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.
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