal-Eliashberg theory to better understand phonon-mediated superconductivity in quasi-2D materials, especially relevant for cuprates, by analyzing spectral functions and phase diagrams.

## Contribution

It introduces an extended theoretical framework for electron-phonon interactions, addressing intermediate regimes and limitations of traditional models in superconductivity research.

## Key findings

- Spectral functions and phase diagrams are computed using the extended theory.
- The results highlight the importance of considering intermediate parameter regimes.
- Discussion connects findings to established theories and Coulomb effects.

## Abstract

I present results from an extended Migdal-Eliashberg theory of electron-phonon interactions and superconductivity. The history of the electron-phonon problem is introduced, and then study of the intermediate parameter regime is justified from the energy scales in the cuprate superconductors. The Holstein model is detailed, and limiting cases are examined to demonstrate the need for an extended theory of superconductivity. Results of the extended approximation are shown, including spectral functions and phase diagrams. These are discussed with reference to Hohenberg's theorem, the Bardeen-Cooper-Schrieffer theory and Coulomb repulsion.