Analytical Modeling of Graphene Plasmons

TL;DR

This paper introduces an analytical theory for modeling graphene plasmons using plasmon wave functions, providing simple formulas for spectra and demonstrating applications in transparency and sensing.

Contribution

It presents a novel analytical PWF formalism for graphene plasmons, enabling simplified and accurate predictions of plasmonic behavior in 2D materials.

Findings

Closed-form expressions for extinction spectra.

Excellent agreement between classical and quantum models.

Successful prediction of plasmon-induced transparency and sensing capabilities.

Abstract

The two-dimensionality of graphene and other layered materials can be exploited to simplify the theoretical description of their plasmonic and polaritonic modes. We present an analytical theory that allows us to simulate these excitations in terms of plasmon wave functions (PWFs). Closed-form expressions are offered for their associated extinction spectra, involving only two real parameters for each plasmon mode and graphene morphology, which we calculate and tabulate once and for all. Classical and quantum-mechanical formulations of this PWF formalism are introduced, in excellent mutual agreement for armchaired islands with $>10\,$nm characteristic size. Examples of application are presented to predict both plasmon-induced transparency in interacting nanoribbons and excellent sensing capabilities through the response to the dielectric environment. We argue that the PWF formalism has general applicability and allows us to analytically describe a wide range of 2D polaritonic behavior, thus facilitating their use for the design of actual devices.