Acoustic phonons and spin relaxation in graphene nanoribbons

TL;DR

This paper presents a theoretical analysis of acoustic phonons in graphene nanoribbons, exploring how boundary conditions affect phonon dispersion and implications for electron mobility and spin relaxation in potential spintronic devices.

Contribution

It introduces a continuum model for acoustic phonons in graphene nanoribbons considering boundary effects and derives phonon properties relevant for spintronics and electronic applications.

Findings

Fixed boundaries create a gapped phonon dispersion.

Free boundaries result in ungapped phonon modes.

Deformation potential significantly influences spin relaxation rates.

Abstract

Phonons are responsible for limiting both the electron mobility and the spin relaxation time in solids and provide a mechanism for thermal transport. In view of a possible transistor function as well as spintronics applications in graphene nanoribbons, we present a theoretical study of acoustic phonons in these nanostructures. Using a two-dimensional continuum model which takes into account the monatomic thickness of graphene, we derive Hermitian wave equations and infer phonon creation and annihilation operators. We elaborate on two types of boundary configuration, which we believe can be realized in experiment: (i) fixed and (ii) free boundaries. The former leads to a gapped phonon dispersion relation, which is beneficial for high electron mobilites and long spin lifetimes. The latter exhibits an ungapped dispersion and a finite sound velocity of out-of-plane modes at the center of the Brillouin zone. In the limit of negligible boundary effects, bulk-like behavior is restored. We also discuss the deformation potential, which in some cases gives the dominant contribution to the spin relaxation rate T_1^{-1}.