# Modelling electron-phonon interactions in graphene with curved space hydrodynamics

## TL;DR

This paper presents a novel approach to modeling electron-phonon interactions in graphene using curved space hydrodynamics, capturing lattice vibrations as curvature effects influencing electronic flow.

## Contribution

It introduces a new geometric framework for electron-phonon interactions in graphene, linking lattice vibrations to curvature in a hydrodynamic model.

## Key findings

- Successfully reproduces linear resistivity scaling at high temperatures
- Provides a temperature-independent coupling constant model
- Offers a new perspective applicable to other Fermi liquid materials

## Abstract

We introduce a different perspective describing electron-phonon interactions in graphene based on curved space hydrodynamics. Interactions of phonons with charge carriers increase the electrical resistivity of the material. Our approach captures the lattice vibrations as curvature changes in the space through which electrons move following hydrodynamic equations. In this picture, inertial corrections to the electronic flow arise naturally effectively producing electron-phonon interactions. The strength of the interaction is controlled by a coupling constant, which is temperature independent. We apply this model to graphene and recover satisfactorily the linear scaling law for the resistivity that is expected at high temperatures. Our findings open up a new perspective of treating electron-phonon interactions in graphene, and also in other materials where electrons can be described by the Fermi liquid theory.