# Quantum plasmons with optical-range frequencies in doped few-layer graphene

## TL;DR

This paper demonstrates that high doping levels in bilayer and trilayer graphene can shift plasmon frequencies into the visible range, using advanced first-principles calculations and improved boundary condition techniques.

## Contribution

It introduces a novel correction method for plasmon interaction across vacuum gaps, enabling accurate quantum mechanical modeling of visible-range plasmons in doped graphene.

## Key findings

- Plasmon frequencies can be tuned into the visible range with lithium intercalation.
- The correction method improves the physical accuracy of multilayer graphene simulations.
- Quantum effects significantly influence plasmon dispersion, losses, and localization.

## Abstract

Although plasmon modes exist in doped graphene, the limited range of doping achieved by gating restricts the plasmon frequencies to a range that does not include visible and infrared. Here we show, through the use of first-principles calculations, that the high levels of doping achieved by lithium intercalation in bilayer and trilayer graphene shift the plasmon frequencies into the visible range. To obtain physically meaningful results, we introduce a correction of the effect of plasmon interaction across the vacuum separating periodic images of the doped graphene layers, consisting of transparent boundary conditions in the direction perpendicular to the layers; this represents a significant improvement over the Exact Coulomb cutoff technique employed in earlier works. The resulting plasmon modes are due to local field efffects and the non-local response of the material to external electromagnetic fields, requiring a fully quantum mechanical treatment. We describe the features of these quantum plasmons, including the dispersion relation, losses and field localization. Our findings point to a strategy for fine-tuning the plasmon frequencies in graphene and other two dimensional materials.