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

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