Plasmon Wave Function of Graphene Nanoribbons

Iván Silveiro Nanophotonics Theory Group, ICFO – The Institute of Photonic Sciences, Castelldefels (Barcelona), Not Applicable, Spain Juan Manuel Plaza Ortega Nanophotonics Theory Group, ICFO – The Institute of Photonic Sciences, Castelldefels (Barcelona), Not Applicable, Spain Javier F. García de Abajo Nanophotonics Theory Group, ICFO – The Institute of Photonic Sciences, Castelldefels (Barcelona), Not Applicable, Spain Nanophotonics Theory Group, ICREA-Institució Catalana de Recerca i Estudis Avanças, Barcelona, Spain

In our work, we study transversal plasmons in doped self-standing graphene nanoribbons described within a classical electromagnetic picture. These calculations allow us to define a universal plasmon wave function (i.e., the induced electron density profile) which applies to any doping and width of the ribbons. The interaction between neighboring ribbons is then modeled using exclusively this wave function, conveniently normalized to represent a single plasmon. The results are in excellent agreement with the full numerical simulations for dimers. We also compare the results with an analytical dipole-dipole model to describe the interaction between ribbons1 which shows that neighboring ribbons cannot be simply represented as dipoles for short separations. In contrast, our plasmon wave-function approach describes this interaction quite satisfactorily.

We show strong hybridization between plasmons in dimers and periodic arrays at separations below a few nanometers between ribbons2. For the in-plane configuration, the interaction is clearly attractive producing remarkable redshifts in the plasmon frequency compared with the single ribbon. On the contrary, in the piled-up system the interaction is repulsive producing more notable in magnitude shifts.

Besides the fundamental interest of these results, our work shows that simple semi-analytical models based on plasmon wave-functions can accurately describe graphene geometries composed of individual pieces, here illustrated by the study of ribbon dimers and periodic arrays.

Plasmon in pairs of graphene ribbons

Extinction cross-section normalized to the area of a dimer of self-standing graphene nanoribbons for different distances d between boundaries. The external light impinges normally to the ribbons, resulting in a dipolar distribution of the induced charge density ρind as depicted in the insets. The ribbons width, Fermi energy and damping are W = 6 nm, EF = 0.4 eV, and 0.02 eV, respectively. (a) We show the numerical extinction spectra (solid curve) compared with two fully analytical models: plasmon wave function (PWF) and dipole-dipole interaction (dashed and dotted curves, respectively) for a dimer of in-plane graphene ribbons. (b) Same as (a) for a system of stacked ribbons.

[1] S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, PRL. 108, 047401 (2012).

[2] I. Silveiro, J. M. Plaza Ortega, and F. J. García de Abajo, in press LSA (doi:10.1038/lsa2015.14)

ivan.silveiro@gmail.com









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