Invited Paper
Semiclassical and Quantum Plasmonic Phenomena in Metal and Graphene Nanostructures

Plasmonics offers a way to beat the diffraction limit. Since with metals one can thus miniaturize optical processes, an important question is when and how classical electrodynamics breaks down as plasmonic structures are made smaller. It turns out that conspicuous nonclassical effects are resonance shifts and broadening of single-nanoparticle resonances, and of larger dimers with nanometer-sized gaps.

For silver and gold, blueshifts are observed for smaller particles. Standard hydrodynamic Drude theory predicts indeed such a blueshift. Our recent generalized nonlocal optical response (GNOR) theory [1] is an extension of hydrodynamic theory that moreover gives a unified explanation of spectral broadening of both nanoparticles and of dimers in terms of diffusive nonlocal response. By contrast, state-of-the-art more microscopic theories ascribe spectral broadening of individual nanoparticles to Landau damping while that of dimers would be due to quantum tunneling at optical frequencies in the gap region.

Some simple metals exhibit redshifts as nanoparticle sizes are decreased, while standard hydrodynamic theory always predicts nonlocal blueshifts. We have recently shown that this is not a limitation of hydrodynamics as such, but rather of the additional assumption that the free electrons are contained within the classical boundaries [2]; our self-consistent hydrodynamic theory predicts nonlocal redshifts for sodium [2].

Finally I will discuss the shifting boundaries between semiclassical and quantum plasmonics also for graphene nanostructures, both planar [3] and curved ones [4].

[1] N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, "Generalized Nonlocal Optical Response in Nanoplasmonics," Nature Commun. 5, 3809 (2014).
[2] G. Toscano, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, "Self-consistent Hydrodynamic Approach to Nanoplasmonics: Resonance Shifts and Spill-out Effects," ArXiv:1408.5862 (2014).
[3] T. Christensen, W. Wang, A.-P. Jauho, M. Wubs, and N. A. Mortensen, "Classical and Quantum Plasmonics in Graphene Nanodisks: Role of Edge States," Phys. Rev. B 90, 241414(R) (2014).
[4] T. Christensen, A.-P. Jauho, M. Wubs, and N. A. Mortensen, "Localized Plasmons in Graphene-Coated Nanospheres" (submitted, 2014).

mwubs@fotonik.dtu.dk