Effect of Electron-Phonon Coupling on the Plasmon Lifetimes in Naographene

Martinez Saavedra Jose Ramon Nanophotonics Theory, ICFO - The Institute of Photonic Sciences, Castelldefels, Barcelona, Spain Javier F. García de Abajo Nanophotonics Theory, ICFO - The Institute of Photonic Sciences, Castelldefels, Barcelona, Spain None, ICREA - Institucio Catalana de Recerca i Estudis Avançats, Barcelona, Spain

We study the plasmon-phonon coupling in graphene nanoislands through a perturbative RPA expansion and conclude that it contributes with a few millielectronvots to the plasmon width, which increases with both the island size and doping.

Graphene has arisen as a promising plasmonic material due to its potential applications to optoelectronics. In particular, its peculiar electric structure, with linear dispersion and vanishing of the density of states at the Fermi level, lead to a high electrostatic tunability, as well as large confinement of its plasmons.

Inelastic plasmon losses in graphene are still not well understood. Scattering by impurities [1] are known to dominate in typical plasmonic samples with mobilities <10,000 cm2/(V s), although scattering by zigzag edges in small structures can also produce large plasmon damping, while coupling to phonons have also predicted to be significant in extended graphene [2, 3].

Here, we concentrate on the coupling between plasmons and phonons in graphene nanoislands, and study the contribution of this channel to plasmon decay as a function of the size of the island. We describe the graphene using a tight-binding model for the electronic structure [4], combined with a mean-field approach for the response, which we calculate in perturbation theory to the lowest order needed to sustain the plasmon and its losses to phonons. The latter are described by only including the stretching C-C mode, which accounts for the main characteristics of the optical-phonon branches [5]. We find the phonon-loss mechanism to increase with the size of the island as well as with the number of doping charge carriers. Interestingly, the spatial distribution of the dominant phonon modes shows strong deviations with respect to the regions of maximum plasmon charge density.

We show the spatial distribution of the phonon strength (mean square atomic displacement, represented by the size of the circles at the carbon positions), summed over all phonons after weighting them with their relative contribution to the plasmon-phonon decay rate for an armchair graphene triangle made of 60 carbon atoms. The plasmon induced charge is represented by the underlying colour plot (red and blue areas correspond to opposite charges). Two different doping states of the island are considered, as indicated by the number Q of additional charge carriers.

References

[1] Bostwick, A., Ohta, T., Seyller, T., Horn, K. Rotenberg, E., Nat Phys 3, 36–40 (2006).

[2] M Jablan, H Buljan, and M Soljačić, Phys. Rev. B 80, 245435 (2009)

[3] Principi, A., Carrega M, Lundeberg, M. et al. arXiv:1408.1653 (2014)

[4] Manjavacas, A., Marchesin, F. Thongrattanasiri, S., ACS Nano 7 (4) (2013).

[5] Viola Kusminskiy, S., Campbell, D.K., Castro Neto, A. H., Phys. Rev. B 80, 035401 (2009).

jose.martinez@icfo.es









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