Scattering of Graphene plasmons by defects in the graphene sheet

TL;DR

This paper presents a theoretical analysis of how graphene surface plasmons scatter when encountering various defects in the graphene sheet, revealing conditions for reflection and radiation dominance and the effects of defect type and size.

Contribution

It introduces an integral equation approach to model scattering of graphene plasmons by defects, providing analytical insights for small defects and exploring different defect types.

Findings

Reflection dominates over radiation in most cases.

Sharp conductivity islands can have zero reflectance at specific sizes and frequencies.

Cracks larger than one-tenth of the GSP wavelength reflect almost all plasmons.

Abstract

A theoretical study is presented on the scattering of graphene surface plasmons by defects in the graphene sheet they propagate in. These defects can be either natural (as domain boundaries, ripples and cracks, among others) or induced by an external gate. The scattering is shown to be governed by an integral equation, derived from a plane wave expansion of the fields, which in general must be solved numerically but it provides useful analytical results for small defects. Two main cases are considered: smooth variations of the graphene conductivity (characterized by a Gaussian conductivity profile) and sharp variations (represented by islands with different conductivity). In general, reflection largely dominates over radiation out of the graphene sheet. However, in the case of sharply defined conductivity islands there are some values of island size and frequency where the reflectance vanishes and, correspondingly, the radiation out of plane is the main scattering process. For smooth defects, the reflectance spectra present a single maximum at the condition $k_p a \approx \sqrt{2}$, where $k_p$ is the GSP wavevector and $a$ the spatial width of the defect. In contrast, the reflectance spectra of sharp defects present periodic oscillations with period $k_p' a$, where $k_p'$ is the GSP wavelength inside the defect. Finally, the case of cracks (gaps in the graphene conductivity) is considered, showing that the reflectance is practically unity for gap widths larger than one tenth of the GSP wavelength.