Interaction of Flexural Phonons with Electrons in Graphene: A Generalized Dirac Equation in Corrugated Surfaces

TL;DR

This paper derives a generalized Dirac equation for charge carriers in corrugated graphene, incorporating flexural phonon interactions via an induced metric, predicting non-linear effects and control of conductivity through strain fields.

Contribution

It introduces a novel generalized Dirac equation framework that accounts for flexural phonons in corrugated graphene, enabling analysis of non-linear effects and external field interactions.

Findings

Predicts non-linear effects in electron-phonon interactions.

Shows possibility of controlling conductivity with sinusoidal strain.

Identifies resonances between phonons and electromagnetic fields.

Abstract

A generalized Dirac equation is derived in order to describe charge carriers moving in corrugated graphene, which is the case for temperatures above 10{\deg}K due to the presence of flexural phonons. Such interaction is taken into account by considering an induced metric, in the same spirit as the general relativity approach for the description of fermionic particle moving in a curved space-time. The resulting equation allows to include in a natural way the presence of other phonon branches as well as an external electromagnetic field. It also predicts non-linear effects which are not present in the usual vector potential approximation used in most of publications on the subject, as well as the possibility of controlling electronic conductivity using pure sinusoidal strain fields. The non-linear terms are important at high temperatures, and can also lead to interesting effects, like e.g. resonances between flexural phonons and external electromagnetic fields.