Symmetry-derived selection rules for plasmon-enhanced Raman scattering

Abstract

We show how to obtain the symmetry-imposed selection rules for plasmonic enhancement in surface- (SERS) and tip-enhanced Raman scattering (TERS). Plasmon-enhanced light scattering is described as a higher-order Raman process, which introduces a series of Hamiltonians representing the interaction between light, plasmons, electrons, and phonons. Using group theory, we derive the active representations for point group symmetries of exemplary plasmonic nanostructures. The phonon representations that are enhanced by SERS and TERS are then found as induced representations for the symmetry group of the molecule or another Raman probe. The selection rules are discussed for graphene that is coupled to a nanodisk dimer as an example for SERS and coupled to a tip as a TERS example. The phonon eigenmodes that are enhanced depend on the symmetry breaking when combining the plasmonic structures with graphene. We show that the most prominent optical phonon modes $({E}_{2g}$ and ${A}_{1g})$ are allowed in all scattering configurations when using a nanodimer as a plasmonic hotspot. We predict the activation of the silent ${B}_{2g}$ as well as infrared-active ${A}_{2u}$ and ${E}_{1u}$ modes in SERS for crossed configurations of the incoming and scattered light. There is a systematic difference between spatially coherent and incoherent plasmon-enhanced Raman scattering, which is responsible for a dependence of TERS on the phonon coherence length.