Probing LO phonons of graphene under tension via the2D′Raman mode

Abstract

We use ab initio simulations and perturbation theory to study the $\mathit{2}{D}^{\ensuremath{'}}$ Raman mode of graphene subject to biaxial and uniaxial strains up to $2%$. We demonstrate that $\mathit{2}{D}^{\ensuremath{'}}$ Raman measurements, as a function of polarization and laser energy ${E}_{L}$, can probe the LO phonons of graphene with arbitrary radial and angular extent around $\ensuremath{\Gamma}$. The $\mathit{2}{D}^{\ensuremath{'}}$ profile is highly sensitive to uniaxial strain and depends on both polarization and strain orientation. The Gr\"uneisen parameter ${\ensuremath{\gamma}}_{\mathit{2}{D}^{\ensuremath{'}}}\ensuremath{\approx}1.71$ has a mild dependency on the laser energy ${E}_{L}$, and is found to be in good agreement with experiments and comparable in value to ${\ensuremath{\gamma}}_{G}$. The shear deformation potential ${\ensuremath{\beta}}_{\mathit{2}{D}^{\ensuremath{'}}}$ depends strongly on the polarization and strain orientation, becoming negative when the polarizer and analyzer are perpendicular to each other. Finally, we describe a robust method to determine the uniaxial strain by relying solely on polarized measurements of the $\mathit{2}{D}^{\ensuremath{'}}$ mode.