Uniaxial strain in graphene by Raman spectroscopy:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>G</mml:mi></mml:math>peak splitting, Grüneisen parameters, and sample orientation

TLDR

The study investigates graphene’s constitutive relation and optical phonon physics by measuring its Raman spectrum under uniaxial strain. Raman spectroscopy under controlled uniaxial strain is used to resolve the G peak into G⁺ and G⁻ components and to determine Grüneisen parameters for the G, D, and D′ phonons. The G mode splits into G⁺ and G⁻ components polarized along and perpendicular to strain, both redshifting and increasing in separation with strain, while their intensity ratio varies with light polarization; the 2D and 2D′ bands redshift without splitting, and the measured Grüneisen parameters provide a quantitative strain gauge for nanoelectronics.

Abstract

We uncover the constitutive relation of graphene and probe the physics of its optical phonons by studying its Raman spectrum as a function of uniaxial strain. We find that the doubly degenerate ${E}_{2g}$ optical mode splits in two components: one polarized along the strain and the other perpendicular. This splits the $G$ peak into two bands, which we call ${G}^{+}$ and ${G}^{\ensuremath{-}}$, by analogy with the effect of curvature on the nanotube $G$ peak. Both peaks redshift with increasing strain and their splitting increases, in excellent agreement with first-principles calculations. Their relative intensities are found to depend on light polarization, which provides a useful tool to probe the graphene crystallographic orientation with respect to the strain. The 2D and $2{\text{D}}^{\ensuremath{'}}$ bands also redshift but do not split for small strains. We study the Gr\"uneisen parameters for the phonons responsible for the $G$, $D$, and ${D}^{\ensuremath{'}}$ peaks. These can be used to measure the amount of uniaxial or biaxial strain, providing a fundamental tool for nanoelectronics, where strain monitoring is of paramount importance