Modelling electron-phonon interactions in graphene with curved space hydrodynamics

Ilario Giordanelli,Hans Jürgen Herrmann,Miller Mendoza

doi:10.1038/s41598-018-30354-4

Ilario Giordanelli, Hans Jürgen Herrmann + Show 1 more

Open Access

https://doi.org/10.1038/s41598-018-30354-4

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Journal: Scientific Reports	Publication Date: Aug 22, 2018
Citations: 7	License type: open-access

Affiliation: ETH Zurich, Universidade Federal do Ceará

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.

Highlights

At finite temperatures, phonons interact with charge carriers, and contribute to the electrical resistivity of the respective material[1]
We considered doped graphene samples, i.e. we are away from the charge neutrality point, where charge carriers are induced by a gate voltage instead of thermal fluctuations, and the Fermi liquid theory applies[21]
We first use the covariant formulation of the hydrodynamic equations in curved space to determine the terms responsible for the inertial corrections, and afterwards, we introduce them as a forcing term into the respective equations for flat graphene

Summary

Introduction

Phonons interact with charge carriers, and contribute to the electrical resistivity of the respective material[1]. For low electron densities, the Fermi energy can be substantially smaller than the Debye energy, and only phonons with energy smaller than two times the Fermi energy, corresponding to a full backscattering of electrons, can scatter with the electrons This defines the Bloch-Grüneisen temperature TBG3, which for doped suspended graphene is around 100 K4,5. We present an approach based on the induced metric, where we account for the electron-phonon interactions by including inertial corrections due to the deformations of the graphene sheet. In this work, we use an approach in which the thermal fluctuations are responsible for inducing curvature in the graphene sheets This curvature generates dissipation[24] and electrical resistivity in the sample.

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